This dissertation has been microfilmed exactly as received 69-11,654

IANNA, Philip Anthony, 1938- AN ASTROMETRIC AND SPECTROSCOPIC STUDY OF THE GALACTIC CLUSTER NGC 1039.

The Ohio State University, Ph.D., 1968 Astronomy

University Microfilms, Inc., Ann Arbor, Michigan AN ASTBOXETRIC AND SPECTROSCOPIC STUDY

OF THE GALACTIC CLUSTER NGC 1039

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By

Philip Anthony Ianna, B.A., N.A,

*******

The Ohio State University 1968

Approved by

Adviser Department of Astronoiqy PLEASE NOTE: Appendix pages are not original copy. Print is indistinct on many pages. Filmed in the best possible way. UNIVERSITY MICROFILMS. ACKNOWLEDGEMENTS

I am grateful to many people at a number of institutions for their kind assistance throughout this study. I would particularly like to thank try adviser. Dr. George W. Collins,11, for his encouragement and guidance over a rather long period of time. Also at The Ohio State

University Drs. Walter E. Kitchell, Jr. and Arne Slettebak have given useful advice in several of the observational aspects of this work.

Travel and telescope time provided by the Ohio State and Ohio Wesleyan

Universities is gratefully acknowledged.

The astrometric plate material was made available to me through

the kind generosity of Dr. Peter van de Xamp, Director of the Sproul

Observatory, and Dr. Nicholas S. Wagman, Director of the Allegheny

Observatory. Other members of the staff at the Allegheny Observatory were most helpful during two observing sessions there.

I am indebted to Dr. Kaj Aa. Strand, Scientific Director, The

U. S. Naval Observatory, for the opportunity to measure the astrometric

plates on their automatic measuring engine, and to Dr. Victor Blanco,

I'ir.'R. Kip Riddle, and other members of the Naval Observatory staff for

assistance while the measurements were being made.

The major portion of the computing for this investigation has been

carried out through very generous grants of computing time from The

Ohio State University Computer Center. Kr. Edwin R. Lassettre of the

Computer Center has also been very generous with his time in giving

ii help in numerous ways.

I am also indebted to the Center for Advanced Studies of the

University of Virginia for aid with computing time and support during the final stages of this work. The staff of the Leander McCormick

Observatory has given further aid by making available telescope time and equipment with which to do the photoelectric photometry.

I am grateful for a N. D. E. A. Fellowship which provided financial assistance for one year.

iii ; \

VITA

May 27, 1938 B o m - Philadelphia, Pennsylvania

I960 B.A., Swarthmore College, Swarthmore, Pennsylvania

1960-1962 Research Assistant, Department of Astronomy, Swarthmore College, Swarthmore, Pennsylvania

1962 M.A., Swarthmore College, Swarthmore, Pennsylvania

1962-1965 Teaching Assistant, Department of Astronomy. The Ohio State University, Columbus, Ohio

1965-I966 N.D.E.A. Fellow, Department of Astronomy. The Ohio State University, Columbus, Ohio

1966-1967 Teaching Assistant, Department of Astronomy, The Ohio State University, Columbus, Ohio

1968 Research Associate, The Center for Advanced Studies in the Sciences, The University of Virginia, Charlottesville, Virginia

PUBLICATIONS

"Aberrations and Field Errors of the Sproul 24-inch Objective." Astron. J., 6£, 273. 1962

"A Flare of T Ccronae Borealis." Astrophys. J., 139. 780, 1964

"On Aberrations and Field Errors." Vistas in Astronomy, 6 , 93, 1965

iv TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS ...... ii

VITA ...... iv

LIST OF TABLES ...... vii

LIST OF ILLUSTRATIONS ...... ix

CHAPTER I. INTRODUCTION ...... 1

II. SPECTROSCOPIC OBSERVATIONS IN NGC 1039...... 7

Spectral Classification ...... 10 Rotational Velocities ...... 11 The Radial Velocities ...... 13 Radial Velocity of NGC 1039 ...... 20

H I . PHOTOMETRY IN THE REGION OF NGC 1039 ...... 25

The Photoelectric Photometry ...... 26 The Iris Photometry ...... 31 Accuracy of the Magnitudes ...... 38

IV. ANALYSIS OF ASTROMETRIC INSTRUMENTATION ...... 4-1

Characteristics of the Sproul 2^-inch Refractor .... hZ The Thaw 30-inch Refractor...... ^6 The U.S. Naval Observatory Astrometric Refractor .... 5^ The U.S. Naval Observatory Automatic Measuring Engine ...... 5^

V. THE PROPER MOTION REDUCTIONS ...... 66

The Observations ...... 66 Plate Measurement and Data Editing...... 66 Rigorous Plate Reduction Methods...... 71 Choice of Plate Model ...... 76 Formation of Normal Equations for the Full Solution...... 80 Solution of Normal Equations from Complete Data Set . 83

v CHAPTER Pago

Plato-Pair Reductions ...... 86

VI. ANALYSIS OF THE PROPER LOTIONS ...... 93

Comparison of Sproul, Allegheny, and Dieckvoss Proper Lotions ...... 93 Reduction to Absoluto Lotions ...... 101 Cluster Lembership ...... 102 Cluster Color Lagnitude Diagram and Distance Lodulus ...... 107 Space Lotion of NGC 1039 ...... 109 Further Discussion of Ap Stars in NGC 1039 ...... Ill APPENDIX ...... 115

LIST OF REFERENCES ...... 1^9

vi LIST OF TABLES

Table Page

1. Summary of Galactic Cluster Internal Proper Motion Studies 3

2. Radial Velocity Table 8

3. Rotational Velocity Standards 12

Lines Utilized in Radial Velocity Determinations of B-A Stars 16

5. Lines Utilized in Radial Velocity Determinations of F Stars 16

6 . Spectroscopic Results for the Brighter Stars in NGC 1039 17

7. Mean Error of a Radial Velocity from One Spectrogram 19

8 . Stars Rejected from Cluster Membership on the Basis of Radial Velocity 21

9. Radial Velocities of A-Stars Common to Wilson’s General Catalog 23

10. Calibration of Rakos D. C. Amplifier 28

11 Fan Mountain Photoelectric Photometry for NGC 1039 29

12. Fan Mountain Photometry - Extinction and Color Coefficients 29

13. NGC 1039 - Photoelectric Standards for Iris Photometry 33

14. Observational Data for Photometric Plates of NGC 1039 35

15. Johnson - Dieckvoss Visual Magnitudes 39

16. Ianna - Dieckvoss Visual Magnitude Fainter than 11.0 40

17. Sproul 24-inch Refractor Chronology 43

18. Thaw 30”inch Refractor Chronology 47

19. Observing Data for Thaw Hartmann: Tests 50

20. Constants of the Thaw Objective 53

vii Table page

21. Calibration of Mann Engine 422D54 56

22. Measured Separations and Setting Error of the KRI Engine as a. Function of Image Size 60

23. Plate Variances and Proper Motions from Direct and Direct- Reverse Measurements 6l

24. Variances from Reduction of Direct against Reverse Measurements of a Plate 63

25. Observational Data-Astrometric Plate Material 67

26. Sproul Plate Variances for Various Plate Constant Material 77

27. Allegheny Plate Variances for Various Plate Constant Models 79

28. Sproul Plate-Fairs 87

29. Allegheny Plate-Pairs 87

30* Sproul Reference Stars in NGC 1039 88

31. Allegheny Reference Stars in NGC 1039 89

32. Average Internal Mean Error of a Proper Motion for a Single Plate-Fair 92

33. Linear Correction Constants to Adjust Allegheny to Sproul Proper Motions 100

34. P-eduction of Relative Proper .Motions to the System of the FX3 102

35. Color Excess of Brighter Members of NGC 1039 109

36. Summary of Data on Peculiar A-Stars in UGC 1039 112 I

LIST OF ILLUSTRATIONS

Figure Page

1. Transmission Curves of the Fan Fountain U3V Filters 27

2. Determination of Color and Extinction Coefficients 32

3. A Comparison between Visual Magnitudes from Inverted Least-Squares Solutions 37

4. Sproul Zonal-Focus Curves 45

5. Recent Sproul Hartmann Test Results 45

6 . Thaw Hartmann Test Results 51

7. Magnitude Dependence of Residuals from Sproul Plates 246-23703 62

8 . Magnitude Dependence of Residuals from Sproul Plates 246 and 38703 64

9. Proper Motion Differences vs. Color in X 94

10. Proper Motion Differences vs. Color in Y 95

11. Proper Motion Differences in X vs. X 97

12. Proper Motion Differences in Y vs. Y 9°

13. Proper Motion Differences with Common Reference Stars 99

14. Proper Motion Diagram-3proul Motions 104

15. Proper Motion Diagram-Allegheny Motions 105

16. Proper Motion Diagram-Combined Motions 106

17. Color-Magnitude Array, NGC 1039 108

ix CHAPTER I

INTRODUCTION

The segregation of cluster members from the stellar background is of vital importance to investigations of galactic clusters. The criteria of highest validity are a common distance or a common motion of the stars in question. Few clusters are close enough to allow an accurate direct distance determination, so one must measure proper motions or radial velocities in order to adjudge the presence of common motions.

The proper motion criterion has been most frequently used. In this century we find some 120 astrometric studies of galactic clusters,

40# carried out between 1950 and 1959. that account for only about 10# of the known clusters owing to some duplication. Regrettably the desired degree of reliability is not attained in the bulk of these studies (Vasilevskis 1962). There are a variety of reasons for this.

A contingent virtue for results of precision is the patience to allow the accumulation of sufficient time between the earliest and latest plates used in the study; an interval of 30-50 years is desirable.

This means that much early plate material is just now becoming ripe for proper motion studies. Furthermore, the formidable task of manually measuring and reducing the photographic records of many stars practically limits such proper motion studies to several pairs of plates. There is thus a clear and present need for the wide adoption of automatic measuring and reduction techniques to take advantage of current and future plate material for the determination of proper motion with high accuracy.

Important steps have been taken toward the utilization of modern machine techniques in astrometry at the U.S. Naval Observatory under

Strand and at the Lick Observatory under Vasilevskis. This investiga­ tion is in part intended as an effort in this direction.

The observationally related problem of the internal motions and dynamical history of star clusters is most difficult. The few proper motion studies that include an estimation of the mean internal velocity of cluster stars are among the most accurate positional investigations to date.

In contrast the theoretical aspects of the dynamical problem have been considered in some detail. We have now, for example, a fair notion of the rate and mass spectrum of stars escaping from clusters and the resulting structural evolution of the cluster. The modem work has been carried out in particular by Chandrasekhar, Spitzer, Schwarzs- child and Harm, King, and Mitchie; a summary of these studies of the dynamics of star clusters has been given recently by Mitchie (19&0.

The astrometric studies of galactic clusters that have yielded estimates of the internal motions are summarized in Table 1. These are examples of the sort of accuracy to be expected from material with a long time base. The column headings are for the most part self- explanatory; column six refers in several cases to the maximum number of observations of a given star. The probable error in the proper TABLE 1

Summary of Galactic Cluster Internal Proper Motion Studies

Time Plate Interval Scale No. No. Mean Error of Internal Object Reference Years "/mm Stars Plates Proper Motion Motion

Hyades van Rhijn and 16 60.1 49 41 >0.0034M/yr ±0.007 "/yr Kleln-Wassink (1924)

Hyades Van Bueren - - 40 - -0•002 ±0.0022 (1952)

IC 348 Fredrick (1956) 35/31 18.87/20.75 31/27 73/60 ±0.0004 ±0.0006

Pleiades Hertzsprung (193*0 -- 42 78 ±0.001 ±0.0009

Pleiades Titus (1938) 64 28.01 44 15 ±0.00082 ±0.00079

Pleiades Binnendijk (1946) - - -- ±0.001 ±0.00079

Praesope van de Kamp (1935) 20 20.75 35 31 ±0.0012 ±0.0011

Praesope Schilt and Titus 65 28.01 37 23 ±0.0008 ±0.0006 (1938)

Praesope Hershey (I967 ) 51 20.75 35 25 ±0.0004 ±0.00095 motions is given for the most accurate case if different for different stars, and, owing to various means of estimation, may not be strictly comparable in all cases.

Early attempts by Pritchard (1884) and Trumpler (1914) to find evidence of an internal velocity dispersion in the Pleiades failed to yield adequately accurate results. In the modern studies one notes a tendency of the estimates of the rms internal velocity to decrease -with improved accuracy. Indeed the estimate of the internal velocity dis­ persion depends directly on the estimate of the errors in the proper motions, the former quantity being computed from the expression £ p. 2 1 - e v = n 2 (1) where v is the rms internal velocity, M- the difference in proper i motion from the cluster mean, e the estimated mean-square error, and n is the number of stars. The estimate of the mean-square error in the proper motions is not a simple task in view of the many ways in which systematic effects may influence the result, and especially with a small amount of plate material a comparison between plate pairs may be inadequate. We note that an underestimate of the errors leads to an overestimate of the internal motions.

Van Eueren (19^2) noted that the large internal motion found by van Ehijn and Klein-Wassink (1924) (Table l) in the Hyades might be caused by the presence of undetected errors in the motions. After eliminating systematic differences a comparison of Groningen and Yale proper motions suggested that the real mean errors of the proper motions in both catalogues must be about +0'J010. Another aspect of this problem concerns the definition of a

"cluster member". Without a marked differentiation between cluster and non-cluster stars, the dispersion in the cluster proper motions is utterly dependent upon the stellar sample.

In any case one can never be completely certain that non-members have been excluded. It is thus desirable to attach a probability of membership to individual stars taking into account those field stars whose proper motions may fall within the range of the cluster proper motion. A possible approach is to assume the proper motion vector points for cluster and field stars to have bivariate frequency dis­ tributions given by the functions F'c(u) and F^(u) (Vasilevskis,

Klemola, and Preston 1958). The probability that any given star is a cluster member is

Fc + Ff These matters shall be considered in somewhat greater detail subsequently, as we attempt to apply rigorous reduction methods to the determination of proper motions in the region of NGC 1039.

The galactic cluster NGC 1039 (M 3*0 is a moderately young cluster located in the direction of the constellation of Perseus ( 1 ^ = lW*, b ^ - -16°) at a distance of about ^40 parsecs. It is described as a moderately rich cluster with strong central condensation (Trurapler

1930). It has not been very thoroughly studied even though it is one of the nearest clusters and contains relatively bright stars. Classi­ fication of the stars into spectral types has not been done on the MK system, and only incomplete proper motions are available from two studies. Limited photometric results exist for the brighter stars.

Since a large quantity of astrometric plate material is extant, the cluster was deemed suitable for investigation. We proceed with this in the chapters that follow. CHAPTER II

SPECTROSCOPIC OBSERVATIONS IN NGC 1039

In view of the uncertainty of the space velocity of NGC 1039» spectroscopic information was secured for the brighter stars in the cluster with the aim of determining radial velocities. This material was also suitable for spectral classification and rotational velocity estimates not available previously for this cluster.

The observations of cluster and standard stars were obtained in two sessions with the Ferkins 72-inch reflector of the Ohio State and

Ohio Wesleyan Universities at the Lowell Observatory, Flagstaff,

Arizona in the winter of 1965-1966; the pertinent data are presented in

Table 2. In all cases the Perkins "Y" grating spectrograph and

8-inch "b" camera, having an approximate reciprocal dispersion of k2 A/mm in the blue were used. The projected slit width was 18 microns and the spectra were widened to 0.6 mm. A focus plate was taken before each observing period. The adjustment giving the best appearing spectra in the Balmer line region was chosen.

The spectra were recorded on Eastman IlaO plates that had been baked for three days at 50 degrees C.; a few unbaked 103a-0 plates were also used. Intensity calibration plates were made with the spectro­ graph in the Perkins dome especially provided for this purpose. The accumulated plates were developed together at the end of each night for

7 TABLE 2

RADIAL VELOCITY TABLE

STAR HD PLATE DATE R.A. DECL. HOUR EXP. EMULSION QUALITY V + m.e.(n) NO. (1900) (1900) ANGLE R “

h * +42°572 16605 1564 13 Jan 1966 2 34.5 +42°171 4h05 W 92m IIa-0 f -21.5 + 2.0 (14)

+42°578 16627 1522 21 Dec 1965 2 34.8 +42 15 2 07 W 53 IIa-0 f -24.5 + 2.0 (8) 1560 13 Jan 1966 2 34.8 +42 15 0 08 W 55 IIa-0 f -20.7 + 3.4 (9)

+41°514 16655 1521 21 Dec 1965 2 35.1 +42 10 1 15 W 31 IIa-0 S -21.0 + 2.9 (8) 1561 13 Jan 1966 2 35.1 +42 10 0 40 W 28 Ila-0 g -23.3 + 4.0 (7) 1600 16 Jan 1966 2 35.1 +42 10 3 03 W 58 IIa-0 g -17.9 + 4.4 (7)

+42°586 16679 1510 20 Dec 1965 2 35.4 +42 21 0 36 E 47 IIa-0 g -16.4 + 1.5 (7) 1545 11 Jan 1966 2 35.4 +42 21 2 00 W 60 IIa-0 f - 9.8 + 4.3 (7) 1601 16 Jan 1966 2 35;4 +42 21 4 16 W 80 IIa-0 g -32.9 + 4.9 (8)

+42°588 16693 1498 19 Dec 1965 2 35.6 +42 22 1 27 W 35 IIa-0 g -11.0 + 3.3 (9) 1532 24 Dec 1965 7 35.6 +42 22 0 32 W 62 IIa-0 g -10.1 + 3.3 (9) 1546 11 Jan 1966 2 35.£ +42 22 2 32 W 35 IIa-0 g -21.5 + 3.2 (9)

+42°589 1499 19 Dec 1965 2 35.6 +42 22 2 17 W 31 IIa-0 wk -14.6 + 1.8 (7) 1531 24 Dec 1965 2 35.6 +42 22 O' 28 E 45 IIa-0 wk - 7.0 + 3.8 (7) 1547 11 Jan 1966 2 35.6 +42 22 3 27 W 33 IIa-0 f - 6.5 + 3.4 (9)

+42°591 16719 1524 21 Dec 1965 2 35.6 '• +42 17 3 55 W 30 103a-0 g - 6.2 + 1.6 (8) 1535 24 Dec 1965 2 35.6 +42 17 4 31 W 47 IIa-0 E -17.8 + 3.0 (8) 1559 13 Jan 1966 2 35.6 +42 17 0 56 E 23 IIa-0 f -11.9 +_ 4.1 (8)

+42°598 16728 1500 19 Dec 1965 2 35.8 +42 19 3 19 W 20 IIa-0 wk -16.7 + 3.2 (9) 1534 24 Dec 1965 ■ 2 35.8 +42 19 3 47 W 30 IIa-0 f + 3.9 + 5.8 (8) 1563 13 Jan 1966 2 35.8 +42 19 2 08 W 20 IIa-0 "g -12.4 + 5.1 (8) 1578 14 Jan 1966 2 35.8 +42 19 4 43 W 20 IIa-0 g -17.0 + 4.4 (9)

+42°596 1523 21 Dec 1965 2 35.8 +42 22 3 03 W 39 103a-0 g -12.2 + 4.0 (9) 1553 12 Jan 1966 2 35.8 +42 22 4 25 W 30 IIa-0 P 1573 14 Jan 1966 2 35.8 '•2 22 0 35 W 35 . IIa-0 g -23.4 + 2.5 (9) 1589 15 Jan 1966 2 35.8 .-.2 22 3 22 W 77 IIa-0 wk -33.4 + 6.8 (9)

+42°597 1511 20 Dec 1965 2 35.8 +42 27 0 57 W 72 IIa-0 g -15.5 + 6.5 (7) 1544 11 Jan 1966 2 35.8 +42 2/ 0 12 W 72 Ila-0 P 1550 12 Jan 1966 2 35.8 +42 27 1 14 W 60 IIa-0 - g -30.0 + 7.1 (8) 1572 14 Jan 1966 2 35.8 +42 27 0 38 E 64 IIa-0^ g -53.4 + 6.2 (8) 00 RADIAL VELOCITY TABLE (Continued)

STAR HD PLATE DATE 1R.A, DECL. HOUR EXP. EMULSION QUALITY m.e.(n) VRK ± NO. (1900) (1900) ANGLE

+42°601 1520 21 Dec 1965 2135.9 +42°21' o'*04 U 65m IIa-0 • g -13.6 + 2.8 (7) 1552 12 Jan 1966 2 35.9 +42 21 3 30 w 43 IIa-0 f -39.1 + 5.1 (7) 1574 14 Jan 1966 2 35,9 +42 21 1 19 w 36 IIa-0 g -27.3 + 3.5 (8)

+4:2°602 1533 24 Dec 1965 2 36.0 +42 21 2 21 w 124 IIa-0 g -17.1 + 3.7 (7) 1551 11 Jan 1966 2 36.0 +42 21 2 25 w 60 IIa-0 wk -27.1 tv5-0 (7) 1575 14 Jan 1966 2 36.0 +42 21 2 31 w 60 IIa-0 g -28.5 +-3.6 (8)

+42°607 16782 1501 19 Dec 1965 2 36.3 +42 24 3 58 w 17 IIa-0 wk -54.7 + 6.4 (£) 1576 14 Jan 1966 2 36.3' +42 24 3 16 w 25- IIa-0 f -21.1 + 2.7 (8) 1587 15 Jan 1966 2 36.3 +42 24 0 18 w 24 IIa-0. wk - 8.6 + 4.7 (8) 1588 15 Jan 1966 2 36.3 +42 24 2 00 w 54 IIa-0 P - 9.0 + 9.7 (7)

+42°612 1549 12 Jan 1966 2 37.0 +42 21 0 16 E 100 IIa-0 f -25.1 + 1.5 (7)

+42°615 16857 1512 20 Dec 1965 2 37.2 +42 12 2 34 w 40 IIa-0 g -14.6 + 4.4 (8) 1562 13 Jan 1966 2 37.2 +42 12 1 23 w 42 IIa-0 g -15.7 + 3.4 (8) 1577 14 Jan 1966 2 37.2 • +42 12 4 00 w. 40 IIa-0 g -25.0 + 1.5 (7) a Per 1502 19 Dec 1965 3 17.2 +49 30 3 54 w 6 IIa-0 wk - 8.9 + 1.9 (15) 1513 20 Dec 1965 3 17.2 +4 9 30 3 40 u 12 IIa-0 g - 3.0 + 1.6 (15) 1519 21 Dec 1965 3 17.2 +49 30 1 48 E 6 103a-0 f - 7.9 + 3.5 (17) 1525 21 Dec 1965 • 3 17.2 +49 30 3 42 w 6 103a-0 g - 9.6 + 2.0 (16) 1536 24 Dec 1965 3 17.2 +49 30 4 24 u 10 'IIa-0 g - 7.4 + 1.9 (16) 1548 11 Jan 1966 3 17.2 +49 30 3 09 w 25 IIa-0 g - 4.7 + 2.0 (15) 1554 12 Jan 1966 3 17.2 +49 30 4 08 u 10 IIa-0 f -13.3 + 2.4 (10) 1565 13 Jan 1966 3 17.2 +49 30 3 35 u 10 IIa-0 8 - 8.1 + 2.1 (15) 1579 14 Jan 1966 3 17.2 +49 30 4 21 w 10 IIa-0 g - 6.9 + 2.5 (17) 1590 15 Jan 1966 3 17.2 +49 30 3 45 w 10 IIa-0 g. -15.2 + 1.9 (16) 1602 16 Jan 1966 3 17.2 +49 30 4 25 u 10 IIa-0 v.wk -11.2+ 1.7 (14)

VO 10 t four minutes in D-19 at 68 degrees F. t fixed in Kodak Rapidfix, thoroughly washed, and dried in a vertical position.

For comparison an Te-spark source was exposed to the plate for a few seconds at the beginning and end of each exposure.

Spectral Classification. Although LK spectral classes have not been published for stars in XGC 1039» some spectral types are available from several sources. These include objective prism classifications by Bruggenann (1935) and Wachmann (1939). and the work of Trumpler

(Weaver, in press).

For each star, the best plate was picked from which to make the classifications. Both the author’s standard spectrograms and standards kindly loaned by Dr. Arne Slettebak were used for comparison. Since the majority of the stars are around AGV, the types and luminosity classes were based primarily upon the strength of the K line of Call,

Hel k^02o, and the appearance of the Balmer lines. In a few cases the

Kel k 4471: Kgll k ratio could also be used. The sharpness and strength of the K-line is such that in several cases it may be partially interstellar.

The stars were classified tv/ice in separate sittings by the writer and once by Dr. Arne Slettebak with almost complete agreement between all classifications (Table 6).

It is interesting that three peculiar A stars are found in the region of the cluster. BD + 42° 598 (HD 16728) is of the silicon- chromium type. Lines of Sill, kklKL28-^131, and CrII at k ij-225 are abnormally strong, with the CrII line at k 4078 also probably present.

Judging from its apparent magnitude, with allowance for duplicity 11

(Table 36)» this star may be a cluster member. Its radial velocity

(Table 2), however, may indicate that it is not a cluster member. On

the other hand, on the basis of its magnitude and radial velocity,

3D + 42° 5?8 (HD 16627) is likely to be a cluster member. It is of

the silicon type, showing unusually strong Sill lines at XX 4128-4131.

The most interesting of the three stars is the manganese star

3D + 42° 528 (HD 16693). This is a relatively rare sort of Ap star, only some 15 being known, and none have previously been found to be in galactic clusters. The classification was suggested by Dr. Carlos

Jaschek (1968) and is confirmed by the identification of the following lines from measurements of the spectrum: X 3984 Hg II (Bidelman 1962);

Kn II lines at XXi}-253i 4248 , 4244 , 4137, and 4205. There is also a feature at X4550 'where a ?e II + Ti II blend occurs. The Ti II is the more likely identification since Kn stars tend to have an over­ abundance of Ti (Jaschek and Jaschek 19&?, p. 324). Further discussion of these stars is deferred until the final chapter.

Rotational Velocities. The distribution of mean rotational velocities with spectral type for individual clusters has been found to be different from cluster to cluster and from the field stars (Abt and Hunter 19&2). There is some evidence that these differences may be related to the frequency of close binaries in the clusters, tidal interactions producing slow rotators, and this may in turn be related to the initial conditions in the pre-cluster nebula. It is therefore of interest to examine the projected rotational velocities of the stars in KGC 1039.

The rotational velocities listed in column 5 of Table 6 were 12 determined by comparison :d.th a number of stars with known v sin i.

It has been demonstrated that such velocities may be estimated by eye with an accuracy comparable to that of estimates from measured half­ widths (Wright 1967. Slettebak 1968). The rotational velocity standards made available by Dr. Arne Slettebak are listed in Table 3» & number of the writer’s spectra of these stars were also used. The plates are the same as those utilized for the spectral types.

TABLE 3

Rotational Velocity Standards

Star Sp. Type v sin i (km/sec) A otLyr AO V O

a Del 39v ■ ' 160

l And 58V 90

HR331^ AOV 120

aCrB AOV 130

yOph AOV 210

18 Tau B8V 250

109 Vir AOV 330 13

The mean rotational velocity for the ten normal luminosity class

V stars which are not excluded from cluster membership on the basis of visual magnitude or proper motion give a mean v sin i of 199 km/sec with a dispersion of 80 km/sec at a mean spectral type of B9V. In­ cluding the three Ap stars would lower the mean rotational velocity for field stars of the type, which is about 150 km/sec on the basis of v sin i ’s by Slettebak (cf. Kraft 19o7).

A division of the cluster stars into groups by spectral types give

196, 220, and 150 km/sec for the mean v sin i of three B8V, five B9V, and two AOV stars respectively. These groups are small and not of statistical significance. There is a resemblance to the Pleiades stars

(Kraft 19o7) in that the mean rotational velocities are higher than the field for the earlier spectral types. It obviously would be very desirable to have rotational velocities for the later A stars in KGC

1039. The removal of stars with possibly variable radial velocity

(Table 6) does not essentially change the result.

The Radial Velocities. The plate material for the radial velocity determinations include an average of three plates per star for the cluster stars and at least one plate per night of the radial velocity standard a Persei. Although perhaps not strictly comparable to the cluster radial velocities owing to the magnitude (hence differences in exposure time), the standard velocity star does provide some check on the nightly performance of the system and is conveniently close to the

cluster. The description of cc Persei as a radial velocity standard Ik also requires a further qualification since its radial velocity is variable with a period of four days and total amplitude of 2 km/sec

(Abt 1957)* This does not vitiate its usefulness here since the velocity variation is only slightly larger than the error in an indi­ vidual velocity and only the mean over several nights is used later.

All of the plates were measured during one week on the Spectrum

Comparator with Oscilloscope Display and Digital Output (SCGDDQ) at the Perkins Observatory. After the initial setup no changes were made in SCOBDO’s state of adjustment during the measuring period. All plates were measured at about the same relative position on the screw.

YJith SCCDDO the measurement of spectral lines is accomplished by superposing a direct and reverse scan of a line displayed on the oscilloscope, obviating separate direct and reverse measurements of a spectrum and easing considerably the difficulty of setting on very broad spectral lines. Three settings were usually made for each line and these normally agreed within a micron for comparison lines. The situation is not so nearly ideal for the broad Balmer lines measured here and repeated settings varied by several microns. There is an added difficulty, in that the H-line profiles sometimes exhibited double peaks. The occurrence of these double peaks was not consistent for a given star and therefore attributed to plate defects. In these cases some ‘best fit1 for the central portion of the profile was attempted. SCCDDO itself has been examined (Y/right 19&7) and found to be free of periodic error in the screw within the printout error of Ih and to give results not differing in any systematic way from 15 manual settings with a crosshair on a Gaertner comparator.

The comparison and star lines utilized for the cluster A stars are listed in Table *J>. The 3almer-H e and H9 are excluded because of blending. For a Persei and BD + h-2 572 the lines are given in Table 5»

The effective wavelengths are taken from two lists of standard wv.. lengths (Petrie 19^6, KcDonald 19^8) for radial velocity determinations at 30 A/mm and 50 A/mm respectively, the mean wavelength being used in the several cases in which there was a difference. There were no apparent systematic deviations for any of the lines to suggest that these zero-velocity effective wavelengths needed modification.

The measurements were reduced using a computer program written originally by Kr, William Kovach, but thereafter modified and checked by Wright (196?). The program fits an n-th order polynomial to the measurements of the iron comparison lines and then computes the helio­

centric radial velocity for the measured lines, corrected for the earth's diurnal rotation, the mean velocity for the lines, and the

standard error of the mean. A polynomial of order three gave the best

fit and was used throughout. One feature that especially should be noted is that the program discards measurements having residuals larger

than some tolerance specified in terms of the standard error. The

retention of this option requires some justification. First, the

acceptable tolerance was set widely enough (eventually to twenty times

the standard error) that nearly all lines were admissable. Second,

each instance of a rejection was perused and only those were permitted

that seemed rather definitely to be blunders or extremely poor measures,

the latter always only involving Kll and H12 of the Balmer lines. TABLE 4 Lines Utilized in Radial Velocity Determinations of B-A Stars

Wavelength Identification Wavelength Identification

¥*82.21$ Pel 3933.7 Call ¥*81.3 Mg 11 3930.299 Pel 4466.554 Pel 3923.914. Pel 4404.752 Pel 3895.658 Pel **383.51*7 Pel 3889.05 HI 1*31*0 .1*7 HI 3872.504- Pel 1*291*. 128 Fel 383^.225 Pel 1*2 8 2.1*06 Pel 3835.39 HI 1*2 6 0 .1*79 Fel 3797.90 HI 1*202.031 Pel 3795.004 Pel

4132.060 Pel 3770.63 HI 4101.74 HI 3750.15 HI 4063.597 Pel 3734.37 HI 1*0 0 5 .21*6 Fel 3727.621 Pel 3969.261 Fel 3701.090 Fel

Table 5

Lines Utilized in Radial Velocity Determinations of P Stars

Wavelength Identification Wavelength Identification

4466.554 Pel 4077.710 SrII, Pel 4415.137 Pel 4071.738 Pel c 4404.745 FeI,Ti I 4063.607 Pel 4383.547 Pel 4045.765 Fel 4340.441 Hi 4005.205 Pel

4325.635 Pel, Sell 3969.261 Pel 4294.128 Pel 3933.684 Call c 4282.640 Pel, Cal 3930.299 Pel 0 4260.429 Pel 3923.914 Fel 4254.348 CrI 3875.658 Pel 4250.466 Pel 4215.686 Pel, Sr I 4202.031 Pel Lines prefixed by the c 4132.230 Pel letter "c" served as 4101.742 HI, Fel comparison lines as well. TABLE 6

Spectroscopic Results for the Brighter Stars in NGC 1039

V (Ianna) V (Trumpler) V sin i BD M Sp. Type kin/sec r km/sec km/sec V

+42°572 9.64 F7V -16 + 2 --

+42 578 8.52 AOVp(Si) -23 + 3 - 80

+41 514 8.48 AOVp? -15 + 3 - 180

+42 586 8.98 B9V variable -9 + 4 200

+42 588 8.52 AOVp(Mn) - 8 + 2 -8 + 3 < 40

+42 -589 8.46 B9V - 5 + 2 -14 + 3 100

+42 591 8.33 B8V - 3 + 2 -8 + 3 150

+42 596 8.80 AOIV variable ? - 6 + 3 < 60

+42 597 9.30 B9V variable -9 + 4 300

+42 598 7.94 AOVp(SiCr) variable ? -7 + 3 80

+42 601 8.85 B8V -18 + 2 -8 + 4 220

+42 602 9.37 B9V -18 + 2 -4 ± 3 350

+42 607 8.26 B8V " variable -6 + 3 220

+42 612 9.56 AOV -19 + 2 - 120

+42 615 8.89 B9V -15 + 2 150 18

The results for each plate included are in Table 2; the weighted mean radial velocities for each star and their errors are listed in

Table 6.

The material was examined for possible systematic errors due to temperature variations or flexure in the spectrograph. A plot of individual plate deviations from the mean for a star versus temperature for plates within a given interval of hour angle failed to reveal any temperature effects. A similar plot for all of the data (stars with two or more plates) with respect to the hour angle of the exposure did not show that flexure influenced the radial velocities in any appreciable way.

We can further make a comparison of the radial velocities measured here with work done elsewhere. In Table 7 we give the average mean error for one plate and the error computed from the agreement between plates of the same star for "several hundred" Victoria (single prism, 30 A/mm) spectrograms (Petrie 1962) and the Perkins Yb material in this study. The small errors of the Victoria A-star velocities may in part be due to the greater accuracy to be expected for the later

A-type stars. Hence we have also included the Victoria B-star results for comparison with the B8-A0 radial velocities of the present study.

In another study of 510 A-stars Petrie (i960) quotes a mean error of about +6 km/sec/plate for the Victoria single-prism spectrograph.

The magnitude of the external mean error given above for the

Perkins plates is largely influenced by the plates of two stars, viz.,

BD +42° 607 and BD +42° 597. If these two stars were omitted the external mean error would become +6.3 km/sec/plate. 19 TABLE 7

Kean Error* of a Radial Velocity from One Spectrogram

Instrument Kean Plate External Error Error

Victoria: A-stars + 1.8 km/s + 2.8 km/s (30 A/mm)

Victoria: A-stars (reduced to kZ A/mm) + 2.3 + 3.6

Victoria: B-stars (30 A/mm) + 3.6 + 5*6

Victoria: B-stars (reduced to kZ A/mm) + 5.0 + 7.8

Perkins: B,A-stars (4-2 A/mm) + ^.1 + 8.8

The possibility of attributing poor agreement between plates for particular stars to their possession of a variable radial velocity

should be considered. Petrie (i960) found that 5^/° of Dominion Astro-

physical Observatory A-star radial velocities were non-constant, it being undetermined whether the variable velocity is due to binary

motion or whether it is due to instability in the stellar atmosphere.

For the stars here then let us test the hypothesis that the star has a

constant radial velocity, r, rejecting the hypothesis whenever

where is the plate variance for the i-th star and X a is the

value from the chi-square distribution for n-1 degrees of freedom and probability a. In view of the discussion above let us choose 39.69 2 (km/sec) as our estimate of the plate variance. \'Ie find that the hypothesis of constant radial velocity is rejected in five cases. For these stars we enter in Table 6 "variable" if rejection was on the 5$ or lower level and "variable?" if rejected on the 5-10?, level.

Radial Velocity of KGC 1039. Of the stars which probably have non-variable radial velocities, three have mean velocities between -9 and -14 km/sec and six have velocities between -20 and -24 km/sec. On the basis of numbers we might expect the latter stars to represent the motion of the cluster, although none would be excluded on the basis of apparent magnitude and spectral type. Then the mean radial velocity of

NGC 1039 would be -2^+3 (km/sec) in the Perkins system.

The question of the membership of the three stars with the smaller negative radial velocities can be answered quite directly in the following formulation; we ask how likely it may be that any of these individuals in fact has a radial velocity equal to the adopted radial velocity of the cluster. The comparison of the means between the two samples then may be tested as Student's t.

For mj_ observations in each of the n-Z classes of observations, the total number of observations will be

(4) and an unbiased estimate of the sample variance is

where w^ is a relative weight for the two sets of data obtained by 21 comparing the sample variances. Then the two sample t with N-n degrees of freedom is computed as

r. r t = _JL_____ z______2. (6) a wimi wcnc where w^m^ and wcmc are the weighted star and cluster sample sizes having means r^ and r c respectively. The hypothesis of equal means is to be discarded at the significance level a whenever t^>t^ v . Qj L>~n The level of rejection for the three stars under consideration is given in Table 8 where rejection on the n-th percent level implies that there are n chances in one-hundred that the individual star has a radial velocity that matches the cluster radial velocity.

TABLE 8

Stars Rejected from Cluster Membership on the Basis of Radial Velocity

Star ;V Level of Rejection by Student’s t test

BD + bz° 588 16

BD + bz° 589 16 < ¥

•sr* + kz° 591 16 <6 2/3

There is of course one other possibility which weakens any con­ clusions to be made on the basis of the above test, and that is mem­ bership in a binary system. Each of the stars in Table 8 is included in the Aitken Double Star catalog, although none show any noticeable orbital motion. BD + 42° 583 and BD + ^2° 589 (separation about 20" arc) are ADS 20b8A and B respectively, but a physical connection would 22 not, in this case since the orbital velocities would be quite low, account for their rejection by the t-test. Yet any of these stars could have an undetected close companion (e.g. within 0,1 seconds of arc) and nevertheless also have a sufficiently long period (on the order of several years) to not be excluded by our variable velocity test, but to have a great enough relative velocity to be excluded at this point.

Thus, lacking additional information at the moment, we are forced to defer any more definite statement concerning the membership of these stars in NGC 1039.

For use in computing the space motion of the cluster we must reduce the Perkins radial velocity system to an "absolute” system in common with others. This should be the system of Wilson's General Catalog of

Radial Velocities (1953) which corresponds to that of the Lick Obser­ vatory's Kills 3-prism spectrograph. The calibration of the Lick system can be related to moving cluster and cluster space motions where it is found (Petrie 1962, 19&0 that the Lick A-star radial velocities probably require a small positive correction, but that it's exact amount cannot be found until more comparison material is available.

There are two methods available to us for the determination of the required reduction factor. Eleven plates of aPersei give a mean radial velocity of -8.8 + 1.5 (m.e.) kra/s. The General Catalog value for

a Persei is -2.3 km/s suggesting a correction of + 6.5 + 1.7 km/s.

In order to have a comparison with stars of similar spectral type and magnitude, six A-stars with General Catalog radial velocities measured by Wright (19&7) were reduced here. The appropriate descrip­ tive material and results are presented in Table 9. A correction of TABLE 9

t Radial Velocities of A-Stars Common To Wilson's General Catalog

a <5 Rad. Vel. Rad. Vel. HD Wo. (1900) Spectral (Wilson) (1900) *v (Ianna) Type km/sec Q(n)* km/sec

9^118 I0h46?7 +44°20' A3V . 7.48 +6 o(7) - 7.7*3.2

101549 11 36.0 +44 34 A3V 7.99 -9 o(4) - 17.0*2.2

I02589 11 43.5 +29 21 A2V 7.07 -5.8 b<5) - 9.5*4.7

105388 12 3.0 +31 37 AOV 7.46 -6.5 b ( 12) + 2 .4*4.8

106?84 12 11.7 +40 08 A3 IV 7.20 +4 o(4) + 6 .1*2.9

107427 12 I5.9 +26 29 A3V 9.11 -8.6 b(3) -29 .0*2.7

*Q is the quality given in the Wilson (1953) catalog, and n is the number of plates in the radial velocity value.

i\> V*) 24

+ 4.5 + 2.9 km/s reduces the mean difference between the Perkins and

General Catalog velocities to zero. Finally, then, we adopt the weighted mean of + 6 + 2 km/s for the reduction of the Perkins radial velocity system to the system of the General Catalog.

The mean radial velocity for NGC 1039 then becomes -17+5 km/sec. CHAPTER III

PHOTOMETRY IN THE REGION OF NGC 1039

In order to be able to account for astrometric plate errors which are functions of stellar magnitude and color, these data are required for each star which shall be measured. High accuracy is not a require­ ment as can be seen from the following considerations: the most serious magnitude-dependent positional distortion is to be expected in the comatic images of the Sproul refractor (in contrast the Allegheny and

Naval Observatory telescopes show quite round images over the entire field on all plates); this can amount to a relative positional shift on the order of 10 microns/magnitude near the edge of the Sproul field

(Ianna 19&5)• Thus to be compatible with a relative measurement of position with an error of + 2 microns, we must know the magnitudes of the measured stars to about + 0.2 magnitude.

The primary color effect is to be found in the relative diffe­ rences between the refraction constants for stars of different effec­ tive color in a given instrumental system. Since atmospheric dis­ persion is greater toward shorter wavelengths, the effect, assuming equivalently good collimation for the two refractors, will be largest for the Allegheny telescope operating in the photographic region. A study by Hudson (1929) shows F stars shifted toward the zenith by

O'J093 (or 0.006 mm) with respect to M stars (the corresponding value

25 26 for the Sproul ’'photovisual” refractor is 'J017. Assuming then a

(B-V) - 1.2 magnitude, an error of less than + in the colors shall suffice in this application.

Previous photometric investigations in the region of NGC 1039 include those of Cherubim (1929)? Bruggemann (1935)» Graff (1923)*

Zug (1933). Clasen (1937), Wachmann (1939), Becker and Stock (1958),

Dieckvoss (1955), Kotchlashvili (1950), Johnson (1952), and Mathews

(1963). Since none of these completely satisfy our needs here, it was decided to measure the photographic and visual magnitudes on the

Johnson and Morgan U3V system for all the stars comprising this study.

The magnitude determinations were carried out in two stages.

First the photoelectric sequence of Johnson (1952) was extended to fainter magnitudes at the Fan Mountain Station of the Leander McCormick

Observatory. The remaining magnitudes were then derived photographically using the photoelectric magnitudes as standards.

The Photoelectric Photometry. The photoelectric equipment on the

32-inch reflector at Fan Mountain contains an EMI 6256 (S13 cathode) photomultiplier which is used unrefrigerated. The filters have the transmission curves exhibited in Figure 1. The sensitivity of the S13 photocathode drops sharply beyond 5500 A and hence the photomultiplier- filter combination affords a satisfactory matching of the UBV system for the V magnitudes and B-V colors determined here.

The observations of six primary Johnson and Morgan Standards, five standards in NGC 1039,and 3 unknowns were made in one night -

September 9, 1966. All measurements were made through a circular diaphragm with a diameter projecting to 21" arc on the sky in the 100

T 7 c

8 0

GO

4 0

20

4000 5 0 00 6000 70 00 8000

Fig. I Transmission Curves of the Fan Mountain U8V Filters. 28 star-sky-star for a given color. The observatory's solid-state, pulse counting integrator and Rakos D.C. amplifier were used with an inte­ gration time of 20 seconds in making the observations; the deflections were recorded on an Esterline-Angus chart recording potentiometer.

Since temperature and humidity affect the internal resistances of the D.C. amplifier, said amplifier was calibrated under observing con­ ditions with a standards current source following the observing period.

The gains for each input step of the amplifier in magnitudes relative to the lowest gain step are reproduced in Table 10.

TABLE 10

Calibration of Rakos D.C, Amplifier

A B C D E F

1 0.000 0.496 0.996 1.493 1.988 2.484

2 2.484 2.978 3 .478 3.975 4.470 4.966

3 4.988 5.484 5.984 6.481 6.976 7.474

4 7.503 7.999 8.499 8.996 9.491 9.987

5 9.821 10.317 10.817 11.314 11.809 12.305

6 12.518 13.014 13.514 14.011 14.506 15.002

We give in Tables 11 and 12 the pertinent observations and the results for the extinction and color coefficients; these have been obtained as described in subsequent paragraphs.

For the most part the procedure followed in reducing the observa­ tions is that described by Hardie (1962) and his notation has been retained. TABLE 11 29

Fan Mountain Photoelectric Photometry for NGC 1039

Hour Air Star R,.A. Decl. U.T. Angle______Mass

P Gyg 3 I9h 28^9 27°52* 04 38 3h2imo6s 1.363 27 B Cys A 19 28.9 52 °§ 32 4 15 15 1.677 G And 0 15.4 38 30 06 06 0 02 51 1.000 107 Psc 1 40.6 20 06 06 25 -1 03 18 1.083 a Ari 2 05.2 23 18 06 39 -1 13 52 1.075

K34-517 2 39.9 42 34- 07 17 -1 10 28 1.031 M 34-521 2 40.0 42 33 07 26 -1 01 32 1.024 M34-522 2 40.1 42 33 07 49 -0 38 33 1.011 M34-429 2 39.6 42 31- 08 42 0 15 06 1.004 M34-430 2 39.6 42 33 08 21 -0 05 59 1.003

M34-475 2 39.8 42 38 09 03 0 35 57 1.010 K34-469 2 1"39.7 42 39 09 13 0 46 03 1.015 1*13^-553 2 4-0.0 42 38 09 25 0 57 46 1.022 HR1046 3 27.3 55 18 09 44 0 29 32 1.051

TABLE 12

Fan Mountain Photometry - Extinction and Color Coefficients

Color Coefficients Extinction Coefficients

U = 1.050 = 0.18 Ks* II c = -0.023 * 0.17 11 *5 -0.022 30 The air mass is computed from

X - sec z - 0.0018l67(sec z - 1) - 0.002875(sec z - l)2 - 0.0008083 (sec z - 1)3 (7) where the secant of the zenith distance for any observation is

sec z = (sin pf sin6 + cos pf cos 6 cos h)”^ (8) in which p is the observer's latitude, 5 the declination and h is the hour angle of the star.

The second-order color coefficient, k^v , was determined directly

from observations of 8 Cygni over a large range in air mass during one night (Keisel 1966). This determination need not have been carried out

in concert with the measurement of unknown stars since in general k£v does not vary significantly from night to night at a given location

(Hardie 1962).

An estimate of the first-order color and extinction coefficients was made graphically from the cluster and standard star observations.

The following relationships obtain:

V * v - kyX + E (B - V) + cv (9)

B - V = U (b - V) (1 - kbyX) - y kbyX + Cbv

For the visual magnitudes a first approximation to the extinction

coefficient ky was found from the standard star measurements by plotting

(v - V) + e(B - V) vs. X taking zero for the color coefficient e

momentarily. This color coefficient could then be estimated in a plot

of (V - v0) vs. (B - V) for the known stars in the cluster and ky 31

subsequently redetermined. A second iteration could have produced

little change and so was omitted.

An analogous procedure gave k£v and M- for the B-V color reduc­

tions. The appropriate graphs are displayed in Figure 2.

It is now a simple matter to find the magnitudes for the unknown

stars. In the differential relations

AV = A - k AX + eA (B - V) v v

A (3 - V) = jjA (b - v) - p k£v AX - p k£vA (b - v) X (10)

each unknown magnitude was compared to each of the five measured

cluster stars which mean was adopted.

The results for the three stars measured at Fan Mountain are in­

cluded in the table of Johnson magnitudes (Table 13) of stars likely

to be members of NGC 1039; these are used as reference magnitudes for

the reduction of the iris photometry. The internal agreement of the

Fan magnitudes suggests a mean error of + 0.03 magnitude in V and

+ 0.01 magnitude in B-V.

The corresponding errors for the Johnson measures are + 0.008 . and + 0.005 magnitude for a single observation.

The Iris Photometry. The greatest portion of the required magni­ tudes have been derived photographically from the plates described in

Table 14. These plates were kindly secured by Mr. James W. Christy of the U.S. Naval Observatory with the 40-inch Ritchy-Chretien reflector and made available to the writer through the courtesy of Dr. Kaj. Aa.

Strand. All of the plates were developed at the same time for four minutes in D19 at 68°F. with continuous agitation. >

-V+ £ > o 0.9 0.2 o.e 0.0 0.2 —I I I I I I I I— I I I I— 1— . 02 . 06 V - B 0.6 0.4 0.2 0.0 . 14 . 16 X 1.6 1.6 1.4 1.2 33 TABLE 13

NGC 1039 - Photoelectric Standards For Iris Photometry

Measurement Dieckvoss No. No. V B-V

254 157 9.^5 + .54 256 154 9.64 + .034 257 161 11.94 + .47 269+70 166+68 8.52 + .03 272 162 10.93 + .27

292 174 10.51 + .198 302 188 10.16 + .11 307 179 10.31 + .134 361 221 10.46 + .164 366 226 10.46 + .201

377 222 11.21 + 1.088 396 200 ' 8.48 + .051 429 321 13.79 + 1.03 430 241 12.20 + .645 433 238 11.21 + .350

437 244 8.98 + .001 442 250 11.47 + . 36 14-69 255 13.49 + .71 472 263 8.52 + .001 473 2o6 8.46 + .008

475 267 11.95 + .469 477 274 . 9.72 + .170 1+87 258 11.13 +1.046 ^89 269 11.45 + .351 492 280 9.89 + .098

512 306 11.09 + .398 517 282 8.33 - .006 521 290 ' 13.44 + .72 522 307 7.9^ - .003 526 303 9-93 + .116

527 294 11.18 + .342 528 284 10.74 + .276 529 278 11.77 + .278 540 311 9.30 + .053 541 312 10.45 + .20 34 TABLE 13 - Cont.

Measurement Dieckv.oss No. No. V 3-V

542 315 11.45 + .38 557 301 10.01 + .115 553 308 8.80 + .060 564 316 11.97 + .677 584 331 IO .96 + .95^

586 328 8.85 + .028 592 339 9.31 + .049 62? 351 11.50 + .360 640 343 10.97 + 1.012 641 355 7.33 + .944

672 362 11.45 + .414 686 370 10.27 + .136 687 37^ 8.26 ■ + .010 695 ■386 10.28 + .143 731 391 10.9'3 + .156

808 443 9.56 + .06 810 430 10.63 + .531 846 456 8.89 - .02 35

TABLE 1^

Observational Data for Photometric Plates of KGC 1039

Plate Emulsion Filter Exp Air Mass

^m 17(& 103a0 GG13 1.01

1705 103aD GG11 10 1.02

1706 103a0 GG13 5 1.02

1707 103aD GG11 10 1.03

1708 103a0 GG13 5 1.03

1709 103aD GG11 10 1.05

1710 103a0 GG13 5 1.09

1711 103aD GG11 10 1.12

The measurement of the plates was accomplished with the Cuffey

Astrophotometer at the Perkins Observatory. At least two Iris settings were made for each star with a single check star on each plate being measured every 15 to 30 minutes during the course of the work to allow the drift of the photometer to be taken into account. The drift in zero point was assumed to be linear with time in the interval between the settings on the check star. It happened several times that the drift changed sign or the zero point changed radically. These measures were discarded. It was also necessary to measure each of the plates in more than one sitting. Some care was taken, therefore, to maintain the photometer and plate undisturbed between measuring sessions. In any case, the check star served to tie together the individually measured sections if there was a zero-point shift between them. The reductions proceeded with a least-squares adjustment of the iris measurements to the standard photoelectric sequence. The wide magnitude range coupled with the properties of the photographic emulsion lead us to expect up to cubic terms in the model for the adjustment.

This was b o m out in the subsequent reductions where linear and second- order polynomials resulted in exceedingly poor fits. We expect, as well, a radial term to be required in the adjustment as a consequence of vignetting in the field of the ^0-inch reflector. This arises prima­ rily from the partial occulting of the secondary mirror by the primaiy mirror sky baffle (lanna, unpublished). We thus have five parameters to determine in the relation

(Iris setting) = A^ + Ay m + A^m^ + + A^r (11) where m is the magnitude (either visual or photographic) and r =

(x^ + y^)"a is the position of the star on the photometry plate relative to the plate’s center for each plate. However, since finding an unknown magnitude then requires solving a cubic equation, it is more convenient for the implementation of the reductions to use the inverse relation

m = AQ + A^I + A£l^ + + A^r (12)

In terras of the least-squares solution we are justified only in a pragmatic sense if we get the same answers either way. A comparison of the predicted magnitudes showing that we indeed get essentially the same numbers from either solution is given in Figure 3» The divergence for the fainter magnitudes occurs in the region where we are extrapolating beyond the faintest photoelectric standard. The o 14 £ !! > Iris1 i. A oprsn ewe Vsa Magnitudes Visual between Comparison A Fig.3 B 16 10 12 from from 1 1 1 16 14 12 10 8 Inver. ! es-qae Solutions. :! Least-Squares i i a ] a, [iris = 3?

38 inverse solution predicts more likely (numerically smaller) magnitudes in this region.

The radial distances of the stars needed in the photoelectric reductions are found from a comparison of the Allegheny positions with the photometric plates. Some two dozen stars were measured on each blue sensitive plate representing the four positions of the telescope necessary to cover the cluster. A linear plate constant adjustment, viz..

X - X^neg — aX + bY + c

enabled the positions for the stars on the photometric plates to be calculated from the Allegheny plate positions with the geometrical center of the particular plate defining the zero-point of the reference frame for the radial terms.

The resulting magnitudes are included in the Appendix. Where the same star had appeared on more than one plate the straight mean was taken.

Accuracy of the Magnitudes. Whether or not we have reached the required accuracy can be adjudged in several ways. With a vector T defined by

T = (1 I I2 l3 r) (13) the variance in a magnitude predicted from the parameters in the least-squares solution is given by

var (my) = TB-1TTa 2 (1*0 39 where is the inverse of the normal equation coefficient matrix and

O 2 is the variance of an observation of unit weight. We find typically for a star of about 13th magnitude in either color near the plate border a standard error of + 0.15 magnitude.

A comparison can also be made for these stars appearing on more than one plate. These stars in the plate overlap areas are most sus­ ceptible to plate error. We find for some 6$ stars, each occurring on two plates, mean errors + 0.31 and + 0.39 in the visual and blue respectively.

Finally, the magnitudes determined herein can be judged with respect to the visual magnitudes published by Dieckvoss (1955). The

Johnson photoelectric magnitudes give the mean differences and standard deviations displayed in Table 15; the number of stars is given in parentheses. It appears that the Bieckvoss magnitudes are on the average somewhat brighter, particularly at fainter magnitudes, than the Johnson magnitudes. The same differences for our photographic magnitudes are given in Table 16.

TABLE 15

Johnson-Dieckvoss Visual Magnitudes

" D)/ll “ *0 *10 -°*°3 ( n “ 32> (J - D)m> n < 0 = +0.1? +0.06 ( n = 18)

°(J - D)a11 = + 0.20 ( n = 52)

o'(J - D) = + 0.25 ( n = 18) m> 11.0 TABLE 16

Ianna-Dieckvoss Visual Magnitudes Fainter than 11.0

( I - D ) = + 0.12 + 0.03 ( n = 60)

a I - D = i °*2? ( n = 60)

As would be expected the Dieckvoss magnitudes again appear somewhat brighter. The standard deviation cr-_^ overestimates the error in our magnitudes. If the errors are about the same for each, should be about +0.20.

Thus our photographic magnitudes seem about as good as desired for astrometric purposes. CHAPTER IV

ANALYSIS OF ASTROMETRIC INSTRUMENTATION

It is especially true for astrometry that an observation missed can never be recouped. Indeed, this study owes much to a number of observers, past and present, at several observatories.

The plate material has been collected from three sources. The largest number of plates are from the Sproul Observatory and span the years from 1937 to 1961. The greatest spread in time, 52 years, is found in the Allegheny Observatory observations, the first epoch plates having been taken by Schlesinger and Trumpler in the early years of the operation of the Thaw telescope. Two plates taken with the 6l-inch astrometric reflector were obtained to support the recent epoch material for the fainter stars. The relevant descriptive plate data are collected in Table 25 in the following chapter.

It is evident that we are here drawing plate material from three instruments with quite different optical characteristics. The Thaw telescope is a photographic refractor, the Sproul a photo-visual re­ fractor, and the 6l-inch telescope a reflector.

It seems therefore a particularly useful caution to investigate the behavioral traits of these instruments. Such knowledge will be very shortly applied in a discussion of suitable models for the nece­ ssary least-squares plate comparisons. It would also be interesting ix>

41 42 know, in view of the elastic properties of glass, if the present instru­ ments perform as they did in the past. Certainly both short term and long term instrumental factors are partially responsible for possible systematic errors.

In this chapter, then, we shall discuss the three astrometric telescopes used in this study and also the automatic measuring engine of the U.S. Naval Observatory on which the plates were measured. It can be noted here that this study could not have been carried out in its present form without the use of this measuring machine.

Characteristics of the Sproul 24-inch Refractor. The Sproul 24- inch telescope is a photovisual refractor of 1093*2 cm focal length with the minimum focus occuring at a wavelength of about 5^14 A.

A maximum spectral bandpass of 900A (XX 5100-6000) is fixed by the use of Kodak 103a-G spectroscopic plates behind a Wratten No. 12 filter.

Dates of changes of observing procedure or lens adjustments bearing on this study are given in Table 1?.

Early evaluation of the Sproul objective indicated that it was to be regarded as an outstandingly good one. Killer and Marriott (1914) carried out Hartmann tests obtaining the exceedingly small Hartmann constant of 0,070 (a value of this constant less than 0.5 was considered by Hartmann to be indicative of a very good objective). This, however, does not necessarily represent the quality of the objective at that time owing to the likelihood of mechanical and thermal deformations, nor the current figure of the objective since over many years glass itself may "flow*1.

More recent Hartmann studies of this instrument (Ianna 19^5) TABLE 1? 43

Sproul 2 ^-inch Refractor Chronology

Date Comment

1911 December Installation of objective lens.

1939 July Wratten 12 filter replaces K2 filter.

1939 August Eastman I-C emulsion introduced to replace I-G plates.

1941 October Adjustment of objective.

1949 March New Objective lens cell installed.

19^9 March Eastman G-eaulsion introduced.

1957 February Optical center 22^ west and 3mm south of geometrical plate center. Re-collimation.

1958 January Objective readjustment and re-collimation.

1961 January Optical center il111111 -west, 7mm north of geometrical pla^e center. k k

quite definitely established the existence of thermally-dependent lens

variations. Spherical aberration, coma, and astigmatism were found to vary over a large range in a manner connecting the variations to the

nighttime cooling of the objective. It is clear that the objective lens is rarely in an equilibrium condition.

There is as well some indication of mechanical distortion in the

objective. It is not firmly established that these latter effects are

purely gravitational shape deformations in the lens elements however.

Another likely possibility is that one or both of the elements may

sometimes tilt slightly in their cell as the telescope is moved.

Sample on-axis zonal focus curves obtained from Hartmann testing

of the Sproul telescope are given in Figures k and 5« In all of these diagrams we plot relative focus in mm against the radius of the corres­

ponding zone of the objective in inches. That shown in Figure ^

(solid line), obtained by Miller and Marriott (1913). represents an objective whose on-axis performance is good, though slightly exceeding the Rayleigh quarter-wave criterion (axial aberration of 0.7 mm for

the Sproul telescope). This is in approximate agreement with ray

tracing results (dotted line) (Ianna 19&5). Off-axis ray tracing

suggests a large amount of outward coma as currently observed. No

further direct information is available on off-axis aberrations in the young lens; however, it is the writer's impression that severe coma is less evident on early plates. This may be at least in part due to the longer exposures and better averaging of the seeing image.

The more recent group of test results (Figure 5) are representa­

tive of the range in nightly performance exhibited by the Sproul ij-5

in m m

o Objective u. 3 ray trace 2

0

2 4 6 8 10 12 R

Fig. 4 Sproul Zonal-Focus Cu rues

6

m m 4

2

0

on 2 o °u. 0

2

0

R

Fig.5 Recent Sproul Hartmann Test Results 46 refractor owing to thermal gradients in ihe lens and its cooling. Note that in the first test spherical aberration is severe and opposite in sign to that of the early published test and calculated performance.

In the third example of this group the spherical aberration has reversed sign and we find the zonal-focus relation now to be in agreement with other results. As noted above the thermal gradients are such as to occasionally compensate for the large coma which then appears more or less absent, although the behavioral pattern is not fully explained by thermal effects alone.

The Thaw 30-inch Refractor. The 30-inch refractor of the

Allegheny Observatory is designed to operate in the photographic region of the spectrum with a focal length of about 1410 cm with the minimum focus occuring at a wavelength of about 4300A. No filter is normally used with the plates so that we are relying on the natural cutoffs of plate sensitivity ( ^5000A) and objective transmission (about X 3800A) to define the wavelength passband. The system thus accepts light over approximately a 1200A range. A short chronology of lens and telescope changes for the Thaw telescope bearing on this study is given in

Table 18.

Extensive Hartmann testing of the Thaw objective was carried out by Schlesinger and his colleagues after its installation. None of the details were ever published and the notes and measurements have been lost. However Schlesinger did comment on the performance of the tele- scope and the quality of the objective in the literature at one time

(Schlesinger 1915). Tests carried out in the optical shop "implied an almost perfect figure, and also indicated that the material in the TABLE 18 47

Thaw 30-inch Refractor Chronology

Date Comment

3 August 191^ Lens first installed.

13 August 191^ Lens to shop: 6 mm. positive abbera- tion in zone with radius 12 inches to 15 inches.

13 September 191^ Fan installed. li+ September 191^ Flint lens turned 90 dg.

19 February I9I0 Collimation okay in right ascension. ‘Line of collimation cuts plate 1.5 inches north of center of plate."

11 October I9I6 Position of base: too near pier by 0 .6 ? inches: too near greater decli­ nation by 0 .6 ^ inches.

27 October I9I0 Lens removed. Front lens revolved 90 dg. in counterclockwise direction. (As viewed from plate end.)

1 November I9I6 Rear (crown) turned 90 dg. counter­ clockwise as viewed from plate, 'feo that now the two halves are in the same relative position as before October 27 , but now both are turned 90 dg.," three cleats retaining crown retained.

4 November I9I6 "A critical examination of the plates taken since November 1, I9I6 , indicates that before that date the crown lens had been cramped by the three cleats, and that the insertion of the card washers has cured the triangular wings on images of bright stars on long exposures."

6 December I9I6 After "bump11 Base 1.29 inches towards pier from center; 0.53 inches in greater declination from center. TABLE 18 - Cont 1*8

Date Comment

21 June I9I7 Base: 1.01 Inches too near pier; 1.02 inches too near greater declination.

15 October I9I7 Base 1.07 inches too low; 1.07 inches too near pier side.

8 February I9I8 Base: 1.11 inches toward pier; 0.79 inches towards high declination. 2-9 August 191*1* Lens removed (first since November 1, I9I0 ). Chipped; focus changed by 5 mm. l* June 191*8 Lens removed. Collimation.

10 March 1966 3ase: 1.0 inches toward pier; 1.5 inches toward greater declination. i+9 objective is of unusual excellence". Testing at the telescope showed a considerable amount of positive spherical aberration to be present and repetitive testing gave the result

"..that while positive aberration was found to be always, present, it varied in amount from night to night and even in the course of a single night. A study of the data thus obtained indicates that the aberration arises from effects of temperature and that it is more pronounced when the temperature is falling rapidly."

The addition of ventilating devices at that time was successful in removing the spherical aberration due to temperature. Such devices are not currently operated.

All of the plate material from the original Hartmann tests is extant, so it was decided to remeasure and reduce a selection of these plates. The observing records gave the required focal settings at which the tests were made, but no information could be discovered describing the Hartmann screens themselves. It was thus necessary to make reasonable estimates of the hole distributions over the screen in order to proceed. The usual methods have been followed (lanna 1965).

Observing data for these tests are given in Table 19; the zonal-focus curves are exhibited in Figure 6. We again plot relative focus in mm against zonal radius in inches.

In the same table and figure above we have included some recent

Hartmann test data. These tests were performed with a newly constructed

(at the Perkins Observatory) masonite Hartmann diaphragm during the

same observing period as the recent epoch plates of NGC 1039. Both

new and old test results appear quite similar, the greatest difference being between the first and the subsequent tests reported that were TABLE 19 50

Observing Data For Thaw Hartmann Tests

Plate No. Date Focal Separation

159 September 15, 1914* I60mm 226^ June 12, I9I5 l6omm 2265 June 12, 1915 - 3H65 December 9> 19^5 60111111 2H66 February 20, i960 6 omn 3O HOO**T ^ February 20, i960 - F i fl . 6 Thaw Hartmann T est est T Hartmann Fifl. Thaw 6

FOCUS — mm m m - m m m m m 1 1 E 1- E E 1 E 1 i i -{ 4 8 0 2 14 inches 12 10 8 6 4 2 i f 1 H 1 fc i i 1 ---- / 1 ---- 1 ---- f i r i i i ---- i X ---- 2264-5 2-3 H 66 3 H 65 15 9 Results —4 1— X ^ray trace *

R 51 52 carried out after a lens adjustment (rotation of the front element by

90 degrees). The amount of spherical aberration does not vary greatly between the tests. The shape changes in the zonal axial aberration are likely due to thermal gradients in the objective. The innermost zones

(2-inch radius) for the recent tests appear to have focal lengths longer by about a centimeter than the rest of the lens. Not much significance should be placed in this result in view of the proximity of the zones on the photographic plate and the small leverage in determining the focus. It may be noted here that the error in measuring a separation of images in the Hartmann testing, about +0.0C& mm, leads to an error in a focal determination of about +0.2 mm (m.e.) (Ianna 1965, p. 11*0 .

All the results further show the lens to be possessed of astig­ matism on-axis, hence asymmetry of figure, amounting to a focal diffe­ rence between perpendicular directions on the lens varying between one to three mm, the most extreme case being the last test shown. This combined with ordinary third-order astigmatism might be expected to produce images of varying elongation around the field of the Thaw telescope.

An attempt was made to estimate the coefficient of coma from off- axis Hartmann images on plates 2-3H66. It is evident from the lack of comatic distortion in the off-axis Hartmann images, which are quite symmetrical here (cf. Ianna 19&5* P» 1°5)» that the coma is quite small, an order of magnitude less than for the Sproul refractor. However the quantitative evaluation of the coma coefficient is complicated by the axial astigmatism present. Data averaged from perpendicular axes -7 -2 suggest a coefficient of coma of 10 cm implying a comatic flare 53 of about 10 microns near the edge of the field. This would scarcely be visible on the photographic plate.

The parameters of the Thaw doublet have not been published, but are in part found in observatory records (de Jonge 1$66). These just include the radii of curvature and the spacing of the two elements. We have nevertheless gone bravely forward and ray-traced the lens using the parameters listed in Table 20. The result is a focal length within

5# of the correct value, but for a lens with large negative spherical aberration and coma. The on-axis aberration is plotted in Figure 6 .

This should not be taken too seriously of course, in view of our guesses for the unspecified lens parameters and the possible uncertainties in the given constants (i.e., they are likely to be design values from which the final figure could significantly differ). There is no evi­ dence from further Hartmann tests (Kamper 1968) that the Thaw telescope suffers thermal upset to the degree of the Sproul refractor that reverses spherical aberration.

TABLE 20

Constants of the Thaw Objective

R- = +238.56 in. tt = 2.25 in. (Flint) nx = 1.5241 R2 = -126.83 in.

separation » 0.40 in.

R3 s +127.97 in. t^ = 1.75 in. (Crown) n2 = 1.6318 = +21350 in.

11 + " convex toward source; indices of refraction (n) and lens thicknesses (t) are estimated values. The examination of Thaw plates lends support to the notion that

we have a very good objective that yields round, apparently coma-free,

images over the entire 8 x 10 inch field. The images are a bit large,

perhaps owing to a combination of the wide spectral bandpass and the

large spherical aberration. One might imagine the round off-axis

images as being the consequence of partial cancellation of some of the

aberration but this cannot be checked very well on the basis of what

information we have available here.

The U.S. Naval Observatory Astrometric Reflector. The Naval

Observatory’s 61-inch astrometric reflector has been described in some

detail elsewhere (Strand 1966; Koag, et al., 1967). Various features

of this instrument, such as an excellently figured fused quartz mirror,

long focal length (f/10), and flat secondary, especially prepare it for

the task of determining precise stellar positions. We shall not further

consider the field accuracy of the telescope here since, although two

6l-inch plates were measured and included in some exploratory reduction,

the Navy plates were not retained in the final reductions.

The U.S. Naval Observatory Automatic Measuring Engine. All of the

astrometric plate material used in this study was measured on the

automatic measuring engine located at the U.S. Naval Observatoiy in

Washington, D.C. This machine is capable of very rapidly measuring

large numbers of images with high accuracy and a minimum of operator

intervention.

The main structural members of this machine, built by Nuclear

, Research Instruments, Inc., are made of granite. This includes the 55 moving x, y stages which are supported by air bearings and guided by granite ways. The positions of the stages over a 10 x 10-inch area are read from a Ferranti Moire fringe digitizing system to one micron and recorded by IBM card punch. Ihe machine is programmable in the sense that a punched card deck of the positions of the images to be measured can be used to direct the stage positioning; a single (x,y) position is read at a time on operator command.

Automatic bisection of the photographic image is accomplished by scanning the image in x- and y-coordinates and balancing the image density profile with respect to a fixed reference marker. The profiles are displayed to the operator on two cathode ray oscilloscopes. These, in conjunction with a direct-viewing screen, furnish to the measurer adequate information for a decision to accept or reject a particular image. There is an upper limit of 350 microns to the diameter of an image that can be measured. Very weak, fuzzy images cannot be accu­ rately bisected, although in all cases the repeatibility of the centering system is better than one micron. The combination of auto­ centering and pre-positioning results in a measuring engine which is

6-12 times faster than more conventional metrological equipment.

Since this innovative measuring engine is unconventional in design and was rather new when the measurements were carried out, some ancillary manual measurements were obtained for purposes of comparison.

These measurements were carried out on a Mann (x,y) comparator, Model

42205^, in the Flight Test Evaluation division of North American,

Rockwell in Columbus, Ohio. I am indebted to Dr. Walter E. Mitchell,

Jr., for revealing its existence to me and to Miss Jan Anderson of 5 6 i North American for permission to carry on the measurements.

A calibration of the Mann engine against a high precision engraved glass millimeter scale was carried out at installation and is reproduced here in Table 21 as representative of the progressive error in the screws. An inconclusive attempt at verifying this by the measurement of two small spots of about one mm separation on a plate placed at different positions along the screw was made by the writer. The measuring accuracy was just good enough to show no large progressive error and that there was no significant periodic error. The calibra­ tion is adopted as given and applied to x-coordinate measures from the

Kann engine in the direct comparisons between manual and automatic settings given below.

TABLE 21

Calibration of Mann Engine 422D5^

Progressive Error

Screw position Error in x Error in y (mm) (microns) (microns)

0 0 0 50 -0.9 + 0.6 100 -2.1 -0.5 150 -1.2 -0.5 200 -l.ij- -0.^ 250 -2.5 +0.2 +0.2

Periodic Error

Less than 1 micron for both x and y screws 57 Let us now proceed with a more detailed examination of the KRI automatic measuring engine. During the initial measuring sessions it became apparent that unless sufficient warm-up time was allowed (it is now observatory policy to leave the machine on continuously) and the environmental temperature remained within a few degrees of some mean value, the measuring engine was subject to a zero-point drift. Sub­ sequently the machine was turned on about two hours before measuring commenced and a check star was remeasured periodically in order to discover if any drifting occured.

The automatic centering system was noticeably dependent upon a number of factors, some quite expectedly, such as focus and plate de­ fects. For images approaching the diameter of the acquisition circle and images of low density or broad profile, such as found when bad seeing conditions obtain, the centering behavior seemed to vary to some extent as a function of the adjustment of various servo loops in the automatic setting system. On several occasions a gradual change in how the system "locked-in” on an image was noted. At times there also appeared to be some bias in the centering on poorer images.

Some quantitative estimates of the setting accuracy would thus seem to be in order.

For about sixty stars distributed over each of two plates, mutual separations were calculated from Kann manual measurements and automatic measurements. A scale difference was noted in the sense that sepa­ rations appeared smaller in the Kann measurements. However, the environmental temperature of the Kann engine was about ,'5°F. less than that of the NRI machine, and the scale difference is accounted for by 58 contraction of the glass plate and screw of the Mann engine. We conclude

that to within ordinary measuring accuracy there is no scale difference between the NRI and Mann measuring engines.

A running check on the accuracy of the NRI engine was kept for all

plates having more than one exposure. From the measurements of these

plates mean exposure separations, individual deviations, and mean errors

of a measured separation were computed in each coordinate for each

plate. These results give a very realistic evaluation of the setting

performance of the engine. We find from 3539 pairs of images that the

separation between two exposures of the same image is measured with a

mean error of +0.00^3^ mm in x and +0.0C&23 mm in the y direction for

mean errors of a single setting of +0.0031 mm and +0.0030 mm in x and

y respectively. It should be noted that these data include measure­

ments over a wide range of quality and of magnitude, and hence, include

positional distortions such as magnitude error to some degree as well.

A sizeable number of plates indicated single-setting mean errors as

small as +0.0018 mm, and the writer has seen reductions from NRI

measurements of (McCormick Observatory) parallax plates in which no

residual exceeded 0.001 mm. Thus the KRI measuring engine performs

best over a short period of time with images of fairly uniform quality.

The possible dependence of the setting system on magnitude and

image quality was examined more closely by again comparing measurements

of the separation of images from different exposures on the same plate,

but now with a division into three groups. The first group consisted

of weak images, the second very good images, and the third those

images whose size approached the access area of the centering system. 5 9 Results from this comparison are given in Table 22 where, by group, we list mean errors and the numbers of residuals greater (+) or smaller

(-) than the mean for the combination of the three groups, We note that a magnitude error is revealed in the separations, and, not surprisingly, that the poor quality of an image adversely effects the accuracy of its bisection. This is the basis for applying weights of "I" to weak or strong images and n2V to good images during plate measurement.

The plates used in this study have been measured in only one direction, contrary to the standard practice in astrometry of measuring a plate both in the increasing and decreasing (reverse) senses of the run of a coordinate in order to remove personal setting bias. This seemed reasonable in view of the auto-centering system of the NRI engine, and several plates were measured in the reverse direction to check this. Table 23 presents the results of the plate constant re­ duction of two pairs of plates, each including 45 stars, in several ways. For the 276-38703 pair, in addition to averaged direct-reverse automatic measures, we add a manually measured pair and reduction including linear magnitude terms and linear plus second order magnitude terms. There is an increase in plate variance from direct-reverse to direct only in one case (246-28703), and we see below that magnitude error plays a role in this case. Plots of the residuals from the plate reduction against magnitude. Figure 7, show only that the scatter in­ creases for the direct measures taken alone, but indeed there are then half as many settings. With regard to the proper motions, although there seems a slight trend toward change in the 276-38793 pair re­ ductions, differences between plate pairs are much greater than diffe­ rences between different modes of reduction. TABLE 22

Measured Separations and Setting Error of the NRI Engine As A Function of Image Size

All Images

Average No. of No. of Average No. of No, of X-Coordinate Positive Negative Y-Coordinate Positive N egat ive Group Residual Residuals Residuals Residual Residuals Residuals

mm mm 1 0.0059 8 14 0.0065 11 12

2 0.0030 11 11 0.0030 13 9

3 0.0041 19 3 O'. 0043 12 9

Separation by Grouo

Mean Separation m.e. in K

2 1.0720 -0.0417 ±0.0039 ±0.0037

3 1.07^9 -0.0416 ±0.0042 ±0.0049

On O TABLE 23

Plate Variances and. Proper Motions From Direct and. Direct-Reverse Measurements

Plate- pair 246- 28703 Plate-pair 276-38703

i1 Direct- Direct Direct Direct- Direct- Direct Direct Direct ■ Reverse Manual Reverse Reverse Manual m-eq m+:r-2 var (x) 36 58 60 37 48 45 46 4 7 var (y) 63 58 59 48 17 18 17 18

Proper Motion, Star x y x y x y x y x y x y x y x y %

1 +12 -12 +11 -11 +11 -11 +12 -22 +14 -18 +13 -I9 +14 -? +14 -20 11.3

2 —1 +4 +1 +2 +1 +2 0 -3 -2 -4 -2 -4 -3 • -3 -4 11.1

3 0 0 -5 -0 -5 0 -2 +3 -1 -2 -2 -2 -2 • -2 -3 11.8

4 -2 +1 -2 +11 -2 +1 -3 -5 +2 -3 +1 -3 +1 • , +1 -3 12.0

5 +2 +6 +10 +5 +9 +4 -9 +2 -5 +2 -7 -1 «f' +1 -8 0 10.9 > Units of variances = ^0. (JD’OU’Ol lnm’2 Units of proper motion = O'.'OOl Mean error of a single proper motion = ^OVOOl RESIDUAL RESIDUAL X / O I - -IO/X lO/Ji IO/X IE T 246-28703 DR-E. 246-28703 0 7 8 2 - 6 4 2 DIR.-REV.: 3 0 7 8 2 - 6 4 2 DIRECT! i -36 EIUL FO SRU PAE NOS. PLATES SPROUL FROM RESIDUALS I. . ANTD DPNEC OF DEPENDENCE MAGNITUDE FIG. 7. 10.0 Y -COORDINATE X-COORDINATE 11.0 3 0 7 8 2 - 2 4 6 m. 1-39 10.0 • • COORDI E T A IN D R O O -C X Y-COOR DIN ATE m, O . N

62 Direct and reverse measures of the same plate were also compared with one another with the aim of exaggerating any differences which might occur. In Table 2k variances from a linear plate constant adjust­ ment of the direct against reverse measures are quite .small. The addition of magnitude terms produced no significant changes. Residuals from two of the examples are plotted in Figure 8 as a function of magnitude. Plate 3^793 shows a slight trend caused by a few large residuals. The magnitude error for Plate 2k6, on the other hand, is quite clear cut in the y-coordinate here, and for later plate reduc­ tions involving this plate where moderately large magnitude terms^

(approximately 6 microns/magnitude) appear in the adjustment. I;t is \ curious that such a strong trend does not appear in the residuals of the 2^6-28703 reduction (Figure 7). It is also noteworthy that at the time of measurement the centering system in this coordinate spent an abnormally long time searching for the image center.

TABLE- 2k

Variances from Reduction of Direct against Reverse Measurements of a Plate

var(x) var(y)

2k6 + 0.000029mm^ +0.000102mm ^

276 18 23

28703 32 29

38703 25 21 RESIDUALS RESIDUALS -20/X -10 -10 -10 \OjJL jJL jX DIR.-REV.! 38703 I. MGIUE EEDNE F RESIDUALS OF DEPENDENCE MAGNITUDEFI6.8 R M POL LTS 4 AD 3 0 7 8 3 AND 246 PLATES SPROUL FROM • • • . 11.0 X Y - C O O R D I N A T E - X

COORDINATE 12.0 12.0 X v II.0 mv I.RV! 246 DIR.-REV.! • • Y-COO RDINATE X-COORDINATE * 1 •• 12.0

m, On the basis of the above it was felt that any setting bias of the machine could be accounted for as magnitude error, but more likely such centering errors are masked by larger plate errors, so that under these conditions it is satisfactory to measure in one direction only on the

NRI automatic measuring engine. CHAPTER V

THE PROPER MOTION REDUCTIONS

The plate measurements and their reduction to the final proper motions will be described in this chapter. In the course of this some consideration will be given to recent rigorous computer-based reduction schemes, their practical limitations, and possible modifications.

The Observations. The data describing the astrometric observations are given in Table 25. Many of the recent observations were obtained by the writer at the Allegheny and Sproul Observatories. In each case the observatories normal observing and developing practice was followed.

Eastmann Spectrum Analysis 3 plates were used at the Allegheny Observa­ tory since their spectral and speed characteristics closely match the older Seed 30 plates of the first epoch observations.

Plate Measurement and Data Editing. As has been discussed above, all of the observational material for this study has been measured on the Naval Observatory’s automatic measuring engine. The procedure adopted is described in the following paragraphs; The program deck to, control stage positioning for the measurement of the plates was gene­ rated by measuring the ’’deepest" plate from each series. These plates were oriented to an equator of the year 1950 by matching the plate alignment with the positions for NGC 1039 in the system of the FK3

66 TABLE 25

Observational Data - Sproul Plate Material

Plate Time H.A. Exposure Temp Number Date ES.T. (min) nX time Emulsion Filter Observer* 0 p Remarks

174 7 Oct. 93? 01 28 13 E 1 x 55roin I-G K2 P 66 207 21 Oct. 937 00 12 33 E 2 x 8 I-G K2 k 48 208 21 Oct. 937 00 33 12 E 2 x 8 I-G K2 k 48 224 25 Oct. 937 23 40 30 E 2 x 6,6 I-G K2 K 36 225 25 Oct. 937 23 54 16 E 2 x 6 I-G K2 K 36

244 31 Oct. 937 23 22 35 E 2 x 7 I-G K2 RWD 44. 245 31 Oct. 937 23 39 18 E 2 x 7 I-G K2 RWD 43; 246 1 Nov. 937 0 04 7 W 2 x 9 I-G K2 RWD 42 258 4 Nov. 937 23 50 10 W 2 x 6 I-G K2 H/B 37 275 6 Nov. 937 22 40 53 E lx 6 I-G K2 RWD 38

276 6 Nov. 937 22 51 43 E lx 6 I-G K2 RWD 38 3I9 20 Nov. 937 21 36 58 E 2 x 6 I-G K2 RWD 30 320 20 Nov. 937 21 53 32 E 2 x 6 I-G K2 RWD 30 334 23 Nov. 937 21 55 31 E 2 x 5 I-G K2 . k 335 23 Nov, 937 22 09 17 E 2 x 5 I-G K2 - k

3 66 29 Nov. 937 21 46 15 E 2 x 6 I-G K2 K 367 29 Nov. 937 22 04 3 W 2 x 6 I-G K2 K 31 28702 4 Feb. 955 18 03 19 W 2 x 2 I03a-G Wr, 12 Fr 28 28703 4 Feb. 955 18 07 23 w lx M I03a-G Wr.12 Fr 28 38200 26 Oct. 960 00 22 1 E 2 x 1 I03a-G Wr.12 la 44

38201 26 Oct. 960 00 35 12 W 2 x 4 I03a-G Wr.12 la 44 Aperture=12-ln. 38584 14 Dec. 960 20 42 25 E 2 x li I03a-G Wr.12 la 28° 38585 14 Dec. 960 20 59 8 E 2 x 2m40s I03a-G Wr.12 la 28° Aperture=18-in. 38586 14 Dec, 960 21 14 7 W 2 x 2 I03a-G Wr.12 la 28° Aperture=21-in. 38702 10 Jan. §61 19 01 18 E 2 x 3m50s 103a-G Wr.12 la 34 Aperture=15-in. TABLE 25 - Cont.

Plate Time H.A. Exposure Temp Number Date______E.S.T. (Min) nx time Emulsion Filter Observer*___ °.F_____ Remarks

38703 10 Jan. I96I 19 15 4 E 3xl-| 103a-G Wr.12 la 34 T -65 23 Oct. 1961 23 45 •46 E 3 x 1 103a-G Wr.12 la 47 T -67 24 Oct. I96I 00 03 28 E 3 x 1 I03a-G Wr.12 la 46 T-69 24 Oct. 00 33 2 W 3 x 1 I03a-G Wr.12 la 46 T -70 24 Oct. I96I 00 39 8 w 3 x 1 I03a-G Wr.12 la 46

T-74 1 Nov. 1961 23 11 47 E 4 x 3/4 103a-G Wr.12 la 46 T-75 1 Nov. 1961 23 17 41 E 4 x 3/4 103a-G Wr.12 la 46 T-76 1 Nov. I96I 23 33 25 E 4x3/4 103a-G Wr.12 Li 52 T-77 1 Nov. I96I 23 39 19 E 4 x 3/4 103a~G Wr.12 Li 52 T-79 2 Nov. I96I 00 04 7 VI 4 x 3/4 103a-G Wr.12 Li 52

T -88 6 Dec. I96I 20 21 77 E 4 x 3/4 103a-G Wr. 12 Li 42 T -89 6 Dec. 1961 20 58 40 E 4 x 3/4 I03a-G Wr.12 Li 42 T-90 6 Dec. 1961 21 03 35 -E 3x3/4 103a-G Wr.12 Li 42 T-91 6 Dec. I96I 21 14 24 ■E 4 x 3/4 103a-G Wr.12 Li 42 T-92 6 Dec. I96I 21 20 18 E 4 x 3/4 I03a-G Wr.12 Li 42

T -93 6 Dec. I96I 21 42 2 VI 4 x 3/4 103a-G Wr.12 Li 42 T-94 6 Dec. I96I 21 48 6 W 4 x 3/4 I03a-G Wr.12 Li 42

* Observers: B=Virginia Burger; RWD=Roy VI. Delaplaine; Fr=Laurence. W. Fredrick; H=John S. Hall; Ia=Philip A. Ianna; K=Michael S. Koualenco; k=Peter Van DeKamp; Li=Sarah Lee Llppincott

o\ CO TABLE 25 - Cont.

Observational Data - Allegheny Plate Material

Plate Number Date Time H. A. Exposure Emulsion Filter Observer Temp Remarks

7^ 9 Sept 1914 03 35 20E 1 x 30m Seed JO None Schlesinger 50 Aperture-2*/-in. 280 11 Oct. 1914 01 05 37S 1,2 Seed 30 None Hudson — 34-22 2 Oct. 1915 01 09 52S 1 x 30 Seed 30 Esculin Trumpler — 34-23 2 Oct. 1915 01 38 23E 1 x 10 Seed 30 None Trumpler - 364-9 !6 Oct. I9I5 00 32 34-B 1 x 15 Seed 30 None Trumpler 55

369^ 20 Oct. 1915 23 55 85E 1 x 10 Seed 30 None Trumpler 63 10992 3 Nov. I9I7 01 17 81'.*/ 1 x 30. Seed 30 None Trumpler 36 10993 3 Nov. I9I7 01 4-6 HOW 6,1 Seed 30 None Trulpler 36 99364- 11 Feb. I966 17 4-4- 81V/ 1 X 22 Sp.An. 3 None V/agman 4-8 99376 18 Feb. I966 18 25 120W lx 28 Sp.An.3 None I anna 37

99377 18 Feb. I966 18 57 152W 2 x 10 Sp.An. 3 None Ianna 37 99378 20 Feb. I906 18 10 14-6W 1x33 Sp.An. 3 None Ianna 18 99379 20 Feb. I966 18 4-0 I76 W 1x15 Sp.An.3 None Ianna 18 99332 21 Feb. I966 17 4-6 120W 1x25 Sp.An.3 None Ianna 26 99383 21 Feb. I966 18 17 151W 10,3 Sp.An.3 None Ianna 25

ON NO 70 published by Dieckvoss (1955)• All subsequent plates were aligned in a

similar manner and not permitted to deviate from their prescribed posi­

tion by more than 0.3 mm over the extent of the plate. This corres­

ponds to an angular orientation to within 10 arc-min and cannot signi­

ficantly affect the proper motion since the slight error that might be

introduced is of the cosine of the angle.

Rejection of images from measurement was based upon their (x,y)

profiles as exhibited on the two cathode-ray tube displays on the measuring engine. Images that were too weak, larger than the scan area,

or defective were discarded. Other images were assigned a weight of

one or two at the time of measurement depending on their quality, again

adjudged by the image profiles. Rejected images were assigned a weight of zero and their data cards retained in the output deck to

preserve the ordering of these card decks.

Two particular difficulties were encountered with old plates.

About one in ten "was warped and required special efforts in getting

the vacuum hold-down system to maintain the plate securely and flat on

the measuring stage. A few other plates had slightly rippled surfaces •

(four or five "waves” per plate) owing to the low quality glass used

as the emulsion support, but did not produce especially noticeable

focal changes and so were retained for measurement.

It was necessary in many cases to remeasure plates owing to machine

breakdown or instability. To monitor the performance of the engine a

check star was measured periodically. If at any time a repeat measure­

ment of this star differed from its initial setting by more than two

microns the plate was remeasured. 71

Following the measurement of the plates the data cards were collec­ ted (about 16,000 cards) and given a preliminazy manual editing to remove mis-measures and duplicate cards. The cards were then listed on an IBM tabulator and edited once again by hand. Bach data deck was carefully examined for correct ordering of the stars and weight assign­ ment (occurences of zeroes could be verified on two exposure plates since both images vrere not measured if the image set was rejected).

The needed corrections were made.

Rigorous Plate Reduction Methods. For several reasons the usual long-focus astrometric reduction for proper motions is executed with simply a linear plate constant least-squares adjustment, viz. ortho­ gonal coordinates on the two plates i,j are related by

= xj + + + ° y± = yj + dx3 + ey., + f . between matched plate pairs. Occasionally a linear magnitude term may also be included. It is indeed true that these terms are by far the most important and largely remove the undesireable effects, and that more elaborate schemes may entail more computing than is of practical value. However, there is also the danger here of neglecting field errors, expressed as higher order terms in position, magnitude, and perhaps color as well, that may frequently be appreciable (Strand 1958,

Lippincott 1957, Ianna 19&5)• A well known consequence of this is that systematic differences may appear between the plate pairs and between the results from different observatories.

We would like to be able to derive an estimate of the internal 72 velocity in NGC 1039. As remarked in the introduction such estimates

are utterly dependent upon our estimates of the errors in the proper

motions and this is the weakest point in such studies. V/e suggest an

approach designed to eliminate the above difficulties. That is, by

combining all of the plate material into one massive least-squares

adjustment, including the proper motions as unknown parameters, a "best"

solution is found from all of the material simultaneously and statis­

tically valid estimates of the errors in the proper motions follow

directly from the theory of Least Squares.

This approach is inspired by recent work in photogrammetry by

Brown (1958) and in astrometry by Eichhom (i960). It is especially

valuable when there are partially overlapping plates of a region, such

as is common in the astrographic case. Then, with the additional con­

straint that corresponding stars on overlapping plates must have the

same position, one has the greatest leverage for determining many of

the field errors. In general, with positions and proper motions for a

number of reference stars as a set of constraints, the equations of

observation, including appropriate terms to account for field errors,

are formed into a system of normal equations to simultaneously adjust

the plate constants, positions, and proper motions to.their best

values in a least-squares sense.

To find these normal equations we first relate the measured (x,y)

coordinates of the m-th star on the j-th plate at our disposal to the

position that it would ideally have by a polynomial of the form

(16) 73 where the a ’s are the plate constants for the j-th plate, m is a magni­ tude, and c is a measure of the color of the star in question. An equation of this form applies in each coordinate.

Let us choose a set of reference stars by virtue of their appea­ rance in some catalog so that we know their positions at some epoch and their proper motions. The catalog position of the m-th star at some epoch is related to its position at some other epoch by the equation of condition

i m + - l m + fh C17) where for star m, t^ is the difference in time between the epoch in question and that of the catalog position, and 6" is the associated error.

The rectangular coordinates of the reference stars are to be measured along with the non-reference stars on the plates. The measure­ ment of the m-th star on the j-th plate is related to its position at some standard epoch, t b y the relation w

H IE 4kL ^ j ■0 + ? • • (18>

VJe suppose that there are j = 1,...,N plates on which any of the m = 1,...,K stars may or may not appear. "When the star does not appear on the particular plate, there is no contribution from it to the system of equations.

Forming normal equations in the usual manner of a least-squares adjustment procedure and letting all equations have equal weight for the moment, we obtain the following system of equations which may be rather large: x1 jrJ€.mr .cS .) + (N + H ) h ±krs s mJ mJ (19)

j = (n,l,q,p) = (0,0,0,0),...,(A,B,C,D); m =

It is convenient to write these equations in the form

A X = Y (20) inhere the unknowns in the solution vector are ordered as follows: plate constants grouped by plate; unknown positions ordered by star, and proper motions ordered by star, i.e. Then the symmetric matrix of the coefficients has the form

A n ° ... 0C11C12 C 1N 0 **• C21 V-* * A jj •

■ 'KM A = r* t 0 ... 0 (22) C11 ’•°1N Jll D c'.jm :. mm r » -. -CjJjjO n \ i m

Let pj equal the number of plate constants assumed for the j-th plate J in the solution. The submatrices are then (pj x pj) square mat­

rices containing the various suras and cross-products of the plate con­

stant coefficients summed over all the stars on the j-th plate. That

is, these submatrices consist of elements of the form

x y v m c (23) mj mj mj raj m

The 0 ^ are (2x2) matrices with elements

(*'ra raJ ^ (24) ( E j t j + E h th) + where the summations are for the m-th star and extend over all those

plates on which that star occurs. The K and are the weighted sums

of the unity coefficient for the plate and catalog positions of the

m-rth star.

The remaining submatrices, the C^m , and (2 x p.) matrices with J*** J elements 76

Not© that a given submatrix C i s identically zero if the m-th star does not appear on the j-th plate so that many of these matrices may be empty.

The implementation of the method is considered in a later section.

Choice of Plate k'odel. Preliminary to performing the plate re­ ductions we must decide what terms to include in our model for least- squares adjustment. The choice of these plate constants in the prac­ tical case is dictated by the instruments used and the characteristics of the observational material at hand. We do not wish to weaken the

solution by including terms of no significance; neither must we neglect any effective field errors.

From earlier consideration, for the Sproul data, we expect linear magnitude and coma (magnitude x position) terms to be required in addition to the usual linear geometrical terms. We should also con­

sider higher-order geometrical terms due to plate tilt and color, al­

though these are generally of little importance in long-focus astro­ metry. For the Allegheny material we may be able to discard the coma

term.

To these ends a number of trial plate reductions were carried out

in which plates with both a small and a large time interval between them were compared to one another. The Sproul results in Table 26 show how

the plate variances for a variety of plate combinations change as a

function of the assumed model. We note the decrease in sample variance with the addition of linear magnitude and coma terms, and especially O that an m term seems to be required at times. Higher order magnitude

terms were not helpful. TABLE 26 77

Sproul Plate Variances For Various Plate Constant Models

Unit = 0.0000001 mm2

366-244 366-244 To9-T93 T67 -TS9 n-111 n=lll Model n=85 n-137 2 exposures 1 exposure ax + by + c = L X 84 170 160 326 Y 50 156 93 129 L + m X 64 I60 101 207 Y 41 101 94 130

L + m + mx X 64 143 102 209 Y 39 76 93 130 L + m + mx + m2 X 62 136 83 187 Y 37 75 92 130 L + m + m^ X 61 154 84 188 Y 39 97 93 130

L + mx X 85 159 158 323 Y 49 124 92 130 78 The gains in reduced plate variances from added magnitude terms in the adjustment are less clear in the Allegheny case (Table 27). For one thing the plate variances are larger, especially in the early-late pair comparison where the increase is due to the proper motions of the reference stars. The addition of a linear magnitude term brings some reduction in several cases as does a second-order magnitude term. The magnitude-position term is ineffectual. We provisionally accept the two magnitude terms in addition to the linear geometrical terms for the

Allegheny plate adjustment model.

The possibility of the presence of color terms must be considered in view of the differences between the Sproul and Allegheny systems.

The need for a color correction in parallax reductions at the Sproul

Observatory for observations made before 1937 has been noted (Lippin- cott 1957). There were indications of a return toward the earlier system after 19^9 when the lens was again removed. We have plotted residuals from the linear plate constant reductions against color and noted no dependence. Similarly for the Allegheny reductions no re­ sidual color dependence was evident. It, however, seemed a wise pre­ caution to retain at least a linear color term in the adjustment model for the overall least-squares reduction. Such a term was not included in the plate-pair reductions to be considered later.

Plate tilt is a second-order geometrical effect in stellar posi­ tions arising from a plate not being normal to the optical axis and introduces terms of the form

x = (px + qy) x (2 6 ) y = (px + qy) y 79 TABLE 2? Allegheny Plate Variances For Various Plate Constant Models

Unit = 0.0000001 mm2

IO992-3694 IO992-99382 99382-99378 Model n=45 n»45 n=9l ax + by + c = L X 319 947 521 Y 296 1350 172

L + m X 12? 964 491 Y 297 1325 147

L + m + mx X I3I 977 494 Y 290 1354 149 L + m + mx + m 2. X 127 988 500 Y 279 1218 143

L + m + m2 X 123 968 495 Y 288 1185 142

L + mx X 327 967 523 Y 296 1363 173 80 where p and q are the coordinates on the plate of the base of the per­ pendicular dropped from the center of the objective and x and y are rectangular coordinates on the plates expressed in radians. ?or the

Sproul telescope p and q are 7 mm and H m m respectively leading to positional errors less than 0.7 microns or 0.01 arc-seconds. These numbers for the Thaw telescope were roughly 1 and 1*5 inches for p and q at the time of the observations and imply the possibility of posi­ tional errors on the order of -2 microns or 0.03 arc-seconds. The Thaw chronology (Table 18) shows that the base has been in a similar location over most years of operation, and hence we do not expect the proper motions to be affected.

Our plate constant models then take the form, for the Sproul material, of

X = aX + bY + c + dniy + + f^yX

Y = aY + bY + c» + d'mv + e ’n^2 + f’rn^Y . (27)

The magnitude-position- term is excluded for the Allegheny reductions; a linear color term is included in the overall plate adjustment.

Formation of Normal Equations for the Full Solution. In prepara­ tion for processing the combined data, a card-image magnetic tape of the manually edited card data was made, and a second editing was per­ formed on the IBK 709^ at The Ohio State University Computer Center.

The data were examined again for the correct ordering of the measures and correct weighting of multi-exposure measurements. A position measurement that failed the applied tests was assigned a weight of zero. Gaps in the measuring record x-rere filled with zero weight dummy 81 measures to maintain the order, blocks of missing images having been skipped during measurement, The edited data were written on a second tape with ,each exposure treated as a separate plate.

V’e possess some pre-knowledge of the structure of the normal equa­ tion coefficient matrix (cf. eqn. 22) that can be used to reduce com­ puter storage requirements. That is, we know where blocks of non-zero elements occur in the array, e.g., for n plate constants, n rows of the submatrix from the j-th plate begin at column index n x j -

(n-1) and continue for n elements, and we can compute the appropriate indices as needed obviating the storage of "zero'-' elements.

Anticipating the requirement of a long time for the formation of the normal equations, the program was written to allow stopping the computation on operator command after any plate’s contribution had been added and re-starting the computation from the breakpoint.

The weights applied in forming the normal equations were deter­ mined from two items. First the mean error in the measured separation of exposures from those plates possessing more than one was taken as a measure of the overall quality of that particular plate. Nominal weights were assigned those plates having only one exposure. The pro­ duct of this number divided into a constant with the weight (one or two) assigned at the time of measurement became the \\reight used for the particular star.

To apply the proposed method a set of reference stars at more than one epoch are needed. These were taken from the list of positions and proper motions given by Dieckvoss (1955)• The second epoch catalog positions were simulated by applying 50 years of proper motion to the 82 given catalog (epoch 1950)•

Before computing the full set of normal equations, sample runs on contrived test cases and a sample of the data were carried out. The latter runs had the purpose of checking the scaling of the unknowns to maintain the diagonal elements of the array as the dominant element in the given row.(or column). To aid in this task the ratio of the sum of the absolute values of off-diagonal elements to the diagonal element was computed for each row. Considerable experimenting was done to optimize this diagonal dominance, however, without complete success owing to the wide range in values of the numbers used and the varying information composition of different plates.

We could now compute from a single reading pass through the data tape the non-zero array elements of the Aj^, Cjm , submatrices

(eqns. 23, 24 and 25), and the constant vector Y. The submat- . rices are then left to find.

The arrangement of the elements in the submatrices precludes straightforward calculation since to do so would require reading the data one star at a time from each plate (or 800 readings of the data tape at five minutes per pass). It would be equally time consuming to re-arrange the data tape into a convenient form. Since the matrix is symmetrical the best procedure seemed to be to obtain the required elements of C 1^ from the transposed array elements Cjm which ordinarily would be an elementary operation. In this case however, owing to the magnitude' of the array, it is a non-trivial sort problem requiring 45 minutes of 7094 time and four tape drives to accomplish.

When the transpose has been formed, the time submatrices, Dm , and appropriate lower portion of the constant vector are added so that we have now the full set of normal equations, arranged by row, on two magnetic tapos.

Solution of I-Jormal Equations from Complete Data Set, The edited source tape carried data for 839 stars. It was decided, however, to limit the sample to 680 stars in order to somewhat reduce the number of equations to be solved. With eight plate constants, 107 "plates", and

1360 position and proper motions unknown for the stars, we nave a system of 2216 equations in each coordinate to solve.

The inverse of the coefficient matrix of the normal equations is necessary for the estimation of the errors. It was decided to solve the equations separately as well as to invert the coefficient matrix to provide a check on the solution which might be obtained from the inverse.

The size of the system of equations precludes the accurate solu­ tion by direct methods. A convenient iterative scheme for solving the equations is the Gauss-Seidel method which has the advantage of using the latest approximation of the individual components in the solution vector to calculate the remaining components and also of taking some advantage of the sparseness of the equations. The Gauss-Seidel process will converge provided the coefficient matrix'is positive-definite, as is the case for the normal equation coefficient array, so that con­ vergence is assured. A disadvantage is that "many thousands of itera­ tions are often needed for the iterative procedure to converge to a good approximation to the solution" (Brown 19&5)•

Young (195^0 developed an effective way to accelerate the convergence of the Gauss-Seidel scheme. If is the (k + l)-st approximation to the solution vector in the Gauss-Seidel, then the

(k + l)-st approximation in the method of Successive Qverrolaxation is

xk+1 = xk + v (xk'hl - xk ) (28) where w is some appropriately chosen acceleration parameter. In a suitable computational form

r - =4 + + v <*»

The optimum acceleration parameter can be found from a knowledge of the eigenvalues of the coefficient matrix (Varga 1962), or it can be app­ roximated by examining the convergence of the. solution with w = 1

(Young 1962).

Convergence may also be improved by restricting the iteration to related groups of components. This is the method of block successive overrelaxation.

Suitable programs were written and tested that applied these methods to the normal equation coefficient array as stored on two magnetic tapes. Critical parts of the computation are carried out using double-precision arithmetic. A single iteration through the 2216 equations required very close to five minutes of machine computation.

Several schemes were considered for the inversion of the coeffi­ cient matrix including iterative procedures for improving a first

"guess” at the inverse. Mr. Edwin H. Lassettre of The Ohio State

University Computer Center wrote a machine language program to perform a triangular factorization and matrix inversion, but it soon became clear that it was completely impractical to even attempt the 2216 x

2216 array with the available facilities. Cn this basis it was decided, since without the inverse no accurate estimation of the errors of the unknowns is possible, to re-attack the problem from the more conventional direction of comparing temporally separated pairs of plates.

At this point, after considerable effort, some 50 iterations of the (x,y) systems of equations had reduced the sum of the squares of Q h the solution residuals from 107 to 10 . The slow covergence has several causes. A sufficient condition for the convergence of the Gauss-

Seidel method is that

1

Owing to the scaling difficulties this criterion is violated over the major portion of these equations. Furthermore blocks of array elements for different plates are very similar in character implying that the equations may be very nearly linearly dependent, and hence are ill- conditioned. This is commonly true of normal equations (Taussky 1950) and means that the solution is very sensitive to small changes in values of the coefficients and may not be accurately obtainable.

A suitable acceleration parameter was not found and an incorrect choice quickly produces divergence of the solution. The equations were therefore solved with w = 1, fair convergence being obtained only by carefully restricting the blocks in the iteration at a given time.

A related problem is that the amount of information available for the determination of the unknowns, or the degree to which the para­ meters are overdetermined, is quite diluted by the method. The ratio 86 of information to unknowns was about 6:1. This dispersion of the infor­ mation is a weak point in the procedure. The situation can be improved only by having more plates while reducing the number of stars.

The possible value of this approach suggests that continuing effort should be made toward its successful application to these kinds of problems. The computers with large storage capacity currently be­ coming available will greatly aid the implementation of the inversion of matrices of high order. It may also be that such things as the use of orthogonal polynomials in the plate models could help the stability and convergence of solutions to the equations and ease the computation of an inverse. Finally, it is also possible to accurately account for plate errors,such as magnitude-induced positional distortions, through the utilization of coarse-wire objective gratings quite independently, so that these terms may be eliminated from the plate adjustments.

Plate-Fair Reductions. The final proper motions are derived from a comparison between the pairs of plates given in Table 28 for the

Sproul and Table 29 for the Allegheny material. The pairing was based on similarity of hour angle and exposure time. The reductions treat each exposure as a separate plate rather than averaging the exposure sets on a plate.

The choice of reference stars vras based upon the proper motions of the stars in NGC 1039 given by Dieckvoss (1955)• An attempt was made to include stars with a range in magnitude and with proper motions as small as possible. Identifying information and Dieckvoss proper motions are given for these in Tables 30 ^nd 31 Ton Sproul and

Allegheny reductions respectively. The different characteristics of TABLE 23 8? \ Sproul Plate-Pairs

Early 1*0 * AO . lie cent N o . Ho u r A n g l e T i m e P l a t e S tars E x p o s u r e s P l a t e Stars D i f f e r e n c e I n terval

174 177 1 38702 173 jjinln 23.262 yrs 207 109 2 T65 126 13 24.008 208 2 T93 9? 14 24 . 1 2 9 224 116 2 33535 132 22 23.037 225 107 2 T79 93 23 24.019

244 1 2 4 2 T92 127 11 24 . 0 9 9 245 117 2 38703 114 14 23.195 246 117 2 3 8 5 3 6 144 4 23.121 253 116 1 T70 121 2 23.967 275 120 1 T89 148 13 24.082

276 120 1 T 90 102 8 24.082 319 79 1 T'74 77 11 23.948 2 320 99 T 91 90 8s 2 4 . 0 4 4 334 74 1 •178 74 0 23.940 335 151 2 33534 152 3 23.053

360 136 2 T 67 150 13 23.898 367 105 2 28702 156 16 23.115

T A B L E 29

Alls gheny Plate-Pairs

E a r l y No. N o . Re c e n t No. H o u r A n g l e Ti m e Plate Stars Eiaoosures Plate Stars D i f f e r e n c e I n t e r v a l

74 290 1 9 9 3 6 4 359 lO i m i n 5 1 . 4 2 4 yrs 230 151 1 99376 62 157 51.357 3423 236 1 99379 281 199 50.387 3649 126 1 99377 81 184 50.344 3694 368 1 99373 382 61 50.336

10992 596 1 99382 572 39 4S.302 10993 200 1 99383 250 40 48.301 TABLE 30 88 Sproul Reference Stare in NGC 1039

Proper Motion leas. DiccR. *r/*. Y \ r No. No. A. Y 0.001 ”/yr mv 3-V 134 101 _53nn * ATiEl -1 - 9 11.74 +1.36 130 131 _A3 -37 +2 -10 11.43 +0.36 200 143 "38 -64 -12 10.21 +1.72 269 166 - -23 -21 +2 -21 10.04 -0.03 270 163 -23 -21 0 -18 10.95 +0.04 S * 231 I 93 -19 -05 +3 -7 10.32 +1.59 286 135 -22 -46 +10 -10 12.93 +0.36 305 191 -19 +10 +5 0 9.94 +1.16 312 170 -27 TJ>0 -1 -7 11.23 +1.27 313 173 -24 +37 0 -14 10.66 +1.32 320.1 169 -27 +40 -12 -4 11.93 +0.61 332 21? -12 +59 -2 -14 10.02 +0.36 346 260 - 2 +42 -2 -14 7.92 +1.74 3^9 220 -12 +42 -4 -10 10.60 +0.31 37? 222 -11 -16 +1 -9 11.21 +1.09 396 200 -16 -3? +3 -10 8.43 +0.05 437 253 - 3 -22 -I -12 11.13 +1.05 493 276 + 2 -52 +10 -13 11.24 +1.26 501 302 - 7 -?0 +7 -2 10.30 +0.39 542 315 +10 -13 _2 -13 11.45 +0.'38

557 301 + 7 0 -19 10.01 +1.82 534 331 +14 -35 +3 -p 10.96 +0.95 613 3 46 +13 +35 +5 -13 10.30 +0.05 621 353 +21 +24 +1 -10 10.52 -0 .0 4 655 376 +27 -61 +5 - 1? 10.62 -0 .1 4

on o 692 s ( J +27 -16 -7 -9 11.55 +0.19 330 +28 -20 +1 -14 10.81 -0 .2 4 693 ** 722 410 +37 -19 +9 -p 12.52 +0.43 735 393 +35 +20 -3 -17 11.25 +0.30 741 404 +35 +43 +2 -6 8.22 +1.63

754 423 +44 +31 0 -15 10.91 -0.02 773 421 +42 -34 +5 -9 11.99 +0.95 782 417 +41 -40 -5 -11 12.30 +O.96 810 430 +46 +1 0 -5 10.63 +0.53 841 449 +53 +2 +2 -13 11.54 +0.41 910 478 +64 -43 -5 -10 10.24 +2.08 918 474 +63 -67 -1 -8 10.81 +0.42 89 TA3L2 31

Allegheny Reference 3tars in NGC 1039 Proper Notion Me a s . Y Dieck. X m v No. No. y 0 . 0 0 1 "/fyr B-V

115 -75 -25 12.53 +0.80 134 101 -68 +10 -1 -9 11.74 +1.36 180 131 -55 -42 +2 -10 11.43 + 0.36 I99 122 -59 -84 —- 12.14 +1.05 212 144 -50 -18 -2 -15 12.68 +0.44

248 143 -50 +64 12.15 + 1.68 257 161 -40 +27 +6 -18 11.9^ +0.47 286 185 -27 -55 +10 -10 11.93 +0.36 312 170 -33 +52 -1 -7 11.28 +1.27 320.1 169 -34 +56 -12 -4 11.93 + 0.61

3 45 262 - 3 +65 m m 12.00 +1.38 354 208 -13 +45 +6 -20 11.70 +0.74 377 222 -14 -15 +1 -9 11.21 +1.09 427 249 - 6 -31 - 12.65 +1.54 438 234 -10 +12 - - 12.24 + O .67

437 258 - J -23 -1 -12 11.13 +1.05 493 276 + 3 -62 +10 -13 11.24 + 1.26 542 315 +14 +28 -2 -13 11.45 + 0.38 584 331 +18 -41 +3 -5 10.96 +0.95 640 3^3 +23 -40 +6 -11 10.97' + 1.01

672 363 +30 +15 +1 -19 11.45 +0.41 o73 366 +32 T-rO +1 -12 12.31 +0.33 692 373 +35 -16 -7. -9 11.55 +0.19 700 387 +41 -50 +7 -19 11.89 + 0.36 705 409 +48 -17 — - 12.81 +0.87

722 410 +49 -20 +9 -5 12.52 +0.43 735 398 +46 +32 -3 -17 11.25 + 0.30 754 423 +57 +46 0 -15 10.91 - 0.02 777 416 +54 -40 — 13.32 + 1.-05 77 3 421 +56 -40 +5 -9 11.09 +0.95

782 417 +54 -47 -5 -11 12.36 + 0.96 805 431 +60 -10 +4 -20 11.76 + 0.29 833 446 +69 +50 — — 12.54 + 0.16 841 449 +69 + 8 +2 -13 11.54 +0.41 910 478 +84 -50 -5 -10 10.24 + 2.08 TABLE 31 - Cont 90

Proper Motion Me as . Died-:. \ r Y m V V No. No. X u . oTooi »/yr. B-V

<1 1*1 39 -91 +1*9 13.10 + 0.72 63 51 -88 -22 — - 12.92 +0 . 1*0 92 70 -80 +63 - - 11.66 +1.97 230 123 -58 +32 - - 12.1*1* +0.80 357 - -13 +35 - - 12.79 +0.95

929 1*91 +93 -61* _ • 12.87 +0.33 91*2 1*88 +91 + 6 +3 -18 11.52 + 0 .1*0 967 - +98 +20 -- 13.58 + 0.36 988 - +103 +58 -- 12.1*2 +0.01* 91 the plate material prevented the adoption of tho same system for each observatory.

Plate models given above (eqn 2?) were used in the plate adjust­ ments. An error, e^, was computed for each proper motion in each plate- pair reduction from the errors in the least-squares adjustment para­ meters in an analagous manner as earlier (eqn 1*0. Subsequently, these were applied as weights in the sense

w± = 10"6/ei2 (30) for combining the individual values of the proper motions by

(31)

Mean internal errors follow from

Errors for the averaged proper motions from each observatory were also computed as a weighted mean-sauare combination of the least-squares error estimates. These are invariably considerably larger than the internal errors. Those stars having appeared on but one or two plate pairs were assigned errors in proportion to the mean error of a single proper motion plate-pair inferred from multiple occurences for Sproul or Allegheny. See Table 32. Both internal and least-squares error estimates are included in the full listing of the results (Appendix).

The proper motions for the reference stars may be computed since an individual star residual in the plate-pair solutions represents the deviation of that star’s motion from the mean of the reference 92

TABLE 32

Average Internal Lean Error of a Proper Lotion for a Single Plate-Pair

Observatory unit = 0.0001 arc-sec

X y

Allegheny m.e. (n=5) — +6.4 +0,4 +5.7 +0.3

m . e. (n=l) = +14 +13

Sproul m.e. (n=28) = +5.9 +0.3 +5.1 +0.2

m.e. (n=l) = +31 +27 background plus any accidental errors present. These residuals are converted to motions by the application of the appropriate scale factor and then included with the other results.

The proper motions from the 29 Sproul plate-pairs and six

Allegheny pairs were averaged among themselves to yield two sets of motions. The Sproul plates, invariably having essentially the same reference background, appeared free from internal systematic differ­ ences and were averaged directly. Such is not true for the Allegheny material and a systematic correction of -0.0006 arc-seconds in the x and 0.000? arc-seconds in the y proper motions appeared necessary in the 364-9-9937? pair before averaging. Further discussion of the accuracy of the motions and derivations of final values is deferred to the next chapter. CHAPTER VI

ANALYSIS CP THE FR0F2R HOTIGNS

Before deriving and discussing the final proper motions from the

two observatories, a comparison of the accuracy of the motions and an

examination of the data for possible systematic differences is

necessary.

Comparison of Sproul, Allegheny, and Dieckvoss Proper Kotions.

First taking differences between the two sets of proper motion data we

find that on the average the Allegheny proper motions were O'.'OOIO

smaller in x and O'.'OOl? larger in y than the Sproul proper motions,

a not unexpected difference attributable to differences in reference

frame. The Allegheny motions were corrected to agree with the Sproul

values, since the Sproul proper motions can be directly related to the

Dieckvoss F K3 motions.

The possibility of color effects may again be considered with

regard to the resultant proper motions. To investigate this difference between the proper motions in the two systems, residuals in the sense

(Sproul - Allegheny) were plotted against color index in Figure 9 for

the x-components and in Figure 10 for the y-components. There is no

systematic effect which is a function of color in evidence.

Plots of the two sets of proper motions against one another in

x and y did not clearly indicate a simple linear equivalence, so the SPROUl - RLLECHENT PROPER MOTION IN X * (lOM 1.000 L i i I i -6. 250 -2 500 1.250 2.000 1.625 5.000 1.250 8.750 0.B75 0.500 12.500 0.125 18.250 -0.250 -0.625 .000 - 0.625 Fig.9 Proper Motion Differences vs. Color in X in Color vs.Differences Motion Proper Fig.9 Ha «!• - V - B 1.625 CM CD 9^ o in ta tn o 000 O W W 95

o o w X It

-1.000 -0.625 -0.250 0.125 0.500 0.875 1.250 1.625 7.000 — 1-- I I r — i-- !-- T

K ■ K k M m M » a K K ,a o J o .

o Q O

£Ll_i ° o QO _ cv. O O C C I CM Q_

Q a:

co CO Q_CC 00 C3 a

1.000 ■0.625 0.250 0.500 0.875 8 - V

Fie. 10 Proper Motion Differences vs. Color in Y (Sproul-Allegheny) differences were next plotted against their respec­ tive coordinates (Figure 11 and Figure 12). In the y-coordinate there is a strong effect which resembles a scale difference. There is some, indication of a non-random effect in the x-coordinate also.

Residual magnitude effects, telescopic scale changes, measuring engine screw differences, plate tilt, differential refraction, and orientation errors were all eliminated as likely causes of the systema­ tic effect. The next possibility to be considered was that it origina­ ted in the reference background. Cne Allegheny plate-pair (10992-

99382) was re-reduced by only those reference stars in common with the

Sproul set. The result. Figure 13, was a considerably reduced functional dependence of the differences in the proper motions of the y-coordinate. In particular a star with quite a large proper motion in y was noticed in the Allegheny reference star set. It would appear that the small distortion of the reference frame results from the different sets of reference stars. Since the effect is not too large

and appears linear in y, we try afirst order correction of the form

X = ax + by + c

Y « a'y + b'x + c»

finding the parameters in each coordinate by Least Squares. We give

the resulting fitting constants and their ratio to their error in

Table 33* The necessary corrections were subsequently applied to the

Allegheny motions.

After adding the linear corrections to the Allegheny motions the

differences become random but remain rather large relative to the 97

o o « *

HOO.OOO 425.000 450.000 H75.0Q0 500.000 515.000 550.000 575.000 COO. 000

CNJ C J CD

O m,o csi

,00

I m

ino Csi C4 o

11or I o O oj 0C ‘ a.

CSI CO

mo. ooo 475.000 500.000 52 J. 000 550.000 575.000 600.000 ALLEGHENY X-G33RDINATE

Fig. 11 Proper Motion Differences in X vs. X 98

o wK

400.000 425.000 450.000 475.000 500.000 525.000 550.000 575.0L0 600.000 i I i n i ' 1 i i

ft » » ft * »

ft f i - ft * ft » ft

h ** n ac o ft Q- 1 * CO^ ft Q *» * * * - * I ft » s ~z. » ft ft * cr § ■ * » * " * L^Cvi * ft * »

*

■ ft

(I. CI o riQ-° OC ' Q_ * . -8.000 -6.000 -4.000 -2.C0C C.000 2.0GC 4.CC0

jJ!______I______I______I______I______L 400.000 42J . 000 450.000 47S.OOO 500.000 S2r.000 55C.OOO S7S.OOO 600.000 ALLEGHENY Y-COORDINATE

Fig. 12 Proper Motion Differences in I vs. Y Proper Motion Differences (Sproul - Allegheny) -o':o2o -CvO'tO J- 0V020 +O'.’Q P0 -O'.'OoO o': o +• -80 i. 3 oprsn f eut fo Dfeet eeec Backrounds Reference Different from Results Comparison of 13 Fig. o + •70 + o -60 o m n eeec stars common reference dpe rfrne frame reference adopted •20 JL 0 I ■V +

+ +20 +i(0 6 Y-coordinate(mm) +60 _L±_ o vO 100

TABLE 33

Linear Correction Constants to Adjust Allegheny to Sproul Proper Motions

Parameter Ratio of Parameter/Error

a = -4.144 x 10 , 4.31 b = -7.548 x 10"6 1.90 c = 2.575 x 10’2 4.12

a ’= 6.569 x 10""-? 9.37 b'= 3-201 x 10"6 1.40 c ’— -3.553 x 10”2 6.82

indicated internal errors, as small as O'J0004/a. in a proper motion.

The root-mean-square difference between the Allegheny and Sproul motions is about +0’.’002/a. A comparison with the stars in common with

the Dieckvoss (1955) proper motion list gives only slightly greater disagreement between the different results. It seems clear that the errors in the proper motions computed from the propagation of the errors in the least-squares adjustment parameters represent the true accuracy of the results. Because of the homogeneity of the individual

proper motion materials, i.e. similar relative positions, reference

frames, and plate constants between plate pairs, internal agreement is quite good. Nevertheless, linear distortions from the peculiar motions of the reference stars and the projected errors from the fitting

parameters show up in a comparison of results when different adjustment models and reference frames have been used. Since all of these effects

cannot be simultaneously removed from the two sets of proper motions, we must accept the results with the errors as given by the least- 101 squares fit.

We can now combine the two sets of proper motions using the relation

n _ wl M l +w2U 2 W 1 + w2 inhere w = g 'q’I&x ' °"0 is an arbitrary constant. The resultant error of the combined values is ,2 . / _ \2 n 4 (IWw^i oO"-il)J +1- IWnO'oJ (w2

The Appendix lists the final proper motions, the corresponding number in the Dieckvoss (1955) list where applicable, relative positions in millimeters at the Allegheny scale, apparent visual magnitude, B-V color indexes, the number of times, K, that a given star appeared on a plate-pair, and finally the probability of cluster membership as determined below.

Reduction to Absolute I-otions. The proper motions for the

NGC 1039 stars given by Dieckvoss (1955) a^d used as reference stars in this study are in the system of the FK3 for equator and spoch of

1950* These stars were used to reduce the relative motions in this study to the FK3 system by ascertaining the differences between the two sets of proper motions and applying the corrections given in

Table 33* Systematic differences between proper motions in the FK3 and FKU- systems can be interpolated from tables given in the FK4

Catalog (Fricke and Kopff 19^3)* These (FK3-FK4) corrections amount to -0.0012 ”/yr in R.A. and +0.000^ u/yr in Decl. They have not 102

TABLE y\

Reduction of Relative Proper Motions to the System of the FX3

X Y

Sproul 0'J0009 -O'JOllO

Allegheny O’J 0027 -O’J 0120

been applied to the individual motions at this time, but are applied later to the mean motion of the cluster.

Cluster Membership. As long as errors remain in the proper motions a clear-cut segregation of a stellar group from the background field is not possible by astrometric means alone. Furthermore, one cannot exclude on the basis of motions alone those field stars which chance to match the motion of the cluster. Then the best that one can hope to do is to derive some estimate of the probability that a given star may be a member of the stellar aggregation.

We follow the scheme developed by Vasilevskis (1958) for deriving the probability of membership for each star.

A dispersion in the proper motions of the cluster stars is expected as a result of the errors of their determination and the internal velocity dispersion of the cluster. The field star proper motions show a spread owing to observational errors, secular parallactic motion, and their own peculiar motions. They should there­ fore exhibit a general trend in the direction of the galactic plane and the solar apex.

We plot in Figures 14, 15, and 1 6 , the Sproul, Allegheny, and 103

combined proper motions. Our expectations as to the dispersions

in the motions appear confirmed. If we represent this dispersion by a

bivariate normal frequency function with axes (u,v) aligned to follow

the trend in the motions, the probability of a star being a member of

the cluster is N F (u.v) _____c c ______P “ N F (u.v) + N_,F_(u.v) c c F F

where Fc and Fp are relative bivariate normal frequency functions

and N q and Np are the numbers of cluster and field stars present.

The proper motions px, p were transformed into the new co­

ordinates (u,v) by

u = p cos 0 - ll sin 0 'y v = p sin 0 - p cos 0 *y the angle 9 being chosen from a number of values assumed by inspection of the proper motion diagrams to show the best resultion between the two marginal frequency distributions. These marginal distributions were then derived at intervals of O'iOOl in each coordinate.

Star counts indicated an Nc=260 and Np=500 for the combined material. Dispersions of +0’i002 in each coordinate for the cluster distribution and (+0'.1007, + 01.,005) in (u,v) for the field stars gave the best fits to the marginal frequency distributions. Since some stars have a considerably larger error than others and thus might be erroneously excluded from cluster membership on the basis of their motion and the above dispersions, their errors were assumed for the cluster frequency dispersion in these cases. The resulting member­ ship probabilities are listed in the Appendix. t

.050 -0.035 - 0.020 -0.005 0.010 0.0?5 0.055 0.070

CD m toa> D O O

H* in to - fM o-j S a o >-*■ ID -p- Q Mr) o 0 “ o •—< o o *8 I— o 3; 0 c+ H* E g O C L O 3 D , - c CC “ a CL M- p> TO CM z 3 1 O ui XI 3 O 3 t—1 a 0 c+ !-«• O 3 QD cn Oin O

-0.050 ■0.035 - 0.020 0.005 0.010 0.025 0.070 SPROUL ANNUAL PROPER MOTION ( R. A. ) -n [150 -0.033 -0. 025 -n.ni3 -0.000 0.012 0.025 0.038 0.050 ~r r r f ~ T f

*> mra 6 to C-iin in a. .aCM LTl o UJ T) a 3 o m *8 Z?" ^ O o o s: h- o o c+ M* s O 3 clrr- oCi * r v «*v IS ll; C 2 J c a Q. ^ > W J -'* H" D ” ** . * > J M O CC CL cm ’' ' V C ' , . 3to 3 C L cm * * CSJ ~3 n o I 2 ^ s'*7 JO: i t—1> a H1 CD z cm U_! m IT 3" X JM C“4 CD O 3 o = *< Lu O S o C+ H- *n0 O a 3cn

o .1__ ...i______l __ _ -_i______L - - V-n -0.050 -o.o3e -0.025 -0.013 -0.000 0.012 0.025 0.033 6.050 ALLEGHENY ANNUAL PR0FER MOTION ( R. A. Y 106 * -- 1 ----- 1 ^++ + + 4 ----- 1 ■P ----- 1 -•v-i*:;-.v4v-;ry + -•v-i*:;-.v4v-;ry i ----- 1 -s=P ' , , r + i "hr ~'r ^ TT'fe1® # + + ----- 1 -O'J 02 -O'J O'.'OO +0'J02 PROPER MOTION IN X ----- ProperMotionMotions Combined Diagram - _5 1:02 Fig. -OW - -- ovoo -- - - o -- +0 ,J02 --

PROPER MOTION IN Y 107

Cluster Color Magnitude Diagram and Distance Modulus. Magnitudes from the previous photometry may be plotted for those stars with a high probability of cluster membership to form a color-magnitude diagram for the cluster. This is given in Fig. 17 for stars whose probability of membership is greater than 0.8. Error bars representing the accuracy of the magnitudes and colors from the photographic photometry are also given in the figure. The relatively low accuracy in the magnitudes is reflected in the scatter for the fainter magnitudes. We note the occurrence of a number of stars which are probably not cluster members even though they satisfy our proper motion criteria. The color- magnitude diagram resembles a moderately young, Pleiades-like open cluster with the earliest stars perhaps somewhat evolved away from the zero-age main sequence.

A number of investigators in the previously-cited references to photometry in the region of NGC 1039 have derived a distance modulus for the cluster. The data is also available here for this.

Information for the brighter non-peculiar stars in the cluster is summarized in Table 35* The membership probabilities are from the proper motions; the color excess, CE, is based upon Johnson's (1963) intrinsic UBV colors for the MK spectral types listed. The mean color excess (leaving out the eleventh star in the table, BD + 42° 615) is

+0.08 +0.02 in agreement with Johnson's (195*0 value of +0.09.

Adopting 3*0 as the ratio of total-to-selective absorption, a fit of the zero-age main sequence around the region of apparent visual 108

KGC 1039

0

0

10.0

0

12.0

0

r

0.0 +1.0 . +2.0 B-V

Fig. 17 Color-Ks.gnit.ude Array, NGC 1039' 109

magnitude 12.0 suggests a distance modulus of +8.3 magnitudes. Johnson

and Iriarte (1958) find a distance modulus of +8.2 +0.3 magnitudes for

NGC 1039 whereas Becker and Stock (1958) give +8.15.

TABLE 35

Color Excess of Brighter Members of NGC 1039

Meas. Membership No. B.D. Sp. Type CE Probability

396 +1*1° 511* B9V +0.11 -

1*37 +42 586 B9V .06 .87

473 + 589 B9V .07 .82

517 591 B8V .03 -

558 596 B9.5V .09 .87

54-0 597 A0V .05 .71 00

586 601 B8V .12 .

592 602 AOV .05 .87

68 7 607 38V .10 -

808 612 AOV .06 .81

81*6 615 B9V .04 .00

Space Motion of NGC 1039. Taking those stars for which the probability of cluster membership is greater than 0.8, the mean proper motion of the cluster is found to be

H = +0.0031 +0.0003 "/yr X ~ H = -0.0139 +0.0002 "/yr y

from 160 stars appearing on more than one plate-pair. As comparison 110

Dieckvoss (1955) found values of +0.003 "/yr an8 -0.018 "/yr for the mean motion of the cluster in R.A. and Decl. With the corrections to the system of the FK4 given in Table 3^ these proper motions become

p. = +0.0043 "/yr

li = -0.01*0 "/yr

It is of interest to compute the galactic components of the motion of NGC 1039. In transforming the proper motion components into veloci- cities we assume a distance modulus of 8.2 magnitudes or a parallax of

+0'J0023 which corresponds to a distance of *440 parsecs. On the basis of proper motions, apparent magnitudes, and spectral types it appears likely that seven of the probably constant velocity stars from Table 6 are cluster members, and hence the radial velocity of the cluster be­ comes -12 km/sec. Then the equatorial rectangular velocity components

(Trumpler and Weaver 1953) are I ) ^-si na -cos a sin 5 cos a cos 5 a + 4.03

cos a -sina cos& sin a sin& 5 +13.86

0 cos S sin 8 v -29.79 \ / These may be transferred into galactic velocity components by the relation (Murray 1961)

m\ /-0.06699 -0.87276 -0.4835*4 \ I x\ /+ 2,0*A

v = +0.49273 -0.45034 +0.74459 y -26.44

w 1-0.86760 . -O.I8838 +0.46020 z - 19.82 \

The velocity components, U, V, V/ referred to the local standard of rest, where U is the direction of the galactic center, and V is in the direction of galactic rotation, and W is in the direction of the Ill galactic pole, then follow from

U = u - UQ

V = u - V0

W = w - WQ where Uq , Vq, W q , are the components of the basic solar motion with respect to the local standard of rest. If we adopt -9 km/sec,

11 km/sec and 6 km/sec for the basic solar motion components (Vyssotsky and Janssen 1951) respectively we find for NGC 1039

U = +11 km/sec

V = -37 km/sec

W = -26 km/sec

These (U,V) components link NGC 1039 kinematically with

Hyades-Pleiades objects and other clusters containing Ap stars of the "Si" type (Eggen 1965). This point in the (U,V) plane is also close to the region occupied by the Ap(Si-\ ^200,Mn) stars. Thus the notion the objects'related in an evolutionary way are as well kine­ matically related is supported further.

The location of the cluster (b^= -15?6) about 120 parsecs out of the plane of the galaxy and the velocity component perpendicular to the plane have reasonable values for older populations I objects

(Blaauw 1965).

Further Discussion of the Ap Stars in NGC 1039. We are now in a position to re-discuss the Ap stars in the vicinity of NGC 1039 and their membership in the cluster. Table 36 summarizes the ob­ servational data for the three Ap stars. The magnitudes for the two close double stars refer to the primary, the secondary’s TABLE 36

Summary of Data on Peculiar A-Stars in NGC 1039 Mean Values for Ty] ADS Star BD No. (Jaschek 1958) K s- . No. Sp.Type m B-V P M V V M B-V (Am,p) V

HD 16627 +42°578AB 269 2038AB AOVp(Si) 8.39 (+.03) 0.85 +0.2 -0.1 -0.08 (+270) (2.4,10")

HD 16693 +42 588 472 204 8 B AOVp(Mn) 8.28 -0.08 0.40 +0.1 -0.6 -0.90

HD 16728 +42 598 522 2052AB AOVp(SiCr) 8.14 (-0.003) - -0.1 - - (0.7,1.4") 113 contribution having been removed using the given magnitude differences.

Magnitudes and colors have been corrected for absorption and extinc­ tion except where enclosed in parenthesis. The column labeled "p" gives the probability of cluster membership on the basis of proper motion.

It seems likely that all three Ap stars are members of NGC

1039. They are not excluded by their radial velocities (Table 2) nor their magnitudes when these are corrected for duplicity. The membership probability of HD 16693 does not really exclude it since the proper motion was determined from only one plate-pair and is very close to the mean motion of the cluster.HD 16728 did not appear in a proper motion plate-pair so that it’s membership can not be judged on this basis.

The absolute magnitudes are computed from the assumed cluster distance modulus of 8.2 magnitudes and are within the dispersion in the magnitude calibration (Jaschek and Jaschek 1958)• Indeed, the Kn Ap star o Her has a smaller absolute magnitude (+0.5)

(Eggen 1967) than does HD 16693*

The Ap stars seem to be intrinsically slow rotators (Searle and Sargent 1967) with perhaps a maximum v sin i of 100 km/sec

(Wolff 1968). This is in agreement with the results here (Table 6),

As mentioned earlier it is particularly important that the Kn

Ap star HD 16693 may be a member of NGC 1039* In contra-distinction to other Ap stars none had been found in an open cluster previously.

This has led some authors to suggest that the Kn Ap stars might have a different evolutionary history perhaps occurring in a post red-giant stage (Wolff 19&8). The data here suggests that this is not so. NGC 1039 has an age of about 10® years (von Hoerner 1957) which would place the Mn stars in the evolutionary sequence with other Ap stars. APPENDIX*

I 1 A lilCl’.K X YV 0 - V PkOPCK ibOT 1 i.j-J INT. LKK. N P V Y

! 1 16 8 ■’ - 7 b . 6 -2 1 .5 17.6 » 0 . 6 J . J 7 ' 0.0012 -0.1,127 >,.0i 12 9 1 1 A 0. 2 I 1 A 1 ) - 7 j . 3 - 2 2 . 7 1 b . 06 0 . i • u. 0. w • 0 0 0 0 . jJ ! lb :J 1 -7b . A - 2 A . 6 1/ . b : 0. M . .-.,0 3 1 w . 66 I 2 - 0 . o 0 08 ...U-;12 b 10 A 0.01 4 I 2 1 8.6 - 7 2 .6 - o 9 . 6 6 . > 0. I 6.^713 t .()<. u; -O.i.Jl I i .O.-l 7 1 b 9 ■> 0 . b ! 26 9.) b - A H . A L 1 . r> T 3 / • 7 • V ' * 0. 0. w . 0 0 J 0.

6 ! 2b 9 A 3.6 -A 7. 7 11.3 .. U. 7 9. 6 1 17 0.06 I 2 -0 . .9307, 9.0013 I 9 A 0. 7 i -16 101 — 6 / . b 9. 7 11.7. 1 . A J . ■ 10 b 7 6 . (J (1 1 1 - 0 .0 0 7 A Li . 9 ■ 1 L 6 b b 0.23 h 16 I 8 6 — / . ’> • U 6 9 . i> 11.77 7.9 j . o 17 2 U.GOLb -0 .0 I iO 6 .0 0 1 b b 3 A 0. 9 I 6 5 8.i -7 2 .3 7 3. A ;. 3 1.2 u . o 2 o L 0.00b2 -0.0 3 30 9.095 7 10 9 2 0 . 10 16 7 -6 -6 3.0 luA . A 11.12 7 . b 0 • 0. 0. 0. 0 0 0 0.

11 1 59 9 7 - ( . 2 3 7.7 1 L . A , 0 . b 0 . IJ I A 8 U.0009 -0 .0 I 7A 9.0910 1 7 7 5 0. 2 9 1/ 160 — It - 60 . A 37. 1 1. 2 . A A 0. u . o o ; a 0.0029 -0 .0 157 9.0133 A 8 5 0.29 1 3 16b 1 1 6 - 6 u . A 22. b 11.16 1. A w. u96b 6 . Oooh - 0 . 6 1 ‘*b 9.0009 AA 21 0.82

1 I 66 1 1 2 -f->2.9 1A. 3 11.03 0 . 6 - 0 . 0 760 O.oolA -0.6133 0.0915 A 6 7 0 . lb If,6 1 3 1 - b A . 8 -A?. 1 1 . A 0. A 0.9 0 8 b C.OOLO - 0 . 0 J 7 2 9.0010 A A 28 0.60

16 162 126 - 5 7.2 -55. A 11.17 0 . b 0. OO'tO u . 0 0 11 -0 .0 13 3 9.00 11 I 5 26 0.89

17 1 9 3 1 1 b -o l .2 -7 0 .7 11 . b 3 1 . 3 U . 0 1 () 9 0.00 1 A - 0 . U 1 i A 6.00 13 8 A 19 0. Id 19b 10 ) -6 A. 1 -7 3 .9 1 1 . 3 * 0.2 0.0196 0.001 / -0.9177 9. 09 1 Ll 7 9 A 0 . 0 A

19 196 9 4 l o 8.2 -7 8 .3 12.2 3 0 . b 0.00 79 0.0 01o - 0 . 9 18 3 0 . 09 1 7 6 a b 0.53 26 197 1 I) 7 - ‘ A . 6 - 7 7 . A 1 3.2o 0.3 0 . 0 1 A 2 O.G'Jlo -0.9102 6.09 L 7 5 A b 0.69

21 1 99 122 - 5 >J. 8 - 8 A . 7- I 2 . 1A 1 . 1 9. 0 I I b 0.0012 -0 .0 0 9 9 (J • 09 I 2 6 b 19 0.39 22 2 00 L A 8 7.8 -78.0 10.21 1. 7 — 0 . 0 0 1 1 0.001 A - 0 . 2 1 0 1 U.00 17 A 5 31 0. OA 23 212 1A A - A 9. 9 -1 8 .3 12.68 0. A C.0U98 0.0011 -0.9153 u . 09 1 1 3 A 23 0.33 26 216 139 -5 2 .0 -13.1 1 l.or. 0 .A 0.00 77 0 .0010 -0.0162 0.09 LU A 3 3 A 0. A 3 2b 2 22 151 - A b. 7 2 . 8 12. AO 0.6 0. 0 I o 7 0.0009 —0.9210 0.0009 2 6 20 0.

*Note:Posit ions are given In mm at Allegheny plate scale (14.60 "/mm); Proper motions and their standard errors are given in arc-seconds/yr; N is the number of times a star appears on a plate-pair and P is the probability of cluster membership on the basis of proper motion. 116 \r> H X •T. 3 Aj N ~g r - fcx. V. rx •A •g G r\l G X 'O sC rsi CO c? C AJO 6 CO X X o Tj K. S-. •••• 4 • * * » • a • • • • • a • • a • 4 • 4 0 0 o 3 o o c 3 o CD CD o 3 o 3 3 o w 3 o •3 3 3 O

PS rs; x .A O !*-- - 3 •£ rvj vO rr\ co —• —i ix 30 —* *1* .0 O rs p a *—* If. — rsl IN i"X f\J - " \ \

-o -j- -J- o vd 'n r> c- -a r*- ^ v* o

4D *X vC '**• O *X 30 f\ o in CO CO O O nT 0 .A lA X X

-v o -g O X rs -A •C rs pW XX ,*7» rf*t XX 7s 3 r> •*4 »g _ t — ^-4 —4 "VJ — 1 — j 3 V rg 3 3 • 4 —4 3 0 —a 3 •• . j 77 - 3 3 3 -• X 3 3 O O O 3 'X •—X 3 S o 3 5 3 3 O O 0 'w O 0 3 77 0 O O C5 0 b 0 b O • •• • • • « • a • • a a a • a a a • a • a a a .' X “X - 3 3 3 3 a - -- 3 3 ■-’ -- -■ 3 3 -J 3 3 3 3* O' AJ rs» n*' r\j in ■—X OO X OO AsJ O O m x7 h- — as­ A- •1 C ", r, x-. : n» *u J*. ,s» "w- 3 "“g -■j •n «7 — Av — a ps •X P-M ■— —* -g -g » 4 rs •~4 —* r— — > 4 g — g *—4 3 3 • X 3 £7 3 3 '7 3 •7 ■7 ' 75 3 7 - 7 —» • • •• • •• a • • a a aa aaaaa aaaa a o -a O O O C O O O O O 3 O - c O 3 c c 1 1 1 I 1 1 1 1 1 I 1 1 1 1 r 1 I 1 1 1 1 1 1

“> 3 3 (0 \ -A *. rs ■>« vsJ N "> X "X. 3 3 O' ~-4 3 p*4 .—4 —. —1 — r\J rs —43 3 «—' Aj 3 O b O •—H 3 *"X 3 3 * 3 3 ,3. 3 sw' 3 3 W 3 3 *,3 C 3 *3 AJ 0 3 3 ") 3 O O O 3 3 b *3 3 O O O OO 3 3 3 3 3 3 ,«■* O • ••• • • • a a a a a a a a a a a a a a a a 3 - 3 - 3 3 3 3' O 3 •***. 7 3 - 'A 3 3 3 3 3 m 4 -A •x. X •r\ X C5 AJX c: •C *C“ 3 .•A s ’ • X M-* O rs X* •"A — < , 7 •;; A, xA 3 •.7 O O •A JX AA 3 fs X Aj rr*. -g 0 — rs '7, •3 .3 \j 7 3 rc* 3 "A- — ■3 _»» 3 ✓ 3 77 7s ■—• O „■* ~x 3 73 3 "X •3 3 3 'X 3* 3 3 7} •• X 3 3 *7 3 S'* 3 •• • • •• «•• • a a a a a a a a a a a a a a '* 3 - .J O ..j 3 'Zi 3 3 3 ™j 3 3 3 O 3 3 O 1

* * *N ^ .-—. V' •0 M* xj X •.A PS •••• • • • •• a a a a a a a a a a a a a a —, ■ 3 ■ 3 X • 4, -g 3 •— 3 3 3 3 3 0 O ,7 3 3 3 1 . - ;- N. X. •A ■ -x M- X ,- -A ^,- A ••v •—4 “X •••• ••• • t a a a a a a a a a a a a a a a rs — *v AJ * N, *3 *■>> .*7 A. C\! -“A, rs '7 a 77 r~ p- 3 — 3 r> — ■ _- • ■* m— *”* """ ' *“ MM •—

3 cv 3 -- ■ : r , p-* .*,•■rs • X ;- „r N J" og JA • •• • a a a a a a a a a a a a a a a a r*. r'"' n 7- Ax! 0 N. A: X lA r?- O m O rs rs CO *» x x •4C r ,-f**, a j fs Ag 1 1 .X AJ XI ^-4 1 1 1 1 i 1 1 1 x X. rs xj* »«-4 r> As O ■0 in rA A- PA Ag UA PA m O 00 X 0 • • • •• a a a a a a a a a a a a a a a ■o -r 3 r A 3 rj 3 *•*. O _r, _7 .r. -x, ' J* :c c 3 C ■JD X

\ - X . X** MX . , ux X X lA. ,x *x I xj" ■G . 4“ i 0 O s'C *0 -0 ^P a' "C >• A- CC .^x P-4 —.4 *"— " 4 —H mmd g ’ J

C V", 7% 't 5^ *A x7“ rs S" ■xD rs AJ •X r s As r^ O >r n " LA s n ■n *x/ 'C fx„ cc eg* X AN 3 3 b r\ xT •"Vi ’• s' % ■*s rs '*1 X *■“ ‘XI X X Pv s X ,xX X*

t i>. _ 4. O ^ o »T *x" V- xT xT xf -X X X n 69*0 18 V V 0100*0 1810*0- 0l0i0*0 8900*0 8*0 ''6*11 0 * 2 V - V*8 1- V2 2 268 <^Z GI *0 V? V 9 0100*0 flVlO'O- 0100*0 V/00*0 G *0 ( G *21 G * 88 - 2 *61 - 102 y 8 8 vz 81 *n 28 V V 1 I 00 * 0 8010*0- 1100*0 1000 *(1 I *1 12*11 V G 1 - 8*81- 222 ZZ8 8 Z *0 9 8 z I 100*0 0920*0- 9100*0 902C *0 9 * 0 '■8*81 ; *91 - 2*9 1- 902 GZ 8 2 Z 3Z* 0 02 V o 6 000*0 U 00*0- f 000* 0 2600*0 2 * 1 Z V * 2 I 9 *81- Z * 81 - 8 02 2/.G 1Z

?P*0 8 V 01 1100*0 G M 0 * 0 - 0100*0 9 ° 0 0 * 0 9 * n 12*81 8*0- 6 * / 1 - Z02 Za8 oz y h*o 18 V V / 000*0 2810*0- 2 000*0 8100*0 2*0 ^ / T l 0*1 8*21- 922 99f 69 V9 * 0 6? V V 8000*0 61 I o*fj- 9 000 * 0 2 ino*0 2*0 9 V * 01 G * Z 2 2 * V 1 - 122 198 0 9 ov*o 08 9 6000*0 8 I 10*0- 6 0 no *0 9GOO * 0 1 *0 0 J * 1 1 8 * G V 9 * Z 1 - 002 VG 8 y 9 VO *0 28 8 8 Z 100*0 900!) * 0- 9100*0 1100*0 8 * 0 09*0 1 / *8G V * V 1 - 022 6 V 8. 99

*0 0 0 0 *0 *0 *0 *0 ]. *1 26 * 1 n * 6 G Z*2- 092 9 V G9 •o 61 6 8 1100*0 09 80*0- 1 Ioo *o 6910*o V * I 00*21 V * V9 2*2- 292 G V 8 V9 ZG *0 Z 01 6 VI00*0 9 f 00*0- VI00*0 0 2 1 f! * 0 0 * 1 09*21 0 *G9 1 *Z- 9 V 2 8 V 8 8.9 VV *0 h i G G 2 200*0 2110*0- 2200*0 6000 * 0 V * 0 20 *01 9 *08 G * <, 1 - Z 1 2 28 8 29 *0 G 91 GG • r% } 8 200*0- *0 9100 *0 8 *n u/_ * 8 8. *26 2 * 8 1 - 0- 08 8 19

63 *0 VI 92 1 1 * 0 1910*0- * 0 6 0 0 0*0 v o c l * 1 T 2*66 V * 9 1 - n— 9 2 *- 09 •o V 18 G1 * 0 G900*0- • 0 2 '• 10 ('■ * 9 8 * 0 2 8*01 6 * VO [ 1*01- 0- 9 0 /8 6G *0 8 V8 81 • 0 6800*0- *0 V lO fQ L *0 V 8*01 G * 20 I » * ( ■■ - 0 - 63 28 9 G *c 23 2 G !TOQ*n / 9(10 * 0- 1 100*0 VO 19*0 9*0 J 6 * I I 9 * G G Z * 8 8- t 91 10.8 y g 90 *0 12 9 6 2100*0 V 10*0- 8100*0 VZ00*0 8 ’ 0 96* 1 I 0 * / G Z * 0 2 - y Z 1 61 8 9G c ft 89 *0 G V 9 90 29 * 0 - 2100*0 21 0 0 * r • n V9*2 l V VG 6 * I ?. - 191 318 GG •n 12 G 9 6000 * 0 89 10*0- 6 i 5'' 0 * 0 t?f. n i' • ^ 9*0 1 O’ * 1 t G * 1 0 7 * 9 2 - I 81 y 19 VG 68 *0 8 8 8 8 9 000*0 88 1 n * 0 - 9 0 0 0 * 0 2 8 n f *o 9 * 1 •■9 *01 9 * 2 G 0*1! - V / 1 91 *. 9 G 68*0 88 *7 V 8 0 00*0 GO! ( *0- 8 00 0 * 0 1 / ‘ If! * (1 8 * I ■ 2*11 1 ' 2 c V * 8 8 - ■zl 218 ? G 06 *0 08 VG 0100*0 1210*0- oino * o «'* 1 (’(I * o 1 *0 1 8 * 0 I 1 *Z2 V * ti 2 - (J 1 Z08 1G

A X d *n>:fi *1N! Mil ll'*K ^ d p l ' d A-9 A A y -Oljl'l V ! I I I 0 DltiCK X YV b- V 2819' 0 8 MU r i 15 i INT. tl<8 . N V \ Y

76 896 2 0 - 1 9 . 8 -6 2 .9 3 .6 , 0 . V, u . 0. 0. 0 . 0 0 0 0. 77 6 oo 19 7 -2 2- 3 -51.1 1 0. 72 0. 1 0 . u 0 1 6 u • -0 .0 132 0. 6 6 27 0.83 7 i\ '.0 2 2.06 -IB . 7. - 5 o.J 12.31 U * *9 J . 0 u 7 3 0.00 I 1 - 9 .0 16L 9 . 0 .a 1 7 6 2 6 0 . no 7 y '• 0:» 216 — L 6 . 0 - 1,1 . I 2 . 3 0. 7 0. 0uU9 0.0012 - 0.0 l UJ 0 . 0 0 11 6 6 17 0.31 80 9 15 2 6'» - 6 .5 - 79.2 I u . 5 6 0. ? o . v) 0 1 3 o . -0 . .Jl26 v . 6 7 29 0.80

8 1 6 1 7 2 3 0 - . 7 - 6 3 . U 1 2 . 6 7 1. 2 j . .J 0 2 1 'J . 00 I 2 - 0 . ■. 1 6 *3 0. 00 12 3 6 18 0.85 «.J «.? 7 2 6 -5 .9 -31.1 1 2 .o i 1 . 3 J . >0 5 7 0. (JO 1 1 - 0 . b09 2 0 . O'. 1 1 6 6 15 U. 65 8 3 9 28 26 2 -7.7 -2 8 .6 1.8. 0v 0. 7 l ■' . 00 6 1 0 . U l; 1 I - 0 . u 1m 7 u . 0 0 I 1 9 3 10 0.86 B*v 6 30 26 I - 7.6 -1 9 .3 12.20 0 . 6 j.ojh 0 .0009 -Ci.O 169 0.050 9 8 6 2 7 0. 82 8 3 '.32 2:55 - .6 -13. 3 1 1. 1 j 0. 9 0.00 31 U .0013 - 0 .0 I 50 0.00 Ip 5 2 6 0. 89

8 6 3 2 3 8. -3 .5 -1 2 .8 11.21 0 . 1 o . UO 36 0 . U 0 0 6 -0 .0 1 6 6 0.0006 2. 5 28 0. 89 y / 8 7 26', - 7.6 0 . 7 8.9; 0 . 0 . .J03b 0. -0.01 .16 1 7 9 5 0.8 7 6 8 6 5 8 2 3 6 - 9 . 8 L 2 . 1 12.26 0. 7 0 . J 0 6 6 0 . 0 0 1 0 -0.0172 i j . Oo 1 0 8 3 20 0.52 89 6 5 ) 26 8 -7 .5 I 2 . 6 i 2. 3', 0 . o J . J 0 6 5 0.0008 - 0 . 0 1 6 7 0 . OOUB 5 5 12 0.61 {;u 'i 6 2 25 u -5 .8 2 2.9 11.67 U • 6 J . 0 w 9 # U. UUU 7 -0.U 166 1;. 00 0 7 3 6 36 0.82

91 6 6 G 29 5 9 . 0 71.8 12.1 9 0 . 5 O.Ool? 0.0018 - 0 . 0 16 0 0.00 13 6 6 23 0 . ar 92 M 6 5 28 1 5.6 2 0.6 1 2 • 3 1 0.7 0 . u 0 6 7 g . 0 0 0 9 -0.UIO6 (1 • 00 G 9 6 6 19 0. 73 9:5 m 6 7 26 6 -0 .6 11.3 11.71 U. 8 U . 0 0 6 ci 0.0007 - 0. ij 16 9 . 0 i.j 0 7 I 6 2 1 J . 6 7 96 6 60 2 71 I . 5 11.7 1 2 . 52 J . 7 U . > / u 6 0 0 . 0 O 0 9 - 0 . u I 76 0 . 0 u 0 9 6 7 I? 0. 6 3 96 '.6 9 25:> -6 .6 7. 1 ] i.‘f I 0. 7 U . J 009 0.002 0 — 0 • 0 0 V, 6 0.0020 L 2 5 6 0.02

96 67u 2 59 - 2 .8 6.9 12.00 0. 3 0 . 0 0 6 cJ 0 . 0 u 0 b -0 .0 1 6 6 0.00 08 I 5 2 6 0. 7:> 9 7 *. 72 26 3 - 1 .2 5 . 5 8 . 9 2 0. 0 . u 0 6 I 0. - 0 .0 176 0. 0 0 I 0.3 7 9f 7 3 26u 0.1 6 .0 8 • 6 5 0. 0 0 . 0 0 0 5 0. -0.0181 0. IB 3 3 0.82 99 . 76 2 o 7 - 0 . 0 - 0 .0 1 1.96 0. 5 0 . 0 0 3 1 0 .0 0 U6 - O . o l 5 7 (j • 0 0 0 6 6 3 30 U. 8 0 [00 't 77 2 76 2.6 -6 . d 9. 72 0.2 0.0025 0.002 1 -0.0116 0.002 1 9 6 19 0.73

00 •o 9Z t V 8000*0 svio-o- 8000*0 0610*0 z*n 5 V ' 0 L 0*82 0*ZI Z 1 £ I V8 OZI l£ *0 8 ZI 9f *0 9(00 *0- *0 V‘/00*0 1 *0 Of *0 V* VZ O’Zl 7 U VZ1 • n GZ f c 8000*0 9880 * G- 8000*0 0510*0 8*0 ( O’Zl 1 * ZZ £ * 1 1 !'U 9£o £ Z1 • r, 81 9 8 1200*0 1 V c 0*0- ozoo’o 5-009 * 0 9*1 :;Vfi 1 *91 z*o £ oz 8£‘- ZZ1 08 *0 8 £ 9 0T:)0*n £910*0- 0 1<10*0 5900*0 Z* 1 5 V * Z I I *5 1 Z*F IfcZ V£8 1ZI

28*0 5Z € 8 Z'H'-O’U 1910*0- 9 *'00 * 0 lVQfi-O r. * o 90* 21 1 * £ V*9 £8 2 I £8 921 8 H * 0 Zf 8 9 £9 ."0*0 £ V1 r * 0 - 9000*0 Z9f)Cl*o £ *0 £ £ * H A *£ V*£ !> £ Z CZr C 1 I / e * o Of. V 9 9000 *0 Of 10*0- 9 0 0 0 * 0 (100*0 £ *0 *oi V*0- 1 *9 V 8 Z 911 (8 *0 f.f 8 V 1 noo * 0 6V 1 r *0- 9000* 0 ( 10 0*0 £ *0 . i*ii 5 * £ - 6 * '0 VC 2 / Zo £11 OP * 0 f z c, 9 8 100*0 1 Z 1 f; * 0 - 8 100*0 £ 0.0 M * c 1*0 f (> *( 0*8- 0*11 £ Q£ 92 o 917

*0 0 0 0 *0 *0 * 0 • n *0 6 * £ 9 * 9 1 —C*1 1 £ Of ZZo 811 5-: 8*0 V Z1 01 0100 * 0 9910*0- 0 100*0 £ Z 0 0 * 0 £ *C 9 9 * £ I 5 * £ 1 - 6 * £ 6 Z IZo VII 18*0 V T T ’/I 8100*0 9910*0- 8 1 0 0 * 0 Vf09*0 h * 0 0 Z * 5 I £ * 91 - V 8 £0Z 0 Z o £1 I iz*n «,z 5 V 8000*0 9 £10*0- 8 000 * 0 £ £ 01 * 0 O ’ (1 18*11 (• * 9 1 - Z * 9 0 8 Z PI 0 21 1 •o 0 0 0 *0 *0 *0 *0 0 * o - V £ * 8 9 * V I - £ *5 Z8Z £ TO 1 I I

88*0 9 z V £ 100*0 9910*0- f 100*0 9£0 0 ’0 H * 0 ,j i * v: i Z *C£- 9 *; 0 8 Z '/I o Oil 08*0 08 8 f £000*0 8VK)*0- 9000 *0 (■>100*0 •/•O on • 11 0 * 9 f - Z * If 00 £ Z1 6 (01 • c- 0 8 *0 yz Z 9 1T00*0 Z £ I i'i * 0 - I 100*0 9 V o 0 * o 9 * 0 z 0 * Z 1 I 8*0 ( ( Z £0 0 801 n *o f z £ V 8 0 00*0 £/ IO*Q- £00 0 * 0 I £00*0 ( *0 ! 8 * C I <- * 99 - £ * n I c 05. 100 £01 ££*0 08 ♦> 5 £000 *0 V£ 10*0- £000* 0 Z 0 0 0 * 0 5 * 1 */2 * 1 1 0 * Z 9 —*/ * £ tJ/2 f CV 9 0 1

18*0 £Z £ 9 *0 i vio*o- *0 V000*0 I *0 / )■ • o «7 * C _ V * V 09 Z 1 ( ‘7 901 88 *0 V£ 8 8 9QO0 *0 29 if. *0- 900 0*0 ££00*0 £ * 0 9*11 8 * £ 2 - vn C 9 Z 0 8 '/ VOI J 0*0 8 8 VV 0 T 00 * 0 £ 0 I f * 0 - 0 100*0 £ 1 0 0 * 0 0 * T r l * I i £ *£Z- o* z- • 5Z £ o v £0 I vb *n 62 £ 9 6000 *0 1,910*0- 0000*0 ZOO 0 * 0 c • o •- z * z l 0*5- 9 * •/ - £8 Z 05? V 201 Vl *0 £ 81 fcl 01oo*o 5/00*0- 0 10 0*0 / V C 0 * 0 r *o ; v*zi V * £ - 8*0- *,9? (>•:/ V I 0 T

A ri N *W INI ?.m i n .v HOHOHd A-8 A A X X 9 3 10 V 1 I DIECk X Y V ti-V h'kOPLK MO 1 Lij.J INT. ERR x o Pxl rP. 'C -H 3 o X o x - » O j r *“* o 3 a 3 *K x IT. 3 3 3 X — x -J 70 - . 3 3 1 • t • • • • « • • « • » w * • • • j i • > o — —i 4 3 <4- o o n r 3 —\ P«H 3* ■'•s V, 3 ->0 4- * 3 H ’ - 1 "4 • • » • * • • * . ; a ■s. /O, N- o . 7 ' ■“> (V1 iS o — ■C X o p-4 -o — ✓ *c <*• ^ . •** I o • • » • • - «— X (M 5 3 o O —- — -j — '■=■ --■ ■- *3 f v sT —* -~s o 3 sT i'N. 3 . o — *■- -*• -<■- , V 1 c 1 1 I • • "• • • • • • • j • . O LTV 3 o - <7 u-« X '7* cvj o T- 3 ✓*» :o 7»\ N- 3 Ste_ ' r o c 1 r- 7 * - • • • • • • • • • • • * t • • » • C*0 CC X X v r —< O O o m O •7*> 3 3 3 p - r 3 o 3 * >r r*» X .*7 , V ;.3 T'xl —* __, — r 3 77 •3 —• T> _ - ' f 1 1 1 1 *1 • • t • • • • • • • • 4 j , t 4 n r O T 3 *T c 3 r .3 *> —- O 'X 3 . x , X vT 3 r— ,N* - . K r-t *“*%, »r 3 O 3 1 '7- J *7, 1 ^ .- • • • • rO 0 p-i O ~-4 \ r >? ^7; O O X r"1, X X *0 33 ■3 2 ' 3 -n ~ ro 3 O 1 - - 1 • • • • j • • « • 1 *»*. —g O ,»i c • pg 0 0 3 r - 3•3 • 13 - 3 O V ‘ 3 3 r*i rvj ■_r\ •*\ •^ f\: _r, • V — ■X X \ r 31 -“\ 3 —< N**, 3 ' S 1 • • * • • • « » • • T\g r-* - N •3 0 O X ■'■3 3 7?v r— iT 4 — CO O 3 *~s 3 •sT 3 3 77 ■X 0 • _/ 3 X! 3 • c -r> 3 I ,., - • • • • • * • • « • • » K- 0 3 >n p 0 3 /Vs r«- x r 3 , ^ 3 m nr, p»* 77 r •7 3 •> - « •— «g .j 1 1 w • • • • p « t • , ^ . p^. , • s O rs- (X «*\.i O O ff"» O O 3 rC \ j O ■3 3 X l »H -H •'"s m —- f\J * “ 3 3 ►— 3 7> O' 3 0 O T\ 1 V r 1 • • » • • * ? • • f - 3 X -X ■ PO O 3 —• ■.r 3 p 3 ‘ 7 / w f O c Lf\ O *p^« *—* O 3 —. p—< H 0X •0 3 a <—* S'* ■*'- ri-» O 3 3 .• 3 3 ^. 1 p n p • • • • • « * t - , 0 0 0 0 r— ■3 t4“\ 3 O 3 ■X —• —* 3 O >*■ 3 • • • • t • • . V r"O c >r s7 V C: w 1 • 4 • • ■ • • 4 1 r-"* 0 7 3 O •H X 3 3 •H «■- 3 O 1 1 1 *0 jt j « • • * • • • • • •s.. •M rvj nr\ 6 o r f s 3 -O p - r — . K r^\ Oto t fO *.) X -O X X *w 3 4 — r>~. -.. p» . ,-p. 3 3 3 3 P-4 X 3 X —1 3 ( c • • • • 4 « .vs ■X \ r •4" 0 3 0 pari ' O 4" O 3 O - O H <3 X O r ria4 -—* O .::* 3 ,-n x^* *0 O VT O c . s 00 -O or* - - 3 O O *< •4 •6 a* K* 3 * #-H X *X 4* X rO r-4 r> X r~> 0 n 3 X - 4 o r b ' X *—* f v .“S 3 3 •70 3 3 3 rvj 3 - N O O >»_ X 3 3 3 3 3 p —V O C* 1 H • • « • • • • • * PP^ H H pp* s’y X »H O X \ v a C5 3 0 *3 3 p P-4 X 3 H*\ .*>*« O 3 —4 i X O ■4 a 3 - 3 O O 3 .O n . « — 1 1 * • • • • • • • • • * X p O •*7* 0 \ r - h —4 O 3 "0 “» t“ 3 X • ^H a p >pp> 3 * c -O O ro >r K. no - 0 3 0 X -O r^. 3 - 4 -0 3 •w. H pp •C n H 1 1 -. ♦ • • » * *. f* .-O O -O -O "X 0 X O C5 vC ■xp> O 0 0 O O O f>- •H 3 0 pp. m f x ."2 LT\ O vT O O 4" 1 *3 1 • • • • * • • 120 CM

OH *0 os; e c 0000 * 0 6 *71 0 *0- noon * 0 7100*0 9*0 9 0*11 v o 1 - o*ov VS I 9 7 L PZl 0 7 *0 IZ v 9 01 r-0 * 0 f-r on *0- 0100 * 0 oc 00 *0 VO 7.9 * 7.1 7 *07 - 7 * 0 V 0 I *7 7,7 L VZ1 «■ I*0 i t V 9 7.1 00 *0 j t: n n *0- 7. 1 op *0 0700*0 VI 1 9 * 71 V ' 7. 7.- £ * 0 V f 01 M / 1/1 ( H *0 9 c 9 t 100 *•) c-n 0 * 0 - v m o * 0 i nno m I *o 1*91 L'ii- H * Z / 90 V •! 1 / 7 Z 1 (. 8 *0 tz V c 91 no * D 9M 0 *c- 71 00 * o 9 T00*n 9*0 V 1*71 } * vz- 1 *Z v 90 V Z1Z IZ1

*0 0 1 9 9 100 • r. LI 10 •o- C 100 • 0 07 7 9 *0 ? * 1 m * z t / *99- 7 * P v / nv 90; OZ t ’ 0 r. V P 1 1 On * 0 90 m * o- 1 1 ('0• r> O7 0 0 * o < *0 I n * 7 I / * Z 9 - V * o V f ov 90Z 091 • *0 I f I VI f T on * 0 ezi ■)* 0 o m o r\ 7 ° 0 0 ■ o 1 * 1 17*71 L *9 Z- 0 * 7. V V H1 TO/ 091 f ft" c 67 f c 9 0 0 0 • o b ito • 0- U 0 0 0• 0 P 1 0 f - • o v * n ( r ’ I I / * (SV - € * 1 V J HI no; / 91 9 *0 9? ?. Z 0 (VI0 * f) V1 1 0 • n _ so no • 0 ?]I0*n v * 1 VI * 71 9 * K V- 9 * o v ' - n 1 bb'} 991

01 *c FV* V 9 901,0 * f! 9 9 I n *0- P one *0 "000 • o 9 ■ r M * 1 I 1 ' 9 V - 0 * 0 V 7 h i: "0 9 r 9 I VZ *0 Z7 9 9 V [ 00 * 1 • SI I r * u- 9 I 0 0 • 0 1 0 0!’ * 0 1 * 0 ■ 7 ■ 0 1 0 * 09- 9 * 0 V "71 son V91 0/ *0 OS V V 1 VO? * 0 1' 1 • 1*0- M. r-o*0 n i n " • o 7 *9- I 1 * 0 t V I 7 - P * Zi 1 o 9 1.91 PH • r> rt V V l m o * 0 i V m * 0 - 1 1 no * 0 S I 0(1*0 v *o v n <; **)i- 9 * 9 t I. Zl 7P9 791 * r<* re *0 z £ 9 ■vino T9 1 0 *0- V too • 0 J 0 o 0 * o S * 0 / n'V t v n - 9 * 9 i ; z c t 0 9 I 91

*0 0 0 0 *0 *0 • 0 •o n • o 7 * 7 7*91 Z * 9r. VZf Z ° 9 0 9 1 of *0 67 c V f TOO * 0 m i o*0- f mo * 0 I t 00 * o 1 *0 7 * 0 I I * *7 1 b * v? PZl 99 >5 09! ( V * 0 67 7 9 o m o • lr't ; 9/ 1 0 • n^ J _ o i on • 0 • n •. • n 1 r- * 7 I t * p h S * 71 "91 1 / " f 91 1; * ;i * 9■ C VS. V V o o s o* n avi * 0- 900 0 * 9 i- i o r -n ■ V 11 9 * P 1 V * 0 1 <: 9 v 7/9 / 91 • 09 *0 8 S. 0 1 o m o 9 " 1 0 •o- n I no • o 9 I 0 0 * 0 t *0 Si * 5 I 1 * 9 1 - H * I V 5 91 / 9 9 991

n • "? v _ coo J‘ • ^ *0 9 S 9 11 00 *0 ‘/Pin *0- 1 too * 9 I I r. r • r- V * 0 ■1*1 1 T 9 <_ V V I / ° 1 '-91 • ■> • n f e *0 9 z 7 9 1 •"> 0 9PI 9*0- z mo - o v • n ,’) * I I 1 * Z V - £ * J I ! J 1 p V91 1 • o Rfl*0 9 7 z ?. 0 I-H) • rt 0 v I •?•c- n ] o n • n / /rn • ,9 f 9*71 v / v- 1*91 p.Z 1 l p 9 191 c: f; < i £t * o 9 i 9 9 • n 811 0 *0- *0 J< 0 0 ■ ’ * 0 I *9- r 9 *0 I 9 * V 7 - 9 * 9 V ° Z1 79 I • j m f ' j * 0 0 n 0 * 0 *0 * 0 • r. VO » v ’ L V. * t v - c r l SPf 1 Vn 191

A d k 1 n t un-. Mdnvj A-n A y a m V I 1 I f’R'H’ER (•’(.! T Hr; iNl.tRR OC o - — - rs * m * -r o vs r> -r -r vs .7 3 JS. --r p- -v 3 3 7 3 ■*«* 3 J ~ O i J • • • j • • • • ■ « ■ • • • • • • CO 1V>1 3 ■n vT r>3* o o 3 3 3 o *— X •” 7 7* 3 3 --. 3 3 3 3 3 7 oo •v. v» .—s >-4 s. -*• T' j ~ 1 rs • • • • ■* • »■■; f Ps. vT “*•**»M“ r*» c .'3 3 o 3 *X «ft 3 -*-. 7 J ?*w■J- 3 >- ■ ' V- V"* P'V -p 3 Z “3 o J 1 - j • • • y • • • * • • • « • • . *-A r* r—^ rs. SJ x y“v o rs -S X x 3 7 —y a TX vT MV . s * "C 3 O r C • > w H,* J T 7* n - J l) 1 - • • • • • • ■ * • • • 0 X x r-*. — ' O •r, c •7 b S. 7; ’v) -r\ *-4 !M » -r> *»k 3 C ■ LC ■sT >r 7' -* ,0 n -'S 3 3 3 3 3 T- 1 1 T • • • « • > « • •s. .-r> sT .r 3n •3 0 C» O ?* 4 _ ,7 ,7 Og *S. 0 (X 3 W- 3 -H 7 Xj 1 3 -* • • • • , fSk. iTO i’J O 3 O r— <^V r-^ * — * — >«. 3 •s. O r*_' K. ».s •*T -7 ‘C ■ *■ sT 3 i Z **H '.V 1 7 X z Z x 1 I ** .. • • • • • « *1 • • • • • • • • • • m . . 13 i"' ! r^* .x. (X •xj * m m O O 4 — »• s *s„ rr~ *■“ .X -3 .X >• - " ,, 7 ■ *S. S.T ■JT: 0 7 ,w 7 I 1 •> -> • « t • • t • • • • • ■n 0 j-s 0 H X 0 0 3 ,7 •2 —^ X rs ' .X «*r'. r .x. 4 — 5O •5 3 - Xi V. -X .7 3 » — XJ O 3 3 - 3 3 3 *ij \ T X ■> 7 1 Z £ 1 1 * • » * j » j • » • • 1 0 X X X r 'X.r» a) 0 0 ’ -, — X ,r ■,v s r 3 3 3 I — J O ■J* T.X sT -3 3 : u > v.' — r- SJ 7 i S I I -1 • • » • • • * 1 » ■ X. O O r«-. •H 0 -r .-4 O O O . — 3 ■- .s» 3 3 -0 ■ <4 rs '.», v.^ 7 n :r. Z 7 **> 1 1 1 r*. j » • « • • t • • " . >r O X ■ 3 > s •— 3 3 .3 3 s* ~ r -_ *- -*s * — 2 Z " 3 7 .y h ~ 3 1 O 1 1 - * * Z> • • » * 0 >. 0 '* * • t • « • • • • • , r«w •s. 3 C sT •J- X) ~ C r -w — —- J—H — -J ,c- —- 3 '0 3 *r •*7 . -> ■ £ 7 1 7 1 *. « • • • • * • • t•• • ft • ■ • ^■4 sj- — 4 m m O 4 — GO b kiT- .7 3 7 ~~t ~ ’~ " 3 J". .7 3 ***v 3 O1": 3 -r* 3 .- 3 rr O' w> - -r •** j . 1 • • • • • • , . O "O •.4 st * 4 — **• ■■ ^ O 0 0 3 3* O 3 O X X f—• 7 3 r** 3 ’. y • 3 ro v» ^ r**4 •^4 — •7* X **C” 3 7 3 rs X 7 1 1 • .-» • • • X >3 7 rs X 3 3 O * — rs cc C X r— *S. *7' T* O . — 3 i-s, vS rr

“H 3 O > ■7 r* 1 ... 1 7 r • • • * t * « * * t•««• « « • ft t• ft t•ft • ft 3 3 3 O 7 3 — 3 1 ■ cc CM * U *C rr rs l 3 1 0 .-* -. O T .„ 1 • • « • • • J — •s. ~4 ’ O -7 — X 3 X *“* •—4 X X LT- 3 O O O 3 O O 3 rs. "vJ sT rr* 7 :.- O fs 1 0 • t••• • • ft • « rr •7 T> — 4 — 0 * m t 0 - - O ( aT) «-* X «—* < — X vj- "0 T. r*^ «-s -p. .3X 3 r. O 3 *«T ■3 >r .3 s > r 1 c r 7 • • • » • ft * ^4 .• X 0 7 ' > >r TX sT 4 — 7 0 3 s • 3 3 ■7 •vs _4 3 7 AJO LA -4 1 — 3 3 3 •*- — 1 .—v .» ;-s. sT vt .n >T T* 1 ** ' 4 ft • • ft tft ft • • t«f • ft « ft 0 XS X 0 r* v! 1— 1 rrt , ~v )O X) • — >r c- X X■TO ■X •—* . O * — X s.. e—V p r^ r* X 3 vs vs sT ,**> ... S < j S y - 3 3 7 t 3 1 • . • ft 4 • «-4 4 — O 3 rsl X »—« G rs. MM •n Mv 3 3 -V X .<“V r\ X O X X 4 — or *r O X> .y •s.. • 7 O 3 G D 7 7* 1 I 1 1 ft • ft • t• ft • t• ft • f .*<0 0 ..4 0 O 7 1 — 0 _ 0 X 0 ,-n G •r rvj 3 ■“* 4 — CO X -*vy 0 •s. <- O . T < >r. rr\ Nk. •X v fX “j L' •*» 1 7 I • • • • • • —* <\ • • • • • lit* — rv* l/H, O O ’jk. • •, C -r* >w" a N?" O v.r O O X A. -** O O O 3 7 7 1 1 7 I I I I „ V

• • • • • « • • # * —J 0 T a X O 3 .. ✓ ■~+ D N u I 1 1 1 • • • • ,*V ■4 nfSI ■n X O 0 a O rv • A O J ‘3 »*> 3 j » • • M •v fO ^ ■ ^ —* —i — O Cv O O C 7- sC », vrv rv O - - £ 1 •> • • * t•• • ft • • • • • f t r* O O —* O O v r *- ■*3 r—* s■3 3s '.*> 3 1 1 t•* • ft ft * I « t » orsj ro s A’A lA rs- r — ■C —4 a O X . V, 3 O ■N Xj rx V v V vj V. (M (VJ J - *-4 "J \ r- -> .7 « i 1 i 1 / cO cc c O —1 O — O O 0 O 3 —< O £} "3 O . >N. X. O -3 A O ' J **** 3 -•mf 1 ft ■si - r • AJ -<* • :V 0 r 0 • mmk * O

.-A a r — a •C CO 0 O s s -A A>• > “A i\. fvj rx ex.- r\j ^ O j rv xj r—4 4 — 33 0 - — 33 x i i x 73 * a >* c v 1 1 I I I I 1 I 1 ft 3 • ft • « I I I • * * * * • » • * « • * • ••••• »*•••

O #-* O ' ■» ' rsj O V^ -— 0 O O O ,-*v Ob ■O O T 0 r rv rv * w ^ o o 0 3 o o •**» •»* 73 7 0 33 •“» ■' 1 n r • t• ft • « • 7 rc J - - r-v ,x rv p >r O » w O ’ v * — •C r* >•« ■3 4pT*—4 X m **i •*r“. O _7 7 Ai .r 3 A •r*t *3. O 1 ft • • ‘ • * * r —* rA c f s !*A 0 O — O v N. N» — — 'V ^ — n c\ 3 33 3 3 0 - ■3 J 3 7 -> — - A T ft ft • • • • • t*• * ft • • • • • • « 1 i 1 r-4 O • |S- O v0O 0 rv Tv. st* —ft — O O —4 •— s* O O * A 3 Q *7 c. 3 •A 1 1 • *>« • ■• ■ • • * A T •— T A *x - x - r x ^ AJ O 1^ O •n r^ - • —< r\j O ;o V t fr fi .VirO ,f «t >- f ■> a 4 — J< — •c v - “C 73 )X! X) O ^ * O' ^ 0 0 — 0 0 0 1 III I I I I 1 I •

« » » * * * • » # a 0 0 • a V A V -- , — A. ,*3 Cf O •“) 0 0 O X 0 7 -3 A 0 1 1 * ft • • • • • « * * J' t-

O O O O •v — ^1 < \ j( \ .r v : A •X IX! CCf ^3. f-4 £ 5 • • • • j t•• • ft • • ft ■■- >- t f —ft — O ■T> a — —4 \r\ A ^0 c ) ' —4 ..Xi A. sT "7 3 O 3 0 A 1 • • ft « *. ro A- sT a 0 O c 4—ft —4 A- O • X O r—* 0 —4 -A ■*vt V JAj XJ O 0 O O O o 0 A A z> 1 - • • • —i - - r 0 0 c 3 rA AJ O >T 7 fX —4 -•o O r*- r- s> •A -r IT. O T' 'T' « v T 'T -T rv O ff, ft -r. rfC -o XJ — -•v x V — ** —V V O N I ■3 -1I III 7 ft - • 1 1 * • 1 • • t•ft • ft • • •A vAJrv c ev 'A O *3 - rA .-A 'O V" 0 A A rv 3 3 fA m—i O —4 ■y* X' ■73 NJ XJ O vArv r r J 7s 0 . * 1 I ft ft • ’.3 . v* * “ —ft a O n ■> rv O 'A rsj A, O O b i.-A Ai — 7 • .7* 1 •^-1 N* ■■* J 73 r" O — *C "— 1 X O A .7 XJ _s O 0 T 1 • ft • • • * ft ft J - O 0 A- a —- ■0 c O AI O N- 3 • — . — O O f\j O r-» 3 t - O —j rv A A rv 1 txi O •«i D I .0 1*> • « • • • « 123 X- A O iA —* -* ''T A •,C - v •X> m o cC O O t - ;o 3 i*> 3 O O-OOO 'JO c c • • • • • • • •• • ••••• * « » • • t • • • ■ •^7 —< a ,-«s o ro Z > r o a ° 3 3 CO 0 O O •,»» 3 0 3 O

rv (Si r+\ —4 —* r— rv m -O rv x •■4 fV - * rv

V 0 '»• Xt 0 0 0 3 r» f*^ 0 *r 0 .t •- 0 3 O x> A O *•4 r\i •w »■* I— 0 '.^0 0 0 0 O 3 0 0 rv 7 7 0 —'3 0 3J'A cc 3f a 0 4 0 x —« '\< *n.

a v X 2* X z Z 3 X) j"\ .*M 0 0 fNJ >”NJ vT AJ < - X mJ *- O • 0 ■i*1, ■tv -J» .J- *s> 7 p- j s* \ •<•, VN •3 , A (Nj •JO • r 3 .‘3 J3 '_ 3 •3 3 3 ' . ; *3 ..- •3 3 3 "3 •3 31 >»< O O 5 3 3 3 O 0 O O O O 6 O 'w-> O O a • • • « • • «•• • •• • • • ■ • • 4 •• • • • . — , s • -v —*, —s •wV J ’ .X -J . -* —’ V X TV 73 X c c *7 ■V, X; a CO s. r-> s*- : n mmd r-4 •«* c x *■• N* "V ;* *^- 3 X — -J* •.7 »s^ r w \Z r-- ,— r v iTs. r \ — 3 M *— '-'i »_ri - — — m * — 4 —1 fX! ■ -» 3 O 0 T- 3 O ..J .3 • 3 \Z 3 3 'Z> •3 . ' 3 . .3* 3 u - • « • • 4 •••• • • .4 • «• • • • «« • ••• • CJ *•> 0 O 0 O O O C O a 0 0 * c r 0 «3> O 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 T ( 1 ( ( t T 1 1 !»/ -- t Cj ■ *. %r 3 > 4»*. *«^. -> Tnj m ■N^ >«. *sT r^. r v 3 r v r \j :A rsj 7*, X O ■ 4 O X *>W >*■ *c C* *J- .3. X -0 •0 - v X ,—> »— 3 3 3 3 Z' zz • 3 zz b 3 O ,3 . O 3 O 3 ■3 3 r * O 0 O 3 3 -O 5 0 3 0 b ’O 5 5 OO O O b O O b 3 ■>4* • •» •••• •» • ••••« •••• • • • • • • ■7 »—• O 3 1 -» o 3 .3 3 O z> • 3 O 3 •3 0 *3 3 0 3 3 \ —. •0 —•* -7 *•*' 3 X 1 -rs 0 X ,*— —< (X r\j x 3 f 'JZ —I 3 —. v.“ .3 3 ! .•^ ► s* >r 3 O -k X* X •C O 3 3 3 'v 3 — 4 • 3 3 O C.' 0 3 ■3 Z' 3 c 0 3 3 -3 3 . j 3 3 3 3 Zj ' ■3 3 ■5 . j 3 3 _J *3 3> 3 • « • 4 • • « ••• • • ** • •* • • •••••• 3 3 **x 3 3 3 ‘i '.J ~j 3 3 O 3 3 mS O .0 3 3 3 O • 3 .«s ■3 3

> , 1" r^- . > •w 7. '■sT x * — r— ■ i rv A 1 r»^ sO 1 t • • « •« • ••••• * • * * * • •• * • •• - j >4 O —4 3 3 ■ 1*4 rv 0 CO — 1 3 0 0 Cj '3 3 -> O 1 1 1 ■* _ . . -, _ _ j -. A _ 1 r > • ^ ’'*■ b N* rN 3 \ r' ~~4 •£ v». ■•*> 'C - >r •^s \£ *r* r v »• * • •• • • • •• » ■ • • » • • •«• 4 • •* 1 <“> -A - 4 - r -j* «7 sT *xT rv c V O ■X- * V v" • v ‘s rv •» ,-4 — r-. r>« r—> r— — *— *-4 —_j —-* — ^-t m "4

A. •7 - 4 X *v *77 3 •3 r v ty“. 3 r v 77 C7 ^7 j.7 vT ‘V 7* A -7 > • •• • ■ • • • •• •• ••• • •••• • »• •• X r r - ^-4 c r "X jV •C rf —- ^7 4.7 X Tv *30 XJ CC r v %r X j »—-4 1 Cv *3 •*4, ,s . *A uA r v r v i 1 1 1 1 i t 1 1 1 i 1 1 l 1 1 "fi rr; X iA X c a - x •O sC -*_ O *> > r r v A 0 A X 4 ■ • » • •« • ••* •••• ■ • • ■ •• * * • ■^4 , «> -V V • s — 4 x A j r^. O 7 - • 0 ■ 0 0 V* X 3 x» x - s «—s *»» I 1 1 1 1 1 1 1 I 1 1 1 1 1 I 1 1 1 f 1 1 1 1 1 r

■*« ,*"■ ■: 5 ..;7 •.71 7. “• r*. - 1 •r 0 ■— VO C r—' •7 i*. <77 ,77 •L< X at\ 'T” X X x t X X. rr x . X X tA X LA t r .

J w~~‘ V a 3 x - > .3 —- **v A O r - *.*.' > 3 iV x , s7 A 0 ■•t v -r 7 O wT. A A A, A A A >A O *0 O 0 ‘O 0 0

“N s X . ^ — j 'j x *7 A r. 3 r—1 7 “A vr •-Z K- > • ,j X X. , x »~-4 r v r v r v rv X 'A X X, X X -v* >7 ■r j - vr 7 b V >r sT •A •AJ rv r v “V r v ‘V rv* • V r v ,VJrv r v r v vVJ r v ^VJ c j r\j <*•} rv <"s r v AJ rv ^ 7 * DIFTfV X Y V FKOPI.K •'•Ill'K!: I^T.cKK fNJ n 4 _ —4 —• o-4 >3- "S . 1 i c r*- o o CV 3 . 1.o *1.. VVJ* "V 77 \ y CV _-r\ 3 v r 5 b 3 o 3 3 o •m* 3 —J 77 — 4 T - - - r ^ c c i - „ » O • • * • • • • • * • • • • > , . -VJ —. 7, T> , -s v r o ■jy v r o o v r . V • ***■ - > *V ,*• *v TX. X vT vT x* ■£> 3 3 i\i o 3 •v J* 3 ■* I 1 *■ • • • • • * CV *—t 3 o o X L -j CL> f\J o 3 -^1 X %'j o •— 3 — X 3 .... rv X 77 3 3 - - '•X '7 £ 1 I t • ♦ « • • • * • • • « • • • « « • ^■4 fXJ —4 v r f^- 0 —4 •J- * 4fc' V r— CvJ . i—> ... ,J7 -■> rv — jy £ 1 f « r. 1 • • • 4 • • “'J v r 3 — 4 l v r 3 6 b 3 ,3 3 T — ■^3 3 5 x X f» P*. fx» 'X. px -r J X 3 77 r> rv '■4 3 vj“ *0 V' -* T1 V 4»> f 1 1 • • • , • V K- ^ V *•* .•3 ~ ■■«~4 *J- — 3 3 3 >*4 VI 0 <— —< V X 3 3 3 D —■ b O 3 sT . X C O: 3 x :A iO *- *- v rj rv r.j rv 3 1 • • • • • • 1 1 1 • • • • • • • • - r 0rv r '0 — -J- —* • " K. 6 5 ^-4 *"* O 1*. c :j ' 7 ' T *3 .•x. " 3 •O' * J -•? i 4 ■ • , « • « « • * » N* —« wmd 0 *n . s ^ , ,*>\ r«j *7 • “*> j x•x. ■x 3 3 3 O O l ‘l 1 7 • • • » 4 • • • • rr\ V 4 a 3 O V. •43 CT1 *v_ •i* O m4 3 - •*\ j*: - r . s . .V •o r^i - - X 3 -s -X 1 1 J t • • • • • « • 4 • • • ■ » * •4-1 rr. •— —4 *x_ r\- rv O .3 rr* O «— -V — .,r - - > 3 f ■ f 4 n x px *x. 3 *", 3 3 3 .3 ' v 1 Zi n 3 S> j T 1 * • • • • • • • • • t 1 -*.- 0 ^ x r* x ^ .0 .r- -x* —1v r O O —a O O , ^ V 3 ■ - r .-3 3 O yy •<\ 3 -V -.0 r . ■£> 3 3 3 3 ; 3 3 .J X fy 3 *r 1 1 j 1 • . • • « • • • • • • • , . -C 0 O -.V O «3 -O 4 — r*“» - 3 3 - r —4 .3 3 :C -S ■*> p . vp 0 c •4 1 \ 1 •i • • « ■ r> • • # 4 0

0 3 r-. o vV rv — .-V C vT 3 ' ■x 3 - _ 1 7 « * * • * t • • • • • • • .3 O O ,3 —4 ~r p*^ O O :,3 »»• •x* 3 3 3 3 3 ■-- ( , . , 3 rv 0 O' X X X .0 x n #•. *- rv -V 3* 3> •£ r 0 1 1 1 T • • • • • • • • • * • • ^ O ‘^4 O O 3 ’• 0 , V V 3 n v rv rv ■Nl X? — 17 r— -X 3 3 r*- 3 -•; T" £ O 3 1 - • • • d • • « • • t • • • ■V O —• 4 - px. o*4 (—\ 'X 3 —v **-* __, 3 0 I • • • * x» •—t *—+ Is - JT x_ v r 3 rv 0 O O •V ■-• <" •3 - s v f ;3 O pr* — * r—■ 3 3 "* rv X' > X r ' •'V ’ 3 1 1 • • * • • • •“V - - 0 0 0 _ r*’' 0 3 3 3 o t •x. "V v r px 6 3 3 Vj 3 X p<> -VI •“ - - j s rv r\i 77 'X 3 0'C •0 ;r> ■-■ - ~j 1 1 I • • • • « • • • j n r^- 7 ' — .^, O -0 x 3 x3 •x. - . 4 — 3 O 3 3 0 rv - r a* *•* 0 . 3 — 3 3 77 •-. 1 1 mj * • • « • ■ # • • «\O '«T\ O O —4 O 3 X zr. ’■“ ' —1 3 . x ' S 3 'VJ —1 •— > - 77 J* - rv 0-4 O TO * - •x rv •x 3 3 T 7 j 1 1 • • • • • • - . r*» 3 r~\ c c ^-4 .3 tV r'3 ■ *X O v r ,3 ’n O v r .3 •+\ ps. -X v r 0 —* v r •—4 3 - r 0 X rv 3 5 3 3 3 3 T. _ . 3 —% — 1 1 • • • • J O < v r O O 33 *3 •VI - r *■4 O a O f>w - -K 1 ” 3 • 0 3 3 ( —4 •J 3 0 CV O 4 - sT - r • C ‘•0 O 3 rv -f*; 3 3 •r 1 \ • • • « • • • 0 » , v 3 r O 4 r —4 - - ^-4 r> r c \ 7 0 r o * A —1 c .*r <\i r v O * • • »• • ■ •• • • * * * « ••• • • 9 9 • 9 9 P~» 3 o 3 3 o O sO a 0 O 0 O -“D O a OO

JNj r v -“Si pi ■! ■W 0 -A > \ i r-“9 - o s f 0 rO 'T ------

"A . s O - n A o O f s o o 0 O O 0 s0 o ' V r v OO 0 • • 9 “V p-J

<■*> o rO *1" o • n ■vO o o O 0 a N-N- 72 ■ n 0 O O 0 r^i r*

7> * - 1 ____ K. * m 4 pp 3 :\i c.7 ■t > 3 r ^ 0 - 0 O O•T • n Xi s ' < > s» . o r v A c* *) ,0 "V rsj r v ■V A •*> 7 . *■* 7* 2 S 7 •'V ... — s 7'i O ' 2 >'7 r ; ;‘; C 'T r s Q O O o o O o «/ 6 h O *2 O O 5 OOOO • • • • 9 * • • • • •••• •• •* • 9 • « 9 # -v —s 3 , 7 *( •7^ ■7 > J 72 “ ■ - - -

* * j •o A •-W A m S'. - r - r~-* ’*wC ■■M r - CV •A rvj sC . n rs. •s V 4 -*v o r v —. tT* >/ .,7 7 — A 7> 23 • 4 V —■■ — M — i - j •* » —J — m>4 —* rv •J p~^ r v ■*« . 7 A P-S 3 -7j i’v 0 '7> O *> H -/ 3 3 • •• • • • * * • ■ ■ • • • •• • • • * 9 9 9 9 9 p“> p' s . r-* 0 ’ S 0 r ; 0 o C.'' C- O u .’ c C r> O c O 1 1 1 1 1 1 1 i 1 t 1 1 1 1 1 1 1 1 1 1 1 1

„ «., .A * ■s rs. p^4 rs. : d ■0 s*- •7* sT J r \ > 5 'ij A V (*** s ’ . 7 lA *v! 0 ■* r v r v •— A i A 3 7 7 7 -x ' ■ 7 7 7 .*2 O \ 2 —. ..j A ■ 7 77 A • 7 C * 3 3 o 3 o rS o o O 0 OO 0 O O O OO 3 1 9 « « ••• ••• •«** • •• • • 9 9 9 9 9 • •*> ,-s 7 S i 3 3 3 3 - - 0 - ■- - A

* - j *s (M • A "VI ' s — ■-. c ■7 A O •.n CV ■ X —N —• a 7>l —i > - —J "O “V 'J C* A r v r v r v •7 . ;7 3 —f 0 — 7 J o o ,*7 “j •7 . 7 ^3 3 O "S •x "x -w/ . * 4 - -4 * > - ■ p»' pS • • •••••« • ••• * 9 9 • 9 #■ 9 9 9 9 9 9 9 •**» •“S n o —J .V ; s '7- . J 3 3 —* 7j —' f t 1 I I t 1 1 T 1

_ v - .. S • . AS a «• *• •• • • • ••# 9 9 9 • 9 9 9 9 9 9 9

V m * — P-* O O 7j> 7 ) O t - 4 O 3 3 O •*— - -

. ■ a -- ... - ... A.. a -x 7 A. / V 7 •*», *s- p .. -,r - nT — *v •*. \*•C •A • • • • * * • 9 9 « «« 9 9 9 • 9 9 9 9 • 9 9 9 9 «**» *0 - r -7 . - sT c r * • r • 0 r •>7 .’V • 0 ■>J •* V *’*• ■7 •A •7 *r M. —— —. PM •—• p ■ 4 r~~l •“ *“* •— ~4 ' “* t—i - 4

- , -P- v*“. s 7 , :r v c A V 0 % .'-.f >»• —1 r s V i*> -H » » • • » •» • » ,- •• 9 9 • # 9 « 9 9 9 9 9 9 •rs ,77 •«* A O o sC 0,i sT“ f ^ r\J ^ ■ 1 O A 7 2 ■A' 0 : r^- ij-v 1 ^ ppM vU lT‘ p"» m m 4 — 1 1 1 r v ■t “O l J ) 1 1 ( 1 1 1 1 1 1

■s. -JS j* 7 s A Z i J o > xT ■%< r\i ,r . 4 * r v sT CC •O sT r - • •• • • • •* ••• • •• • • 9 9 9 9 9 9 9 9 9 •f*! *S, -s r— C v o j — ■”s *7* "*7 A < r 7r\ - j A > iV > 0 — **- X. •s. •s. 'fc- ■ 7 *‘- .O fs. 7 i i i i i i i i i i i i i i i i i i i i i i si i i "- or-, o CC O

,*■ a-! O I"- ' r- o o d o — —

3 *Sp *0 T 7 m 4 *.J «- •C k^ .7 -A — •Nf sT O O .“X.•*c r> /-s r— r*- A- CC A 3, •* j "C .3 *r 3 -C -3 0 rr- 3 T 3 ,7s /> ■3 13 3 rv r-w“Vr s rv rv rs .*v o.i rv V ‘V rv r v ‘*v r v rsJ Ai rw CV VJ CV rv rO 1 I A 0 I er. \ XYV iJ-V t> :\l Ji* t 3 Ml) T 1 to M l.U . t i\ i3 . M P Y

30 I I W -7 2 .2 -3. L L 4 . 4 1 - U 4 4 0 . to'.14 2 -0.U276 to. 00 4 J 0 0 1 ito. JO.' i J J -6 i . 3 - L. / 13.6* L . U . i.j 0 I U Ij. 0 to J 6 -U. Jl 74 0 . 0 J5 6 2 6 I J 3 to .02 303 1 36 3 4 - 73. 7 ?1 .4 14.17 1 . 1 \ i . i to 2 4 vi . to 1 1 to -O.tol7 7 I,-. 01 00 Jo 26 2 U. JO'* 13/ 0 - / 6 . 2. 26. 3 L 4 . 4 ,,j 1 . 1 w . • ! 0 fi to to . to to 7 2 -0 .0 2 74 .i .0673 J to L ij • 30*. I 3:> ri •> - r ;. ? 4 6 . 6 1 4 . J 4 1 . 0 . J 0 4 0 to • to 0 7 to -0.02c. 7 to . Oto 7 7 j 0 1 to.

JO:. I 4 to . 1 -7 3 .6 4 7.1 1 3 . 3 t C. • 0 . 0U4:j 0 . U to ;i 1 -0. to022 0 . 0 0 6 2 0 to 1 0. 307 I 4? w - 7 0 . 6 70. > I 2 . 2 ’■ 1 . u . to 1 toO 1j . to to 2 *1 -O.t, i 15 o. 0024 1 J to 3 0.u2 JO'-'- 14 3 6 1 - ; I . h / 2 . 7 13. A'. 1 • > 0. IJ . Q. ■ to - 0 0 to . JO J 14;> ; i - Y5. 7 0 ’3 . 7 > i \ . i. • 0 . 0. to. C • to to 0 0 . 3 l'j i 61 l(V. - o ■» . 1 7 7.2 1 2 .3 ' L • o to • 0 1 2 to 0 . to04 1 - 0 . toO 7 3 I). Oo 3 7 34 1 3 2 to i

31 1 1 6? I o :> -6 J . 0 to 7) . i ! ? . 4 1 1 . f 0 . ij 0 5 1 0 .0 U 2 3 -O.ii > 1 1 0 . 0to22 4 I J 2 J. 312 i 4 i 0 -<>4 . 0 O 6 . 1 3 . 4 ’■ 1 . 7 u . . 0 6 6.4 1 4 .»J ' • 1 . 6 to . U I 2 7 0.004 6 - 'J . 0 > j 7 to.0101 5 j 4 3 3 0. 314 1 6 7 1 1 ! -u 3.3 46 . 1 3..2 > 1 . 3 w . i) 2 4 0 .0 to * 3 -0 .'0 I I 8 •j . 0 -' J 5 1 i 4 J 0. 2 0 31 3 161 1 0-) - -6.0 36 . 0 i j . > ; 1 . 2 to . to l J 4 to to.0‘J'J 3 -O.tol :• 7 U * 0 o 5 6 4 22 2 to.

3L6 1 6 2 ; - - <. to . 6 3 7 . j 1 4 . 0 . 1 . 4 0 . 0 2 12 (:. 0 u 6 7 - 0 .0 i l l i.. 0to6 7 0 u I to. 317 1 o 3 I 0 4 30. 1 1 4 . 0 7 to . J ij to 1 to . 0 to 0 7 -O .tol10 0 . Oto77 0 j I 0.0 2 1?1 3 I 0 1 to 4 10 i - o (i. 2 2 0.3 1 1.6 ! L . 4 to . to 0 2 5 U . Oto J(- - 0 . i L /> 2 b . 0 to 6 6 2 6 u 3 to. 314 16 7 •! - c i h . y 10. *. 1 4 . 2 J 1 . 1 • 0 0 3 ■ .1 to . u-)4 to - 0 .1,' 132 0 . Uo 50 0 to I U.94 3 2 . .. 16/ -r»v.2 4.4 1 4 . * . 1 . 1 to . i.'iJO 7 to . 0062 -0 .0 2 38 0.00 4 J 0 u I to.

3 2 1 170 ■.* -to 3. 8 -0 . to 1 4 . '! to 1. u U . 0. 0. 0 0 0 0. 1 2 2 1 72 1 14 --..2.3 - i 4 . to 13 .77 n u . o 1 30 0 • 0 v j 4 7 0 . 0 to 2 0 i;. 0 ) 5 2 52 17 2 0 .0 I 'J J2 3 1 7 J I 1 0 - 3. » - 1 6. 2 13.7 ’> 1. ^ to . to to 3 -3 0.0100 - 0 . 0 18 2 0 . UtoOO 5 J 2 4 0 • 324 174 I I 7 - 1 : 0 . to -18. 8 1 3.04 1.4 U . 0 4 48 0 . 0 0 7 2 -0 . 01/65 »j. 00 72 34 32 J 0. 326 1 76 I 1 4 -•>1 . 1 -2 5 .2 1 3 . j 0 . 8 to . OU24 0 . 0 to to -0 .0 128 b . 0 to 4 0 14 10 3 0 • B1 j

to ^sj 128 -y* s f v T *—>« n -v*' X **• «™4 • f m O' O 0 0 X * c c O • • • • • t • * •• • •• » • « ft ft • •••• • • <—> !3 O o o o o o O 0 •O C 0 0 3 3 0 O 0 C 3

•a r A r O x T C - r A — 4 X paari X PW r « r A r A XO «— 1 < r - - dC v X - p -rt o f^\ o O O 'O O - > 0 :A O 3 0 X O O O UJ - j r ^ »■ ^

s+t -A o o 3 x T o o O O X ■ n O P- •7* X) O O O M w4-> w * ■ X X 'M "* -3- r -

-K 7?\ -O O ■T' 7 > i n 2 ■ o < * X X “A — 4 3 : .j 0 * n — ft ' f r A vP ~'l -a — _ « *-4 ■s.?* X X X : x *A > 0 j A 1^- X *5* X a 4 * .» j . j m o 3 ■O c O o 6 0 <77 O a 3 ) ' . y 3 3 O 0 C 3 0 O O •• • ft • ••• • «• • •• « « ft ft • • • • ft • * ' "v •A .7*^ - r e - - ..j - ■■- --' 0 3 3 J n

T' *„A O — 4 CD • > • n ZCl n r-\ X (A u A tf5 * r 0 X X ,•,*«. X PA c *.* r \ - j — j - “ ■ j A ■"A C 3 ,•> • r— —A ■33 X X »— \ • X i —* •**« ' x . * ■» _ 4 — t — » Ps. — 4 > 1 3 ‘2 “ j 1 V ’J . . ^ 7 ? ZD .. Z' ■3 7 * * A 3 . ’ ■^7 • • * • « •• • • ••• » « • « • • ft ft •• ft « • 72> £ 7 r i <»A O Cj C' 0 O O O Z2 C* O O 3-* O O 1 I 1 1 1 l I i 1 1 1 1 I 1 1 1 1 I 1 1 1 1 1 1

J- .-■* ►«— X n o :0 : •*4 'O «■ *4 r A r > r^ - T -A * r »'~4 .-A 7 “ , »v% N ?- .a * n — —- XX t-vw , 7 j-*, r - X V p *7% «*• N. -N —' 17 77 O '2 ', J A ’Ij O 1 3 1 / 0 77 O 0 '3j a 3 3 o 3 3 o O ■ b 0 b "Zi O O 0 b a b OO 0 0 • •• • • * • •• • •• a • •• « • • • • • ft • • -•s 3 3 -- D - - D -• ~ - ■ 3 - ■ - •_ » - c 0 O 0

y * *A * r 0 — .'■( s?" X X _ 4 .,7 *•» c A -I"A •A *** X p > A r * •X ■_7 .P. • A v - » J P ■ A l A X 3 A z z o 3 D r«i o 0 A A X D 3 ) " v 3 3 0 3 3 , • % . ~\ ’- 7 . .:- j 'j Zj _ > . ^ '15 '.j . 3 3 ) ‘3 • v • ■ • •••* • • • ••• • •• • • • ft • • ft ft • . V -*> O . 3 3 5 3 a T 3 ■ 3 3 3 3 3 3 • -w* 2 2 • 0 1 1 1

► , , fc ■»*» * -•«_ ip-' •J"X "«j ■£’. u “ . 0 •V > r O' •» •• •• • • •• ••« «• • • ••«•* •• ft _ y *^i 3 177 1 3 3 3 :- o :- o .:: O * 3 3 O ° —

. — - -H. -> ■. - .- * •* O -. r O ,v^ A\ A- X — j c C p X *i.. '■L1 A •N* X < - .7 —* P, r A r , • • f « • «• ••• • * • ft •• ••• •»• ft a •**> ■V*. N"H *T T f V - n n T ^-v «r» s T c • p n •0 * < t --P — — < •— "* ~ j -~* *— “ ™ **• r— *-“ ‘ ““ •“* — 4 •-h r—

*•. -■ \, X K» ~ 'l s ' .A ■ X V ,*A .*A 3 * *r* XX • » • • 1 « » •• a « • * • ft • ft • * • ft ft * ft ft n ** ■ X i p O * 0 P* A > * r O A s > r * 0 % r r A r A V. A « p4 X x •X > r <-i 1 IJ>, n m O r ^ r ^ r . A X X 1 1 I 1 I 1 1 1 1 i 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1

X «-a CO n .X V; >. X r A s P *3 XIT £ } X LA X r c r A 0 • •••• *• » •• * • • *• • « • • • ftftft • • ,-«-* •*■. *>, *N* r.' j, •7 ; » v v T ••* ^ 1 .X —* ,7 3 3 0 n 0 .j* * 3 1 .“N - r *j“ 1 > t 1 1 1 1 r 1 1 1 i 1 r J 1 1 1 1 i I 1 1 1 l

*s 4 ,.- - - , ^ - — ,«* .«.

L- X r \ -r- X ~ 4 r*. t~r nr* v T jT> i p f-W «g*4 *— ■ ^ p — a r h

-> , ^ , _^1 ; r *C“ •'». r*^ 0 r - •**. i.A > 0 ■£■ , *>. a - > * Is- X V * • O c x :C j a * Zj> 3 > O a f— 1 —* •A —« — 4 «— 4 *“ * +m* — 1 — —J ■x, ■P%* .X I'v 'J X X »'v “

_ I •*» •O r».i - A < r 1 r \ jj .V X r A 0 *71 3 > x x » vj x m -'A rr- m ,v> r A f A ■ vr 7 P -r - r vj* ■*^ > r 1 A •,«l <*a ,*a r A -rs r*-^. /-* * n i*A ■rt •*A •<*! A r** A A “A r A r A UJ L~ V- V*** • w u . u L* 'w~ V- 4*»‘ o - Os' V - ^ «>J o s u -’ ’.V U-r o s r>. - 0 -J -V ISO' 'O' 3 ‘ O' O' o* o c* C C s» * vO w* v~ O ’ J ‘J! S'- _£s X— c* c r *'• »iv X r— r • s,: * v O - -T' ,V,- f— IV X rv. X fv X X •J-. X X :«j x v x r-jX rv v v 'O V -v ■v! "■*40s or O S' vr» -> *' v-w*-’ W*J ‘‘mrJ W».*^.’ X* X X rv iv t— o 4s «.V-p— VX 4— X — -«s, X *—* s •J WW *. | ■C_. w lC. Y L-.-v V Y X DlcCr. O* 'St lc 0s x X w»j f^ C c c c — c r c c c c o c .. r -: c j c - . c r ■; -o c.,

i i i i i i l i i t i I i t 1 i i i i i i i i i i V. «*v , ■% O' > J ‘ 0 , } J •o* w 4*,, "J i ;*•.f- _IV U-‘ O \r> C- c _N u c; 0' -t' r>. s *■«- * r o •s W : C*' “S •• 4 4 4 4 4 4 • 4 4 4 4 4 4 4 4 4 4 4 • 4 • 4 4 IS j X‘X v>J o c> V wJ sC c a CZ- X CO - -J 'V -'• vC c 1 1 1 1 s o» X IV XI •0 *«^- >1^.[l »s Sj Si r—►— u> 'wl«». < sX *>4 O o O •S’ w-> 'v»' X X X c wNi X r-“— • • * 4 4 • 4 • 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 JS i • Vv *^s ,^ V. X r—* '•'- 01 o -

. ^ ►— t r—j ( - .. , ■ . . . r._ . . r_ _ „«, - — 4' '•wS S* 4- ■V. ■wu o* u- S ; ■J* *«• V-' ^: *\w. 4' ’»«•Jn 4' V- s. • • • • ■ • 4 4 • 4 • 4 4 • 4 • • 4 4 • 4 4 4 'S' .s, vV O1 V" S' J- — ~v C’ rv r X —s 'S 'J • -W Cx c- s*‘ O' „s X :- V- - ’ • “r~ * ■ w - ’’ -

c O O C- C e r—»r-~ r— c: . r- c C‘ r. 4 « •• 4 4 4 • • 4 • 4 « 4 • • 4 4 4 4 4 • JS, v c -s' — r-- -' 'V " "■ ** • ■s. '• w

1 1 1 , 1 1 , 1 r- 1 1 1 r i c c <_i c c i r . O c , . c r- r, • • • 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 • 4 4 CT1 C ' C' ^ ' **• J* - r-- c c. o. r c (. * ‘7 r rj *“ o c.- c o c T_ ‘w s. .'* — w o-- :“ O. f C r. X f— rV P— o £ o X U ‘O W. *V P— x UL •Si X 1— c. LI ->4 — c-' X U s V ■S, — - - c X o r~~ c c c. c* c £" • c c c cr c. C ;;■ c- c C- c c pk 4 * • • • 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 • 4 4 4 o c o o S. c c c o r* • c Q v»- s»_ c r o r. c c c c c r* r CJ c /-• — r* c^» e\ c 'Z. O c C- o o c_ c r . • jpck UJex. 2 1— o c.: ■s. —J r O'* O’ _JS •> >—►— *-» v^r sV f'-.v h—s. rs s cc. UT* r*^ Cr _s w rv '•w wr XV X 1,41o . w“ tKK "V y:n 10:J

1 i 1 1 1 1 1 I 1 1 1 t I I i t I 1 1 1 1 ! 1 o o o O Z3 rm\ o C3 o 05 o o o O o O C • « • 4 4 4 4 4 4 • 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ■ c V.." C s ■ r; s. O' c. e '* c »X r— r- r*» X —• zz *— S' •——• p-»— 'V •s O' vp /”• 4" 0. c h— ex •J* L. r—- '-V c x -- -V .N.»X O' v«i OJu. X o VO —I* U-’ o X ■o- a f— SJ 0"* CC vC c- c. c C -■ - r. cr» - #» • C" r; r- c o* cr r; c; r- o w c 4 • • 4 » 4 • 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 c c o c c a c c o c c o o o c c c c. c c c C% c* CJ C.‘ *0 O' — 0- 'O c. c h— .■*• OJ "S, r — X rr w ■>. -o s O (\ -s* r— r—• Vr. »* r* r“. OJ o O X \J\ Ui VO •V. w v»- X u -s* 4> X V. s

J> L*w‘ V r— X C O' c o C C ►—* o c o c*> a Ui V LV o O c o o

XX r~ V- X r» > c O' U1 c- w c c •si c c ws‘ o c o cr ,- u* X Wh> o O %k’ o o

r“ rv X 4^ VJ »—c X *—» - X o ►— w V- h- *■ ►— X ♦—* X »—

C. c; c c c c c c c c c c o C- O o c cr c C' c c o c • • • 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 • 4 4 4 • 4 sO c c U1 X v0 rx V- Sm) VJtf o c c r-^ c r—1 c w* L0 e X 4> rv c* 4— 6ZI -J

•A 7 > 4 r. ,SJ —J 3 0: IN.- ■-*4 rA »—* -4 4 Aj «*•. 1 A. O' ,^s O' 'S C\J O ■03 'C 0 O' ■T -T O O' r7 lA m ■ •••••• • •• • •«* • • • •• • ••• •• 3 3 '..* D Q :3 ’3 • ^ 30 30 O a 0 D vO 0 -O O 3 O O

,-a in •■4 —4 rA —4 7* sT *A - 4 f\J - rvj - : - i\j rA - rA »X 4- rA rA IN •

o OC 30 rw 0 r-- a .*\ j TD ••m* •NJ •4 *A O *0 7% O *—i ^r C\j mm4 rv » u_ n O o o 0 0 0 33> .: O A jA O a s t N. X) sO 3 *— V O «47 vj j

,•>*» ■ *% •s\ 3 7 s .M 7 s N. ■*o A -7 7 - a? 0 x '*V rA O 3 r^ —* Nj 4 3^ •nJ’ ,%— 33 —* •» rA f * jA JA •J* —t "NJ —* h3 O O' 3 •3 •V’ 1i .O ■’0‘ — O —i .3 O o <*3 *“"S O’ ■33 c O ;3 O 0 a a O OO O •33 O 0 0 3 •• • • • • •• •• • •• • • • • • • • •• • • • ,3 1 3 "s o 3. ’J _■ ..;■ 0 ■- -- •13 3* A 3 3 >- 4 -A 3 0- rA C" C O r - ro r 4 •s-. JV A- (NJ OO 1A -7 cc 4 *r. a* •—< 4 .—■ O f-4 j3 —4 z> *0 •A O O A O 37 ■*c 7 s ■0 *44 *0 —* .—j .Nj —* a ; —- -- V N- 'V — — —* — 7*1 •N.> A) 0 #— — j -•, *> ~2 33 •.3 33»33 a"'* \Z ■O .*3 •*o *7 3: '3 7 " '7 7 •3 37 r*\ •3 O i— • • • • • • «• • m « «• •• • « •• • •• • • • w 3 O O O O 3 ■C F ’.*w> —i A ■N, O —4 i--' 0 c -v> O *jA ■% ,'j — .3 33 *■3 — J> 33 3 .2 .3 3 7 .j •A r—» V 3 o O o 3 O 33; 33 0 OO O /*> 5 O 33 O O A 3 3 O 3 b A. • » t • •«• • « •• t • «• ** •• * **• • * .*■ _ ^ * •» 3 3 3 0 'J 1) — ’• .! O - D 3 13 .4 0 V 7 4 AJ ■ * r, >• • % — --71 __ TJ ,-. »' -7 rv — —, :c > . ■N, 4 % 33 -v» _3> 3, 3' A a * T. **- •a .33 ■*A —<4 N. •.A l.A —« - •7 »K •s r-s 7 *33 — “3 —• 3 * •*• — •' 7 A O A O 3 7 33* . 3s j ; Tv 0 33 AD “Z .3 .7 ” j .37 7 0 -3 7 3 • • • ■ ••• • • •••• • • • • • 4 • • • « « • ~> —s o o -/ .0 > '0 Z> A .j > 3 3 O 3 3 I 1 1 1 1 1 r 1 1 1 1 1

«.w - 7 *T» N vT 1* r\. c — 4 1 • •• •••»• •*•«•• • • « « • t * • '*1 j-s - 4 A r— * 4 ■» ■ 4 3 ' 3 3 D jy r~‘ 3 a

. — , , —4 j- ; - -— »4 * r> "\i -’C A 'A 7? — A*. -7 ■ 3' 'NJ O 4 • * •* 4 • • • ■ ••• •• •• » • • •« ••• +**i vs f*' -r\ f 0- vT vT v*» sT r 7 A*; Nj r s T ••A 4* 4 - -4 -■■ — —4 •” r< r— ■—■* ’ ^-4 • ■*

*. ... jN _•*, ( ^ - >r •*>» O V > V- - —N •v w"' 4 O >- • i • « •••• • •* « ••• • • • • • • • »• O IT. *—4 ■_A •0 c O i*"-, * *> •“C O N- V?- **- r* CA rv O f— 1 •A r~ A- 3 1 “S, ro s*' vT* -A "■J* L"' «s_l I I 1 1 1 1 1

ns r £ ■*4 *> O _ CN. “\( •«* S, I l | | | I 1 1 1 1 1 1 1 I 1 1 1 1 1 1 I J 1 1

— . - , ^ .. * __ -*■ ”j) r- "j — **• 3 ' CM " “ »—■*.- ■ «—♦ *

# ^ , S. . —j r -;3 N—. . 1,. *4> ->. -» .-• ’*- ' v> ,■ A — NJ *..•* -7 -.*> *• -- ' ’ *• T' j 'Vi v i s "

, *—i -.•« • 3 _ J _. — c . «-*s ~ T' 0 •v; ■O 'i. r;-. 'C 3s •V 7 7 - **■ .* •w* -- «*> —— — -* — - vT I ' 1 A on; ok X VV ti-O PKOPtK Ml TIG ; INI . l:

AO I ’•21 i_> -33. 6 70. h 1 A . 3 0 . 9 .J . 0 0 A 6 ... . U J6 1 -0... 1 i 7 »j • 0 0 6 L 0 G L 0. AC2 • 2 2 , r - 3 3. 9 3 6 . 6 1 A . O' ' 1/ • 9 0. •J • 0. 0. 0 0 0 G. AO 3 32 9 - ■' A .a 9 ? . 0 1 2 .'.‘A L . h i>. lJ * 0. 1 . 0 G G U . AO.', 126 W > ~ i J .2 ,‘i ?. 2 12.2'. i . S . ) . ) i / / 1 ; j . 0 0 0 9 - 0 . 0 0 3 i . 0 9 G 9 0 0 I 0. BA A 0 > 32 7 1 7 -20. o hi. 1 1 3 . 1 i 1 . A v i . w 0 3 1 O.00 22 - 0 . • j 1 2 A u . 0 J 2 2 GG 1 0.

A 0 oi 3 3 I - ! 0. 0 ;.a .0 ! A . 0-. 1 .0 0 . ^ 0 7 0 u . U 0 9 .j -0.0207 J . GO90 0 0 1 G. ■> A 0 7 3 3 A - ! 1 . A :.3.7 1 i . 2 9 [ < . ., i,. 0 u 7 o 0 . Oo2 J -0.0039 J . 0026 I 10 G. 02 i A 0 ..i • 3 9 : 1 • • 7 ;> 3.0 1 <. ■;> r 2. 1 U, . . *‘ 0 VI A vj • 0 0 9 2 - 0 . y 0 i i •J . On A 6 16 19 2 0 .9 A A 09 : 3o C.1 •2 0 2 . 9 1 3.O.; 1 . 0 w. vOA j 0 . 00 6 1 — (5. L. L ‘ d G. CO62 0 0 1 0. Al J S3;'. 2 2 9 -It. I 7 3 . 1 I i,. .,0 2 i 0 . ill., 2 2 - 0 . 'J I A 3 0. G 9 2 J 9 1 2 0.

All 3 39 2 W - w. 2 6 n . A 12. a-. 1 . 1 U . Oii 1 1 0 . u o 1 7 -0.0 1 19 0.0917 7 H 3 0. AA A 12 3 A 1 0 - I 0 .1 "jb. 3 i 3.0 3 1 . 9 0 • u . 0. 9. 0 G 0 u . Al 3 3 A f 0. 2 97.9 1 A . 3., 1 . 0 . J h b 1,. 009 0 -0 .0 2 SI 0 . 0 9 9 0 0 0 1 0. *> A 1 A 5 9 1 2 19 u 9 . ;i i ., 1 . 3 J . .J 0 3 3 0 .0 w A 1 -0..J 1 3 A o • 0 1., 3 3 lG A c 0 . ‘i Lj 3 9 2 2 3 i > > •9 9 9 . *t 1 2 . A '■> u. 7 0.0', S A O.OolS -0 . 0 0 79 u . 0 J I 2 1 A 3 0.9A

A Li, 3 9 ’> 2.1 2 -16. n A3, i 1 i . • , '1 0 . 9 0 . Ou96 0 • ') 0 A 1 - 0 . 9 0 a9 9. 0.0, 1 1 9 1 9 3 0 .9 A Al 7 3 b:, •] - 9. 6 Al . ) L A • 3 , 1 . L 0 . o G 9 0 J . OOt* A - 0 . 0 2 y 3 0. 00 6 9 G 0 1 o .o t Al -5 3 9 7 2 2 3 -13. A 39. 9 1 2 .7 ' I . 2, 0 . u u 2.9 O.0012 -0.0131 o .00-12 12 5 A G. 5 I A19 3 9 >.'• 19 9 ” t .j • 1 2 9. 3 1 3 . o. ;■ U.0UL1 u . On 36 -0 .9 121 G.09 3 3 I 19 2 G.90 A 20 3 99 U _ ,». 4 >• 1 2 f.s. o I A . 1 • 1 .o J . .J 0 1 9 0 .009 3 -0.9L .11 u. 09c.A 9. j 3 A 2 0. 72

A 2 1 3 0 0 \ - 1 .3 . 2 2 7.. A IA . lo 1. 0 u . 0 U 9 9 0 . 'J ( ■> 6 - 0 . 0 I c,B . 0 f • o 7 A A 27 2 0. A 22 3 62 -13. 6 2 1 .0 1 A . I,A 0. 9 U . UO i)‘» 0 . 099 b - 0 . i.j 2 19 ■j . U . ' O / U 0 1 0 . A 2 j 3o 3 2 1 > -16. 9 17.9 1 3 • H A I . - 0 . JU 3 1 0 . 00 6 b -o.ol.i 7 9 . OOo I 2 3 9 2 0. A? A 3 6 A 0 - 1 A . 9 10.9 1 A . 3 , 0 .7 u . 0 0 1 7 0.00 39 -0.0 I 6 0.00 3 9 0 0 1 G . 1 9 A 2 9 3 6 3 0 -1 6 . 3 9 .0 I A . 3 ./ U. 0 0 . OOOl l,. 00 3 1 - 0 . 0 1 32 0.00’3 I 0 0 1 0 . 9 A CVJ CO

f. • f . _ 09*7 *o i n o 9700*0 If 9 0*0- p zoo * n £ 2 £ 0 * 0 1 * I 0 9 * £ 1 '/ * 7 . P . - v £2 1 1 «/ *0 7 ft 9 7.ZT £910*0 £0Vo *C- l if m* o 9200 *0 V*Z >■£*£ 1 £ * £9 - ZV- (. £ 7 . 0 1 *- ( , *7 */ C V *7 26*c Z 27 V2 7 9 'ifi • o £ £ 1 0 ’ 0 - 9 900*0 Z *7 0 0 * 0 9 * 0 • I * *y I 9 * */ — 2 * 0 1 - £0-7 t *. '>1*0 I o 0 P <7 00 • 9 £720*0- 9 V>'' *•) * 0 ' j • 0 ' *7*91 J * 19- t * I 1 - VO l' Z VJ7 •

1 t •

0 c n *,• p 2 * n I n 0 9 900 *0 £729*0- £9 ('0*0 ] 1 O 0 * 0 " * 1 c':m *?] ■ .~V O *7 * 2 2 - ■ j *1 *7

*0 6 7 f:i £ *n £f 2 ' > * 0 - *7/ 00 • 0 0 *7 (if ■ * n j * n 1 2 * *? 1 9 * 1 9 - 9 ’ / 1 - ( 0 2 1 0 9 9 V v U6*0 V 9 f 1 I 0 0 • 1 6M ('*■;)- 1 I *) 0 * 0 op ;1 * o (,■ • ,q ' ■> * £ 1 v *£'.’- £ • 9 I - i I Z f h V. V V V *n 0 0 0 * o *0 * 0 * M • * 0 f * *7 1 9 * 2 9 - 1 *£ 2- V- £ 0 £ ' *: *7 *0 1 n 0 OSOC’O f:Pl-J*0- 0 900 *0 9o io * n 9 * C. 1 9 * <7 1 9 * 2 '7 - ■/ * 2 1 - 96 V 2 V '0 n n 0 * i *0 • 0 * n ( * 0 1 £ * £ 1 2 * 2 * 7 - 2 *t 1- 2 2 £6£ 1 W

* • Vi* rj P. PI 6 V2n9 *'■' 9Z I 0*0- i/ ,.’!in • q ( ; c»q * r } • 0 , q • i t - 0 V - •A * o ’ - ( 2 2 I Of 0 V V *0 T 0 c rc.-.Q •«••, <;**?‘‘0 0 * r v * 0 : r- * *■-, i 0 * 6 £ - 9 * V 1 - r i f 19 < ' £ *7 VO ’ 0 c VI r z O',; j>o ’ 9 CO m * 0 - or on * o 0009*0 1 *0 *’ V • v 1 9 '9 c - 0 • Z. 1 - 1 I 2 v-'p £ Z £ V 19 •n £ 6 ij< p z ^0 • o OZ I 0 * u- 9 2 00 * 0 0 p o q ’ n J *0 •Z -f : o * 0 1 - P * 7 2- O 6 1 V P£ Of V c. • 1 2 9 9 ( 9 00 * o i t I ('*<)- q / {', 0 * n '/ 2 0 0 • r 2*0 > 1 ’ '/ \ £ * 6; 7 - l) • f- ! _ i I -,i £ 9 £ V V/ *n 7. 9 O pion • n f 0 I •' * 0 - £ I r o • o ('if.qn • n 9 * 0 11 ’ I •; * p 2 - r * < i - (■ I 2 OOf *- V *7 I - q n * n 7 rr VO /poo ’ 9 9Z10*0- 0(00*0 t. >, n n * n f * V ! £ * 9 2- 7 * 7 - f /.'■ v 6 *’ -P ,j • f. *n pz <. f. £ J Li O ' 0 91 2'* *0- r,;oO * 0 9 2'. "' *o : v * v i Z *9-2- V * Z ! - 7 J £ •• £ V f *, 10*0 1 M 0 9< 00 * 0 f f 7~ *0- 7 fno * q 2 £ 0 !. • n 1 * 9 1 2 * £ 1 - f ? ! - ,J£ V 1 f v

nv *o £ £7 V I P f 00 * O 2/10*0- £ ? on * n 7 p (•.(•■• r * ft 1 ■ * £ 1 ( - r. i - * <• l - ' ' 5 V .■ (. l * c 2 VZ £ *: £-.> GO* o p; i•• ■ *o - 90 0 0 * 0 0200 * o 9 * *' / * v i 'J * 7 l - £ ' £ ! - £ £ 1 ' 2*7 If *0 £ 21 Z I <7*700 ‘ 11 £ *• 1 ■; * 0 - f v-iQ *0 p >.n • n f. • M ’ 1 * *7 1 0 ’ 7 I - 2 * 1 7-. £ (' 1 I£! 2 *' t' - n (: 0 * n £ £2 f-Z Z *’ 0 0 * ° VZ 10*0- I von • n I « o " • o / * 1 I * •/ 1 7 * H - £ * o : - . 1 ? ( V 1 Z 2 V 9 l'('Vi • o 9*7 *o V £ 01 r o n n • n n ri'*c- ( 000 * 0 V * 0 ‘ V * f i Z * £ - 6 * 1 . - ( 9 9 V 9 2 V

ti *>!>!?• 1^1 A -' I AA y M 'J L» J 0 \( I I —■ <7 X I’K.iPcK -inn,)] IMT.cUR 3 o n i s o o n i <\i rom —< O C 3 O O C o o o rz> — a m o cr •—< '* '* 3 o I I I I I I— •j- —< -3 -5 'V : *—4 0 3 ro ro *; ,"■* grg og \ rg rv r g r c\j r-m- f-"* y - A a.- — — A *v o v — 2 3 3 \ 4 » • • t o

o o r> 3 o N_ •i* n - X 3 3 3 3 — ,f\ *n- n 7* ", n 3 I I I 4 • • *n j n - — a — . r 4 - -* C r“ d Z 1 k r • • •

.\ r\ ' A O O 3 O 3 x>x -x x r %r O , « 3 c -r •c % * v% I I I I I t — I I — t I 1 • • • • « * * i • • • • • • r o g i n m ?n xi rg rgA m ; \ / JL ;5 5 o * — ,3 —J •'j ;*» :c ■ Ct n *— eg sr 3 3 .r. n I j • « • • • _ L r -vr a “ vT *r -r V J" ( m j • • * • • « • . • v . - > — rg rg a ' O x r *r, a x 3 i i i i r ;

rg rn —* '■•S -3 •*rs ■V* n M LM " l O O — o fv'O N ‘ -'• - O ‘M - v rg nj 3 '1* .A .A '1* t * r c* vt — I 1 II — i * i a * • t • • * m i O O ■O 3 O r*> 3 3 3 • « O" O O ■vj* -uo o D ' 3 C * » * • - » 3 o o O O ,~v, r^i 3 3 r n vr 3 3 3 3 '3 A . r*» 3 1 1 I I I I I j • • • • • • • * • * • • 4 • • • • • •

— vN r -y y j -jy rr- , ■•» rg O O o oOa O rg :o o o (V, S- r— X “K a — - 3 *; .V 1 <■> > • • • • • • ■>

- C\ o 3 —• rg O cz in. a *“ •r» -n -n 6 a ” < 3 3 xT 3 — r A - •"5 "Z C 1 • • • • • • • ■

n •ari ——g 0 *— 5 ' *J' n •<- 3 — — m r.-s , O r •^ „r r >r >r ' ' j 3 3 3 ' ' j - - c- 3 3 3 3 3 t 1 T 1 t • • • « • • • • a * 'r ^-4 m rg O rg Jn >J 1 r o gm rg r^> ; n —i 3 T - X "Z 3 J 1 • • f

rn rg *S. - r rr ■rg O r r . r X g r » ^ *x» 7 .77 * vf “j xT 3 t s _ J . n A <■ X A 3 3 1 ^ *. 7 • t • • • • • • « * • • • « i • • k rg O o rg i r rg r j A m — mm* sT - ro .~ n ,3 O X s" j ' 3 .7 r> 7 3•3 .3 —< 5 3 5 1 1 I « • • *n O t.r ° 0 c i- r*- i*- - n g- — a >r >f ^ 3 X A o - 3 J- , x _> 3 4 • • • • 6 O t7 »— r r •X— r> 3 O O •> -**N g- mm* -0 rg O a sT 77 -.3 . A A 3 -■X,77 4 2 1 • • • • • • « • « • i - - •NJ rr\ fA a O •H rn O c r* r r Al N» <^v *n O gg- ., | 4 ••» —* ■A 7, •* 1 • • • • *

133 X X Y V j’-- V »'•!{,';i»L>< .'j 0 T 1 0 * INT.CR* • 3 V f • 'VJ s v CD v r *r, D O o -\; -S ,— .— —- M, • i —• ■ ’ ^ — —i ->V O •3 4- CD j*'. "V /; J, . 1 - ;•"- • J • • • ,, • • • • ■ I • » \ o r v r CO —< .*7 x . 5 --- y* -T, '*s. x -*-- N- .. ... ■ A - • -i- n -f '0 — j-s “ *■ i 3 a M • - . • • • • * « * • • ’ - 3 lC* o x - r V. — - 3> 3 ~; X ID d _ “O 7 rs sT sT N- ro .Xi r— s ••x •sT TV *V» • V '•C -■- •- -13 3 3 3 'JJ - V s 0 1 1 *-» * * • « • • • • • • • * O f~S 05 r** s. .s N- -•'*■ ‘-;V 0 o - _-> 1 c -■ • • * * • • « • • • • • • > » • ' : m a — O AA. o *'•». r „ r ■C ^ nr, r^. ■*N rv_ C3 , ” - h x 3 -- *; . 1 • _ « • • • * • « -''.i 3 • n »\ •V — 6 — •n '.3 —» - 3 a --- N sT vr - _ j . - - ,-v /3 4/ T i 1 i • • • - > % • • o o o O' «r> ■ -i - *■'- r^_ — 3 7 3 >• r c ■rj TV' TV • ” 3 3 i 1 A • • • • • • • • • <-o r*\ X X ' s ; T3 ■;_T - r s v 3 X A*, 3 AA -A. X X rs. 3 v‘ 3 ' N r* 1 1 ! i _ A • • • -. • o p r o O m <*’ o **" «r> —« w - A v r rv 3 •x -.- -3 7- 3 “•1 v- »S vv*- Sj N» . j 3 3 'V ~j i 3 .. 1 i -*1 • • • • • • • • • • 4 * • « , ^ _ o O AT, 3 —■ — 3 ““ "V» si- 7 ■A -_> — ■3 -~ f'A 3 „. 3 3 -3 Xj 3 3 3 '* ' * .«> - i 1 •« 'S L 1 iT - - • • • j • • • • • 1 » sT - o . v o >* C'i —4 3 . . -4 3 O b o O O 3 •7 O N o 3 X 3 v' .r - - 7 J 3 “• T f _ 1 I • 4 • , %» -O' .' *. o 3 — X" -r A *A -A-* — fv* - ,A ' •*— a a -.-J -3 x D ••> 1 1 - "v » ■ * • • • • • • —. '*0 s v ^-4 —A r*>- ■ -0 3 »c* »*s '.V Tv X - x — 3 X* r> .V -•> 3 O' o \ 7. 1 r 7 1 1 r- A * 2 • • « » * 1 - r 3 .~j. ,Nv v r C'J *w #— - f •■\l .3 - ■D s » *\. •+\ ^ * TV ,r -As 7' *SJ X‘ vs ~\ J, .A. 1 1 .A. V 1 V • • • • • • • • » • ■ • • • • • • 1 •js, • a —4 rv ■x» • • \ — —4 . s — — j a ■j* — V •*s —4 < Xi V- X. v-'‘ -r o r*s A-, rr X k y -* i ;Xi :; 1 2 -4 t • * • • . • • • — - 3 •-N - ‘ C ■J> 'V ’ O 'TS J X 'r *v V 1 • * • • • • r 1 ,A> V) 3 o - O C5 3 X xx ■x r*** 13 •“-Ai \ r rv c - Tjs “v, ;3 **; Cr v> s* VO TV ’ X - '*’• A- A _ •A, 7 o 3 -1 1 «. I . . • * • • • * • • • t • «-v X x o r O o IV rv -H rs. •—4 *J _ v.** r*sj CT‘ • -7 ‘ VS A*, • *.» *> a 7 0 x 3 ■■-• -■ t» .f D .r 1 1 1 « si , • • .. . - CO a O 3 — «sT 0 TC — X- —• •. . XO' •X ■X •;S “A O' v . x AS 0 .V 7 X j «. t 1 1 I • * • • —. * • • • O i 1 3 •— *sj b s - s v 'X 0 i m r** sX ' • - r 3 ' f\ f »‘S •%», Mi 1—1 -•4 X rp 3 O* 3 r> n b 3 n P. -* - T 1 1 0 • « • • • • j • • s 1 . ■ -r — .' N 0 X •3 XO 'X •* •O' 1 —I “*si - c x X —4 v r V. “7 * 0 r, V 3- cC c c . sj- A.r 4 X / _ : * s . 1 1 3 * • A A ^ • • • • • s • •

. .vs r r <“-J •«». V w3 r*4 0 3 M. A ^ *A. X O - r (V O “ f's: X- •r> -SJ *** —• ,3 .Q 3 b O' 0 •X X 3 O “ :> c 1 r 1 ", • • a s ~ * * • • • • • \ r O <-n O O - 0 »»* •s* rv O s • <* X — rX CD T ,3 A _p, «As CD ID VJ -3 -O' >r "■s 7> X- O a 'rsi O' A* IT *7 3) 1 rs 1 A. * • • • * • • • « * • • • 1 0 0 0 0 • 0 CO •O’ X X 0 0 <—i 5 n r*x- mi rv 0 sf' f v CV, Vi VT \ f X r-' *“* xT C7 b — .-S 7 3 1 1 I • , • > — * >* * A 7 • -A“ 7* TO % >< 1 4 j I* b H • J T ! >! i I <11 • h KK rA rv rsi o p— f*\ . O '.O 3 S ,!*■ X — O — — X — Vr .%, rv *V r+* *-4 f7 : x > x >- x •:c 1* WM L.A >■■■4 O - 7 '; v rv 'A; rv V 75 '0 .5 .:■ -7 ■*N 2 1 J 1 1 1 • • * • 7..A .7 • ^ ’* * • • « • * « ■ • • • • • 1 ...... • * • * • < —. CO Ai«4 AA f\. p— '0 6 O O r*> ■ -• - p—4 - *"> 77* -O •y '. ^\- o» 0NJ70 - —\ .A A 3 - ,7 A 1 3 ••- • • « • - —4 ^-4 O; 0 O —4 AJ 70 . O — -4 O :J 77> '-A ^ c ^ ■0 '77 •O ""C ,7 - -TO 3 - a • N 0 1 A • 0 • V > * J • • r>— ° ro .“2 “A TO •—\ —* O rA Aj —* %0 Aj »4 p ' ' *'w l O A 2 :o -? 2 .v a ( 0 1 1 *^ ; • • W A — « • • • • • • •

•; » O' •»p ■■ *0 N- Ar- rA O •■*. r Q —4 —. *A *v ■- - 777 O ■ -* v >* ; J \r a O O •0 2 ,,A a «_> 1 — 2 r> J1 - - - • • • • » , rv O P-J A5 a •vN Q Tr rv rv >T •17* to —. rv a —s x r.‘ CO _ 'TO . .J~ —. —y . — ~j ..J _., :"i *3 j O O TO 7 •0 “■ 75 0 C A l lA a l A 1 y—«•-y ■s > * • •s ••• •* ■> • t ••-, - 0 0 * • v' *’*' --y • • • • « • • • • • ' vT -A 0 O rv —« c Ov V " —4 -r T' D - ^.4 P-~ — .0 r*1-* N i; O'; i'; *N. a 0 i 7 ^ 77 sio 70 — ( i 0 J •*. ) • J • • t • • • • • 1 . A '7 A .A : 0 0 — JO “J 0 0 0 ~ r r ,0 «—1 O rv *r 07; A . —4. ^ .‘J .r- -V jn A A7C rA r s: v •r fc >. S 2 3 A 3 V • • • • • • • • • • • • t • • » . —• * *• 1 O O - 3"7 •3 O N• *v ^_, p^s Pf* A *r ^ O A .O ,*0 »vs n 3 .v O V -7 'V * ’ 0 .v 1 T 0 t -4 • •

a l is ■n t<^ 0 1 — r*“ 0 — ■C” -0 C“ vC O •_7> O 7 ; z> - . j '"If 1 71 • A « • • * • «*✓». rA O rA — sT — c •-- rv O - O -T ’ - O p-. — - '7 p— 07 'Z 77- *— v -vjrv " A" ^ 7 77 > T A •> r~^ 0 •N n —» -j* j 1 - «p -P A A- 0 • • • • « • « ^, * ,* * • 1 « • • • * • ,* • • • • * • • • O AJ O O O **4 —* :A •*■ .. > TVi 77 *A 0 - T V7 TO* • . “ — p— A —4 i“" C ’A ■"'J 7/ LA A P A; *> “S A ( n • • p t • • * » » • • * . 1 -ys • *■* ’•- - '0 0 _^-s •V p OO TO O O r— ■1— :o 77 *r n n TO ■yf — c i 0 •* ~1 7 T 7i • » •' • 75 — ‘.A •■*A O 0 O —- 'O •77 •y*» •T 0 • •V — ■C rv a O 7 ■vO . ■•. *“1 ■O' v AA J" -' '2' 1 r* “ -• • s t n ✓ * • « h 1 .A

IV fw 'V rv sT O 1 -A -A — v*7- *v •w rv 7 — ^ 3 —. cc- l - •0 — *N_ V 7> ■*-. - -* s j >t •C — s 0 1 r ,t ■ j • • * • • • > • • .—4 ^ O O A* n ^5 -* P»4 S a l 70 ^*s A 75 *— T 7 •A .A -C' 0 a 10 •■' • • • « • • • • • " % - > V LA p. c 0 0 s. N- — S X sf 0 n . - ^ r r- n 0 • • • • • -, •7 j • . J • • j • • “T

vT ■n TO rv 0 C f'S V 0 *o sT O p-^ •>r rv O V V 0 'A 2_' •\l "5 O - 7 i 4 • • • • - N -5 _7*i ■y *> •>» ;A J , , J • • • • * • • ( » • i 1 p** As) •V V ,*y*i »T\* . V', 77 N-. PA —* — — - rv rr*. *— p-< •r .0 A LA LA J P — .7* — 7<» - O •ji r r> 5 ■'•.* ‘5 r> *r. 'V *7 O 2 " T? •"* >^—>-> ."N ,A 7 1 .y r • • • • # # • • • • • t « • • O p— 'T' 0 VJ '7 —* *0 > —< V -J * V fA «— - V -*7 0 r i rv JA rv V *) .5 .P 1 1 ^ 1 • • • j * "A "* • « J j

-O ’y l~— CT- r— K~r 0 •* — 0 0 <—i p X •*7 >r a 7** uA «VJ ,.r. O —• JA 7s ..A O •—4 •••v - 75 -s — - 1 ! • y t • • i 'A 3 - O -.75 r-~ a O rv -0 07 D -r*» *ss ‘::i T O py — L*“v LA "J <■ —* m— LA v r y ss D ■O -o 0 N. J> O O p».— ■ i .“S *s 1 • • • • • * » • t • CO «—1 Tjs .■A rA C - ?•" O '..7 rA *-4 -V 77 r^- i f V TO —- r*S '—^ *-0 '-~y •— :'5 O C ->\ TO -A -; •O' ** 1 0 “N "0 1 7 * O O A r> 1 • » » • « • 136 A pvj ^ j". 4* r;v O' 3? J> ^ 3 'V v0 CM * . . . * • • • • * • • * • » 4 4 4 4 4 • # 4 0 0 0 3 O 3 3 3 3 b O 0 *2 0 0 O

r\j cm rvj r\j —• mi m ^ ^ ,\j - rO n "m n*i Ml 0 O

■ y ■ s •3 O 3 f- •s- - r O 3 M) r- 3 CM 0 CM N. O O 0 a I • ' —I 'V vt ^•4

c n -o >r 3 —» o o o 73% *r

_r « w — 1 ■ r f**. •s*\ 0 . 3 7 vT 0 77. r^ ■MJ Cj r> •r\ r-» •s lM _ A .- — -< r \ •0 J .Ml —> 'si V ■*vJ *» •*-, M *» *. -> - » - ■ •71 . -♦, ,J7- O o 3 o 6 b 6 5 6 O O ■77, b 6 b b O O 5 • «« • * • « •• • • • « • •••« 4 4 # 4 4 •% _77 -s 77 J - ■7: ...5 0 - 0 0

vs r*- o r*» •v. N- 0 r- ,r ^4 rn a - a 0 ,-o ■■r. M ••A *•'• • r /**N —* r r J M -m —^ Mi — M. .— > —w CM m •O 'M — — rv "T* .*7* 7 J .”‘ 0 *7 7j O 0 771 77 7V v 17‘O- o ' j O • • * • • • • • 4 4 « 4 4 4 4 4 0 ' 3 O .'3 C O O -3 o o O O 0 0 0 1 I 1 I I I I I i i I I i I 1 1 1 i 1 1 cc ■J 3 «r 3 <* 0 -a s- o O 3 >r \ C O Ml 0 ■CM ta V* •j 3 ■ •' 3 -3 3 O 77 77 •>4 O 77 0 -5 3 3 3 3 3 .3 3 O n 77 O O O 5 6 • • 4 4 4 • •• • • 4 4 4 4 4 4 4 4 **» -' 'Z> - O _✓ ’Zi -V 0 CM ^r f\! 1 A*, ■7% 1 r*—< » V. » \i vj 'M .7 •M — O rv »M* 0 3 ~ —1 n —j r n o O 0 iM O ■7 7. ■™5 '7' ,7i O •7 r> •77 • • • t 4 4 4 4 4 4 4 4 72 73 7> > ■- 0 O 0 0 I I i 1 ( r

s. — 4 rv . — c 4 4 » 4 4 4 4 4 4 3 o r-* -v - i n 0 0

9 _, sT b "si r- 0 _c rVS t « ■ * « 4 4 4 4 4 4 4 4 ■7 — r (M V. Mj rr *“ • -j «— •A -^s r— r* ■ *, i.‘ c* ^ r.1 7s v**‘ *4 • *■» -* r •** V ■>- • % • ••• • • • • * • • 4 4 4' 4 4 4 4 4 4 O .7 ’C' -""• r^ 0 .r» r- ro sT —4 •0 CM. e * . 72 37 0 'C i \ i*"V. 0 0 r- •X' t f i 1 1 1 1 1 ( 1 1 • 1

• 2 ,*n T* O ■C ' .J 1^" *0" 0 •“* -7 ^ v\ 3 " -j _ r\ Mi if sT • • « • • •« • « « p * 4 4 4 4 4 4 4 4 4 4 . *s *AS •M r— — 1 V — ,1 . * -> r— — 4 fv. .Mi vC —' r- — ’ v 7,, — ; , — — 1 r ^ M *v- ‘v ‘ ‘s M

J* s*. 3 _ r*3 ( M '"V sT ,-rs ■y'. n"'

"5 » •A -w* rv .4w o o N. N- rc mj •> O O O 0 O r -. m ~*\ r o i •0 -»v 0 jO rv

• 0 •- 7* ■ ^ — 1 :M -*■ .♦ f. 3 ^ O > .*N rs. vT *> M CM r\i CM CM rr, "**■( r*“S ro cr r~ rr, vr vJ- •& *4* s7 > r sT sT ir\ .« /\ n -0 ^ * r. -rv UV u -“73V•av* .rv n r\ :m r * •rv r. rv t r • r or r\. p r.j rv V r"*, - ; ..r 137 -a. s* CC d o r-

•■a* o 3 c m - rP - rv p4 o #—4 rv *v - • V rS 3 3 c *7v '..J T) rv c *v 3 o o 3 o o j j ■V -"J — 4 S' w • ,r 3 O o O s ’ 3 D 3 3 a y> V*" >c 3 3 o ■3 r c o *-4 i 4 —* •a o .y', r.

f W J rv rv A • i CO a 0 a p + 3 rv »r ;n sT A J- ■0* p p- 7; 7 > ,p c »“> o ■ c 5 3 d o o C d 3 O d o o • • •• • • • » ♦ • • • • ••» • • • •• p *7 •*V p. p 3 ..* ■*j . j 3 - 3 3 >- 3 a V** IP rv tV r«*' •A A *N* p -ft ■** ~ 3 *-• C "vj V vT" • C r v —* 3 — -J A r— rv V r\. —y rv A —1^ p* — 3 Ti p. 7“ p;. 3 7 p H- • • • • • • • • • •••• • •• • •• O r—• -ft O O o o 3 C- O T j O o o 1 1 1 1 I l l i l t I I I I I I

Trl J ;-. ."V —. p P • O J- 0 >- .3. 4- p. A •C* •V (A-' •C A r. >r P; > ' 3 .*3 .«»• s w */ 5 3 3 ■5 o 3 C 0 3 3 3 O p_ • * • •«• • •• • • • • • • • • 3 O *• p ■*“ »-«4 3 'V N- -« 3 3 3 oO „• 3 • » * • * « » • • • • * • 3 3 .O "3 3 1 1 I I 1 1 I I I

a V —* ftft 1 i • i • ■ • • • • • • ••• • • ■ i * ■- 3 3 3 1

•*— _ V **» , >P - r- .p A ~-4 • • • • • • » • • • • • • • • • • «*■> •p .v» ^ p p . . *■ , ft ° A •V vT

_ _ VJ p lA >* • • • • « • » «• • • • « • rv —< r-* T* 0 ,3 p r>> a X ^—4 3 o O •—> p A-N rr, £ r ' "’'i i i rv -v >T Sy" A 0 i I i i I I I 1 1 1 1 1 r^, CV -C- •Nj Cr x O A 3 c: X r*"', x • • ••« • • • • » « • « • •• • •ft*. T •* J A rs* ■ ■/ t “ :V *■ ' • ■' r>’

• /

‘ Ij \r- : r •—< —■*

—j •««_ j 's.1 *A A C ■r. iV -p A - ■3 r— r.-. .*■ r-~i —I f . ~-i •V rV V ^ .-A rP Y*, v< - f vT >-4 7 ■ •J **• O •Z- Z' V A' 'U **" 3 1

~V •A * -j 'T\ - 4 .v . p — •4 '.V ft M A A Ip p . “S ip •P N* r^ r- , a P ft • p. p lP. 3 P •p. A A. A 138 n x •J* O *r •Xj X r“v rT„ r*j -•^N Tv' vf >*> Cu 0 ro O' cC 3 n O C^* O? 0 s sC • •••••• • •• • '• * • •• • •••••• •• ■> O O OOO 3 O C5 O Ci O 3 O '.v - O 77 3 3 O 0

•—> ,«r*, ►—< x - s.r X/ f's OJ O - XX 3 ■ 4 O X 'T « v 0 nT 0 0 c ■J- ,V* .3 us 3 X 7* .•3 O 3 3 C O m Jl X iXi rO — 4 **4 X

,■% 0 -r *3 V c *■* •~\ “h. O 0 3 X 'n 3 3 ■O O T. *3 0 A a LT* a*» X

x 0 O -C X 7 nT X 0 0 3 3 O 0" X ,n „7 nT ■~p, X *.**. X *n *> 7 7 r —4 r-»*N •r '0 ^r A . ^ *—i . J »■, N 0 O 6 O 3 0 7; O O 0 O Q O 3 O 0 3 O •* • • • «• • • ♦ • • • • « *«•*••• # m 3 - . *7 3 - 77 - *- - Ji - 0 - - 3 - 4 “■j "■ x - — *“« O 2, ■' > ‘vl *>* A _r\ —. -2 — j X — < -j x —* fv. —— ~s , X *►— »—4 —-— X X —' : j .:. j 1“ W 7 2. 1 ■'7 7 s 3 .77 3 • * • • «•••••• « •• •• • « • • ••• • • t i— 0 0 O rZ2 O O cs O " J n r; 0 : > O O 1 1 1 r 1 1 J 1 1 1 1 I 1 1 1 1 1 1 I 1 1 I

-* ^ , - .'.J •'"‘nj (V v*( n ■C X ,VN 3 ZZj f3 X J'' r. — j J^. ;s“k 0 7 •C" —J X cT "O .r r- p. jjn ;7 ■ “2 O 0 O 'j .‘7 . V *~ ."7 •7 3 ,*7 ,7 7 3 77 O 3 ■/ O 7> 3 J) *2* Zj *b 3 O O 77 3 5 O 3 3 O O ui. * • • • •• » • t • • ••• • • •• • • •• D “ r. - - - -• .7 - - .3 - O - f -> - >J •7 ’ *•-* mU ✓ ' - — —■ - - ■ - -> ■+ • J j , •—. •» J • • ■ •• • • • • t « ••• • • • • • • ■ • • • * *> Zj ? .3 -J ‘ - ■* .J j • .<• 3 3 3 3 •3 1 r 1 1 1 T 1 1 1

. _ mm it •<^ X .. X ~N •jy i t • • • « •• • ••• • • • • » •• • • • — ■4 3 ' rs a —- c 'Zj 3 O O 1 1 r- - . , , .. • . -s ■ ■ 4 .'“*V *7 X •“■vj r*~ 7 . K- C 7' •*;• -A ■•"1 X 1X 1 — 7* • « * * ••••• » • • * • • • t * *« •• « • • r> ■7 c* *r~. .r r *7 •v. ,\ *T ■r- \ V, -* •C •T

r, .7 t ■ .v» — ,- ■ r\ j ,0 1 % • -1 -- -.•l - •s • ."X X sT >• ••• • «•* 4 • • •••••• • ■ • « • ••« •n X PP 222 ^—. r^. '1'*. -r, cr: •** •77 >5" 0 3 A ■ «*l S. 1^- •>» j •X X ■ •C 'O 0 m X 1 1 1 1 ( 1 1 1 1 t 1 I 1 1 “T. ,—N . P — tl* >T i."\ 0 •<* <77 CC ”»7 :> X i7> /■n O x • • ••• *••*• «• ••••• t » * • t • •• * >•» rr*». S *N"1 %r -Z> — u c "* J 7 >- J .n r. _«ip

...... * % i"* .. * - 0 > j. > ,*. J’n O [V- ■ J s *o O N-, or T*\ r* 1 A

. _ n •-» •s V> m-mi > c , O x "V X A 0 - A %-t ■C C* .7 7- ./> O ■■Q > - f*^ r - 0? A 3 "s.* 2 ;j • Z : j. j c ,7 *7 7. ■C 7 0 ‘■'‘J ;“» 3 I, O 0

»*-. -- - .-Sj r. p. ■ -s f*— ■^S •O *C r*> 3 > - p- r- *- c;- ';*■ r. •*0 f/> .*7 : c ! 7 r> O' O' rr> 3 7 * O' 3 j-\ A •«n .0 uX ■ 7s ‘7, n L'y •T^m •.n iX J' 'A n J/N A A -.n O c<\cn

• p 1 0 0 VF 00*6 IPUI’C- Vi. 00*0 Z I 0 0 * n 0 * n IZ*VI 9 *6V 9 * v,. r. bf.J 9Z9 *0 1 0 0 f 2''0 *(■ 2'; 1 o*o-' 0 Z 0 0 * 0 ( X 10 *0 V *0 ."■9 * VI 9 *V9 V * u V f , 'JVZ VZ9 V6 *P I 0 0 Vf on • 0 SMO-o- vfnn*n 2200*0 ; *0 f-0 * ^ I 1*99 f * r- V Z V; v: Z9 (19 I 0 0 1 Z " 0 *n 9ZP'i*0- f ?''C* 0 V 9 0 0 * O 1. * n 9 1 * V I : -1» z Z * / v '' ZCZ Z?9 re *0 0 0 0 • • > *0 *0 * P 9* I . I ' 9 • 0+- 9 * f V 7 b i 9FZ IZc

• n 0 0 n * n *0 • 0 * P 9 *n ■; ; * v i 9 * 1 F. 0 * 9 v i 0 V Vf Z 2 9 • 0 c VI r £ • 0 • ■■; f,,nfn< f)- 0Z"O*0 I ZOO T v ■ r * 0 i ! ' I.- 7 9 * ! '• V p 1. f Z (19 t : 0 • r- 1 nV. 0 Z v r 0 * < ■ ?;»? n*o- 1 *-nQ • 9 7° V (10 * 0 < * 0 9 * v: 1 F * 9 Z 9*9'* 1 0 9 6ZZ 019 ii ? • 0 Z VZ 0 f v c o * ;j 9;- [ '.'*(’- 9 V 9 0 * 0 O / f: n ■ < ‘ <: •' t C**,] \> * 0 - Z * 0 V s' i Z Z Z 1 f 8 ’ n I 0 0 Z<;-o*>i If Zf,*0- 9900 * 9 n 9 0. r ■. • 0 r--. * 0 *r 1 P*t- V * 9 0 ) i i z zz r-1 9

pc • 0 1 0 0 vzon * '•* i VI (•*:.)- 0 TOO* 0 1 [ nr * 0 * 0 • • O- * c ] ;■ *z- 6*iv 1 vzz 9 1 9 /. * 0 2 Z 1 9 ? IPO* L 9 I 0 * 0 - c I on • 0 } do ■' • n Z 'f' W * f 1 ■' *91- V * 1 V •'Of f ?/ VI- V f. * 0 1 n 0 zvoO’o 6 vZ0 *0 - ?VOO*o Of fo.' •n >> • 0 ' 9 * t I V * 9 T - C * f «; l tv M l t I 9 2 9*0 0 0 1 21 2X00 *'■ V V1V' * 0 - 9 I 00 * 9 0 I 0 0 ■ 0 / • 0 : V * V ! 7. ' 0 Z - 1 * z f. >'z; 1 “7 26*0 21 z f> 1 r ’ 0 * 0 9 9 [ p * 0 - '1 I 00 * 0 ( 2 n o • n >: ' 0 9 * V 1 » ‘b 1 - V * 7 V f rf-' i <• 1 / 1 1 9

7 6 ' 0 1 0 0 C./tlO *M oozo *o- V I 0 0 * 0 v X 0 n * 0 9 * 0 ^ V * 1 I Z ■ VI - /. * V 9 ;'6f. 9 1 / ’ 1 9 ,; • r. *0 1 0 0 6 0 r n • 0 01c. •: *o- ri 9 ( 0 ' n l/fif'O * 0 : ( ' 0 1 ; * vv - f * 9 *> f: FI Z f 09 * 0 1 0 0 7. r- ' i 0 * C 9 0 /0 • 0- pono • <\ noon• n 1 ' 1 • * 1 9 * Vf - Z * Z v 1 1 Z I / 6Z *C I 0 0 2 V f ! P * '! f. <-Z'> *0- I v 9 n ■ n 7 7 *:0 * f ' ‘. * f) vf * V ’ ! * 9 V - Z *9 V z 1 z. J 09 OQ • 0 0 0 i • .1 99 1 0 * v. Z • 0 r / f • n 9*0 * V I ■; * >; v - V * V V I r '■ ■ 09

* 0 V 1 1 1 OZOP*-' j r j 0 •0 - i Z O 0 * P • 0 (■ ' I: ■ V * J. 1 V * 9V- p * C V '•of 1 I z c 0 9 • 0 V 0 V Cl(0*o b ron * 0 - V I 0 0 • 0 :■< 11* - • n Z ' P. ' I'll 1 * -• V - 1 ' V •; V f f M Z one V ?. M p • 0 f z *o t 9 7. 91 j; 0 op • 0 0 Z Z1 “ 0- 1 i n n * 0 V * [ ' -9 1 !' *0V- i * V V ' 0 V S’O; i. Oy 90 *0 z V I 9 I r, y 0 0 * n p z 1 0 * n - 9 Z 0 0 * 9 f 0 n • n o'O ■' Z * < ! f * H O - 6 * '■ v *. f ZOO 20*0 c- 7 9*7 20 1 0 V 1 0 • 0 7 7 z 0 * 0 - 1 9 1 0 * 0 Z l0 0 *0 z * r 1 1*91 i * f - V * 9 : ( 06>- I 09

K y «! u *yvi? *j m or‘I j c ’-j >91 —'! a X v 0 9 I 1 V I 1

"•s. o -3-

18*0 T 0 0 f o r r. • ' i oojr *0- 9 9 C 0 * 0 1 $ 0 0 * 0 9 * 0 v 9 * 9 I 9 * Z 9 - 0 * 2 9 0 1)0 J CSO '•0 *0 1 n 0 ° 7 F 0 * p o; i r • p- G2P0*0 7Z on * o «. * 0 <0*91 I * Z 9 - *7 * r b 0 (1.1 0 */<> ry 0 2*0 Z 1 9 <7 *7 C P 0 * 0 FZ 10*0- 9 9 P 0 * 0 21 on *o V * 0 ' 9* V i 1 *F 9- i. * 9ZZ 9 9 10*0 T n 0 2*00*0 9F'P' *0- 19 0 0*0 pi j p ■ <7 * 0 7 F * *7 I 9 *99- f * O 9 f l 1 z.z Z. 90 •o 1 : 0 0 J C!’p • P * c - Z ‘JP0*o 1:100 *0 : • o i 9- * 91 9 * K 2 - I * Z LI o*/9 r ? P * 0 U’ 81 0 990’0 c r, [ o * 0 - c v. ■1 0 * P r: j pri • p 9 ' ' P * ‘/I t * 1 ?.- Z * Z TZZ 9 99 A ■ ( • C 1 v ! 47 V «, Q 1 t *c 1 0 p T P o • fl I 1 1 < * 0 - 0 ? p 0 • 0 <7 <70 P * P z ’ o 9*91- <7*99 ( 9Z l.G T. T 0 0 ^9.:0T FZ 1C *0- 7 9 PC * 0 2 I 00*0 9 ’ 0 ■ 0 * »/ I 9 ‘ 0 Z *Z ! .7 6- 9 ?■?/ f 99 '•) Z * 0 1 n p 1» :• 0 *' Z Y n *0- r.tjCO* V * 0 . <)■•/! . ' ‘ f. 6 * V 9 p Z9Z Z 99 ■ 0 I 0 n 1 9 H) * 9 91 2<'*0- Z '■ c 0 * p 9V PP * P * P ■:o * >*. [ 0*t 9 - o - ; V9Z 1 99 j * 10*0 1 0 0 0 V ■ •P • o 2Z 11*0- orop * o 2pru • o 9 * n - 9 * P 1 F * F I Z'l ' V 9 Z 9 9 0 Z * 0 7 61 t V 1 ' • 0 ‘ r f. '/9' * 0- z .roo*o f z 0 o ’ o >/' 0 ; v • >51 9 * 9 [ 9*9' 0 /9Z .9 $.9 *0 1 0 0 Z b M ) • ■”* *7 1 lr-*0- 15 >/r'P * 0 l,( p p • P ■; * o I/ ' 9. 1 9 * 9 I 9 * c <- 9 1 9 < = fi / P t 9 f9 r;; b(.mn I 0 0 2 9. >0 * 0 ff zn,c- 7 900 ' 0 | ')!' ■ M > • * n w * 9 ; 't:f. 9 * P Z 1 9 / > *0 I n 0 ceoo *<• ! ? 0 0 * 0 - 9 ? o r • o 9 2 00 * C 9 ‘ 0 1 9 * 9 t 1' 9v < ’ C, Z 9Z O f o

. \ 91 * 0 1 0 p 1 ?00*0 1 1 10*0- 1 7r'0 ‘ o ^ P P P • ?5 9 *0 • 7 • 9 1 9 ‘ 91 9 * 1 9 9GZ 9 F 9 F 0 * 0 1 0 0 0 V ;.i o * 9 9Z 1 0* u- !; f n 0 • o 7Z * F .0 ' 1 1 L * 9 V. 9 • 5; ‘. Z 2 9 G9Z 9 V 9 * 0 1 0 o fl'PO ■f' 9 1 2 •’ > * o - o Gun • p 9<7Op • O <• * 0 - 9 * 9 ’ 9 * f, F 1 * P i, 4\ rc./ Fl 9 * 0 T 0 f c-1 m* :: P O V *0- o, i r s n * o TZ/O’o Z *0 0*91 9 * 9 9 ft * 1 f- n ] GZ 2 F 9 •o 1 0 c 9 i n o •p 0070*0- 9 1 00 * 0 <: 1/ P 1 * n ,■ *p i • r t i *09 9 ’ 9 1 ■'2 9 0 9 Z U 9

* 0 1 o C 91 9 0 * P 0 9','n • o- 9F00 * 0 Ml oo • 1 9 ‘ !'■ ■ 0*1 i . 9 * Z G G*f >• f 9 Z i'F‘? *0 1 0 0 1 .'90 * 0 ocno *o- F *70 0 ’ n <71 or *■•' Z * P ; 1 * 9 ! 9 * Z 9 9 * Z. (; ■. :• 9 Z 0 29 f > f! 9 * 0 n 0 p ■ P • p * M • p * P V F * 9 1 1 * < Z 9 * Z ’• Z9Z. ppc ( ? / *P 1 0 n 01.00 *0 9r- 1 (: * C ~ ( FPO"' * 0 9 * I I * *• ! 9 * Cft 2 * f. G r 1 Z Z r * p. ; I l)7Q 20*0 n 0 p • p *(' * • * • i' F * 9 I G * 7 9 Z * 9 9 :

A ,\ J K •«>n* if.I ! V 11 ,i •: YrUWVd •9 A y V " J I (’■ V 1 1 >* ‘.i.;(. 1 ► ’ 4 3 r« < t 4;■ ' X X 'X ;'■; <4 INI. L-Ri< — _ ^"1 ■S._ ( 7 O —1 %o 3 - , 3 •p <—4 * — 4 — ».- r s ". *«,^ ' x. ‘x . 's ^ * «^, '"X.. r. i 7* 0 • I 4 • • ; • • « • • * • • • • ft • 7* .Ml iM o * c 3 3 r“ r c xT 3 3 ■3 — #-4 3 3 7m '7 X C _ > 3 . «4 J " x n - rxi o x . r “) - O 1 -X 3 '■ \ • « m 1 s • • • • • • ♦ • • m ' O o - N*1' C \ * ■rs MJ .*3 ■M ? r ^ *M * -\ •- • “ ^*j v- o b -v~ 3 . M' -** •'? i 4 M; 7 J 1 • - • * * •

O o o C 3 * * ■ 3 3 vT 4 .M 7 3 m ^7 3 • ' - O 7 • ■ -4 1 • • a * ■71 “■ ■ 1 • 1 0 -s • •s • • • • • ft p o . S o *J!' * • o ■M 0 X. o 5 3 ^ — a . - , 3 TM sT 3 .. •*% ►,r\ 3 r . «4 «/. *. - 3 y> X M 1 O j 3 •7 ft 1 1 r • 7 j • • • • • • • ■ • • » ft s . — 3 - 3 < 3 . . 3 r-» -<-> :' ^l” *^ ..*> X *\‘'l ' '• «T' 3 3 3 ..r- — •sT 3 O 3 3 3 3 . y 1 - • ? • • • ft *

- o 3 • —4 v r i m 3 -**, o • 3 O O 3 77 7 • c ? ■■? -? *c 1 *b ■•*'. •0 j < * • • . j \ r I '-' • ■ • • -C' O r-- JM O t x o 3 3 3 • l C 3 7 O ;7. . _ - - CM *■“ "v) 3 'x ■ r 7 X* 7 ~ 1 • « • « • • • • ft • • • * • ft ft *. , r 3 . *-•4 CM — j x r^\ 3 < — 3 3 O < c — 3 •*. 3 3 ; -1 .%7 3 ■0 3 3 21 t ~ 3 I ~j ■ * • • 1 - - ~ —4 «~4 i m O ,*A —* *■— »-4 r*^ '3 . 3 >* % 3 , - 3 r— -7 *— .3 r . 3 3 3 0 3 V. -- X -> J * 1 7 • • • • • • • ■Ml M 3 X o c o - 3 _ 3 _ ✓ N- l^-l. 7*- ft.. 3 - 7s Mx -r\ x CM *v_ ‘ C .r r< ■X 7 — *7 3 . 3 •A r 3 x J -. J » 1 • • • • • • • • • * ft a o L Q •"«. c 3 s 0 •3 V r-* — ■.— i— ■ ‘3 O 3 . 3 - 0 vT •V .7 7 j 0 0 r _ 1 1 5 • • .7 * • • ft • « . 4 .- -4" X* .r - 0 / X r^j • —< o -.*\ ’sT s’ t<*>. — vT“ *M —• — •— >— *•■“. 3 c 7* 0 r: V* —'• - D 2'i - 3 v 1 • • • • t* ft # • •

O m ‘“C O *Nj O ■j**. *— 0 “ 0 "0 r^v r— »^_ 0 C 3 c , T j 3 3 c 0 3 j Z 3 3 1 — ' 0 - 7 • \ 7 7 * • ft • - . ■r\ 3 . j \ r \j r --O ■O 3 c •3 i—1 x 5 3 CM 't2 * j r X 3 .r- n r < • . — O '.7 w ’3 3 «7 ~ T i -7 '.*• -.7 Hi, 'T C~ 0 **-. • 1 • *■ 0 • • • « • 4 • O i O O O — 3 • X % 3 *3 fw (Mi * 31 \i '\ •*- -D ■H^' 3 *>“ *"1 1 7 - r * • t t - • • » • • * * • 0 . q 0 a n 0 7 .-n r\; - -r — ■V, •X O T x* 7 “*v. ,7 - _• 1 7 • • • ; • * • • • ft •,*X* -jCM *-\j r < - > •> ■ij •"•o O 3 (V -M O — ■^x O 3 ’ 3 * , 3 C -— -,* 3 *0 •'•X -7- 3 ***, •C 0 3 3 1 .*•' 3 # ft • « • ft ft • » 4 1 : \r- :X\ »—* - h - r — r*; -Kr r~> 3 O 3 « —4 w ■< O 3 ■J- X 3 3 “*x •C “-■ >• 3 - - ,Z 0 ••» 7‘ 1 > ■% • ft • ft ft t• ft * C O O O 3 ?*— cn oj —»— »— -0 * — Is- 3 -O 7 w • *x • • • « • • ft • <*n - \ n 0 • ^ . S 0 O 0 X~\J JX >- 3 i^*i 31 O a 3 -'‘J » 7- S» r~"4 V* xT 3 *3 O X . 7 . 3 -i" *r *r 3 3 7 1 • • ft • • • ft • • rvj x»"^ ' O O 6 O 3 — X, ■«o, — x _J — .—v 'j - ;r> 3 .77 •r^ .f% *7 or? 3 3 3 3 — *X, J* , 3 ■c - 1 0 • • • • • ft • • t• ft ft » ■>4 -^ w r-^ (N ' C 3 —. O 3 I'M r*- •—4 3 CM ^ ‘Xi •O C' • • • • • • • 4 • « • • • • 4 4 ♦ 4 4 4 - 4 4 4 4 . 4 r*s o o 3 o 3 o o O 0 O 3 O O 3 ■ 3 O O . 3 3 . 7 0

r j —j <■4 ^ 4 «M4 r \ o o - - - • *v «*./ v«« o 3 o o a o- *v O OO rM O .-7 O 0 3 O 0 o 0 Jj r\j rsj •

,-7 * - T* o 3 a o N- -5 n — *3 O O ■ 7 O 7 0 1,7 O 3 0 0 0 —« tx .“V

-p * .j K- 0 ,*0 n ,7 r * r-“ 74 lV> *0 .-SJ 0 —4 n ■‘1 "7 > — < ~-f rv — i £, ,*vi . /*. O’O’ •O 0 n ■*\j ■7 "• —. 7 3 7 3 _ s 7 7. 1* ' 3 — - 7 J *-\ -5 o 5 a C •3 6 O 0 O 1 5 OO CO O 3 . 3 • 3 O ••• «• • • * • 4 • • * 4 • 4 4 4 4 4 4 # 4 4 4 , * -< 3 “S .”** ,*ji J 7 7 3 .1 i; S' .j - w O .3 3 3 - . 5 -- >- O rs o n 'O . *> i n n r \j O ■»4 : c x 'V 7 * 3 •7s O i n *V *5 • * *»* “*• N, r'*' /. ;•“ -*, O r - O’ ■*0 . ■*■'* —* «—• 3 — i > ;*> •4 * •4 -c (V * J .“',1 T\j r \j X, 1—"• -* Z j o •7, 7 7 '*> 7 /■) ,7; 7 7 . ■ 7 • 3 j . 7 3 • • « • • « 4 • • ■ » • • 4 4 4 • 4 4 4 4 4 4 4 4 <—. C o c c 0 3 * -i O •O 7 1 .y 3 0 c i i i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 1 l 1

- ' ___, .J —* ■C 'C «r». •■0 .-*3 ->v ^ i n j O “ft4 0 ,-A —* \, —4 —« -C n j .\ i -»*, O* -r, .7 3 r - 7 O 0* -“N "2 2 O -* i 1 7 3 — • 3 3 •3 '.1 7 . 3 —» 7 3 7 n V -> .7 o •0' o ■7 .3 3 O 3 O 3 OO O 3 O 0 • • • ••• • ■ * »*• 4 4 4 4 4 4 4 4 4 4 4 4 4 >• — — _. . -> "“I -*'1 —s ■*% ••> i . i •«y -y “** ** - - ®* w "

- , *> % r* ..1 .7 >- O’ - 0 0 '\J 3 - r •C y \ “» t-vw n 2 7 “V ,7 5 ; *. — —» ■3 ,*N <%J * 7 3 O D . "J, 3 — . 7 •7 7 * '3 7 7 7 5 " 3 —• O 3 y » “ft- y«, s? -\ 7 J .1’ —' • —' » * * ) '■—»' .J •••• • •••• • 4 •* 4 • 4 4 4 4 4 4 4 7 ; 2> *> > 7 *- 7 7 . y 73 3 7 0 3 O 1 1 1 I r r t 1 1 1 1 t

_ m ** «,,-- > — .4 •4 r .7 7 ..7 “J I • • • • • 4 • ■ 4 •• • • ft » 4 4 4 4 4 4 4 4 S) 13 .5 '3 3 «— 3 O — <4 3 z> " ■-* •-' — “ —*

- - O Zx - j .7 7 * 3 ' 1V 1 7 "•? 3 _ ' 3 —* » "j :o x «« 4 * ♦ * 4 « 4 4 # 4 4 4 4 4 4 7 ri* -'w >*- r- •c • r 0

r . ,r ■*\ ’• r .; ■V ■ * s • mi •A 3 , O ■O > • • • « • 4 < • 1 » •• • • 4 • 4 4 4 4 4 4 4 4 4 r - .-*• - 4 1-^ 7 * —J O' r - 7 O* 'C > ? * 1 7 O --4 ft** c: > • 4— i ■ ■ 4 'V*! y *4 >fc u .r. *c 7 3 rs, 1 ^ * 1 1 i 1 1 1 1 1 l I 1 1

0 D •C* > r O 0 r*^. * 7 ' V n vT vr 0 m 3 ■-*\ C c c T' 4- O' » • « ¥ » • 4 4 4 » • • » » 4 • 4 4 4 4 4 4 4 4 4 -•s • 'S N_ r- *r 7 f ^ — r'3 r* —< -*• -r, 7. O N 7 0 i-n "T > 4 < . *■— •»-. *s. s •*- *

- .- t.: .- , 0 7 ; y * •7 V-J •7, ’C s* •o ■~* ,% ‘ r c

t - . 7 « 1.- ' 3 *Vj 3 *0 (V r x Tv. r v ,v^ - 7 3 1 S' n> O O 1/ r- \: * ■- •* :’ ■-: *c -

— , **■». ■■\j *«7 3 . «•» s.1 ■^N 3 — 4 n- r - ■S» .T.4J Xs Zj3 O' O' O' O' O' rr» -> ■7 > O •C 3 C 3 «0 6 w7 O O ftfty 0 5 0 0 0 c O O C O N« I 1 A n I :-r.K. / V ti L > ~ V I’rU.f'L-K M.1TIU-J INT. t ;

■J 701 6 3 ■j 7 3 . !) 27. 2 I 'i. ' j } 0. •> 0 • 0 0 6 9 0 . 00 7) 5 -0.0202 . u.; 6 o 0 0 I 0. Or, 70? V 6 A V » 0 • A 3 2..-. 1 A . ?'« 0. * 0.0 O' A Oi 0 . OoA 0 -0.i)109 L-. 0. A 1 0 0 I 0. 70 3 6b A o •J 7 A . o 3H . o 13.3 0 . '1 O . 0 0 A A 0. (Jo2 A - 0 .0 19 1 11. 0 \ '• 2 A 0 0 1 0.0 7 70'. o 7 ■4 C) / J . 2 A 1 . ■> 1 3 . r» • ij * (j u • ., (( I 0 .00 2 6 — o • > > 0 j I I.. • 0 o J I 3 6 3 2 0- 70: j 1 0 7 6. 5 6 3 . 1 1 A . tj . 0 . > j - 0 u A 1 o . Do2A - 0 . 0 1 7 7 1. . 0!1 su 23 9 2 0.55

7 0 6 .'70 7 A . A H 1 . ‘J 1 > . C1 t O'. A U . 0016 u . 002 2 -0 .0 1 A3 : i.0022 . 0 0 I 0. 70 7 c 70 , i / 7. 7 £ 5 . 5 12. 7 > 0. .1 0 . 0 v b 7 0 . 0 U L 3 -0 .0 1 3 9 ■J. 0 0 L A 0 0 1 0.73 70 M 7 9 0 7 i. 1 6 2.7 i 5 . 9 o . -A u . o 0 1 1 0 . DO 1 A -O .D 120 w. Ovi 1 b 0 0 1 0.91 7 0 0 .. 7 d IJ < ’ 0 . 8 8 3 . 1 2 . h 7 1. A o . Ot/O 3 U.U021 -O .ol 1 7 O.002 1 0 0 1 0 . 710 .5 7 o ( ; h A . 0 7 0 . A 1 a . i.:. U . 7 u . 0 . 0. 0 • 0 0 0 0.

7 1 1 d 77 AbO '.A. 2 69. 7 l i . l ■; U • '.* 0 . o 0 1 C> 0 . OOA 7 -0 . w 170 u . OOA 7 0 0 I 0. 712 O /« o C) 1 >. V lA.i! A 0 . 0 0.0 13o 0.00 12 - 0 . u 1 i> 1 u .00 12 0 0 1 U . 8 A 7 13 : 7o L- > 7. 7 Ob . 2 ! A . 5 ’ 0 . 5 0 . o j 0 7 0.003 A - 0.0 I A 2 0 . 0 0 3 A 0 0 1 0.82 71 A 6 80 A 70 02.1 0 7.7 13.31 0 . 5 0 . J 0 2 1 U.CG37 -0 .0 1 5 6 0 : 0 0 3 7 0 0 1 0.9 A 710 b 1 A 7 > ■ - j , I 5 A. o I 3 . -J ! 0. 2 0 . 00 o .1 0.0017 -0 . 0 I 2 I L. 0 0 2 U 8 1 3 2 0.61

7 1 o 6 8 3 A fi :> : >2 . 6 A H. A 12.2" 0 . A J. 2O'01 0 . DO?? - a . 0053 0 • 0 0 3 0 I 5 1 2 0.93 71 7 3 * i A A 7. 7 / i. 8 lr> . r I 3 . A • o. ; 0. JUi't U.002 1 - 0 .0 I IA 0 . Uo23 2 7 0 2 0. 93 7 13 6 b '7 A CO, 7 0.7 9. i. 13.02 l . ? 0 • \> 0 2 I o . O u ? b - 0 . U I 3 2 0 • 00 3 3 2 7 7 2 0. 7.-1 717 0 3 9 0 I .7 10.2 I A . 2 7 u . 7 0.OO I 1 0 .0 0 AO -0.O I28 0 .OOA 8 2 2 3 2 0. 90 720 8 9 1 .. 0 3. A A. A 1 A . 2 0 . 9 0.0031 0.0031 - 0 . o I 5 1 0 . 00 5 I 0 0 I 0. A1

721 6 9 2 A 7. ' i 1 . 3 2. A 12.67 0 . A 0.00 09 i; • 0 0 -♦ 1 -0 . i; 206 1 •• C 0 A 1 0 0 1 0.9 2 722 (.9 3 A 6 ■ ■ 79.8 1 . -v 1 3 . b ; 1 .7 0 . 0 0 1 A 0 .0 ij 1 2 -0 .i- I 32 u .0 2.1 3 1 A 3 2 0. 72 3 0 9 A 0 ,2.2 -1 1 .3 1 5 . 3 A U. A 0.0 I 5b 0 .0 0 A 2 -0 .0 151 0 .0051 30 3 3 2 0.0) 72 A A 7 1 02.2 - I A . 5 I 1.3'. 0. 7 0. 0 0 6 I 0 . 0 0 6 3 — 0.026 0 1,.007(9 0 0 I 0. -'3 6 0 'NJ fO ..7 1 7?b .•196 0 7 b • U -1 7 .0 15.1 0. A U.GOA 1 0.002 9 • 0 . 00 35 15 17 2 0.95

-P- •0 r *7 * — 7 . 0 V*x “7> 0 O 7 3 ‘'O •* • • »• ••••• • • ft « « •• « • ♦ • • ft • 77 0 o *- :- •3 3 O O 0 V 4 O 0 O O 3 O

^ * Ml Hj o l m4 <■4 - - .3 —rfr-H rsj -vj - rg IN - O % r\J - •^J

a o 3 7>j O *r -0 0 O j OO -4 3 a 0 7 O 3 WM ?•-. ,7 ' /?•-VJ - ^ ■v. •sT ro r** r^- o o 3 3 |V* •««4 3 IT. h- ■O -O *— -vs O ■3 3 3 O ■‘V '■J ‘3 ■“"X s’ 7 ••v. -C .7-* r*^ .T •> ’O -O <7> 3 3 x vC C .r> s* r i O 0 s7 -^s r O X “7 w ,-r* —4 rr, LT\ c .7 Vj •T .7, s7 — 3 u7 »‘*j r c 0 t VJ ■3 "3 7* O ■7 3‘ 7 •*S 3* 3 ■ 3 O o 3 a 3 O 3 3 71 3 O O • 3 ;3 a O 6 -5 c c *• • •• • • •• ft •• • ft ft • • ft • ••• * ft • •V 3 ■- .-• ■:'- 3 :- 3 •« * ■ Z/ •3 -- 3 - -j - 3 ’3 —» K. O O 7 rvi CO CC 7“ *\ 3 3 3 .r T *V 7 — £ Ts, *•.7 3 >..♦• 7 s .7. ♦**. 7* wmA r\. 7j m . — -»• — 7* 7 -7 —j *1^ "sj rv: Ml T s 7 J rv Ml — 3 72 3 .3 7 r* v.. 3 ,“s V .2 3' 3 7 71 . j : 7 3 ft • •• * • * •« • • • • • •• • « • • • • « ft » .75 O 3 ■C .-0 r.) v_«- /•* <3 O p—« V4 O 1 1 1 1 i I 1 t 1 1 1 1 l 1 1 1 1 1 1 .* ... . ^ ■s. c vT" ,,7 NJ 7\ - r ‘0 v\ O 3 r. .7 >* A. •N. — 4 **— 7* r**“ r*"v —4 .7 r- £ •M iV' J*. 75 rv. 3 '•*> ■ -* 3 • ~ —^ 7 . 3 ' ■ £ £ 3 > 3 3 <■ s 3 3 a o 3 3 3 3 3 3 '3 3* D 3 5 Z j ’3 3 a O • • • ft ««*• • « • # •• * ••• • ft « « ft « ':* - - - ~ - '-- O 3 3 w' - - -p' —H — «u Tv T, ‘.7* - _4 <7 3 '- s O O • - *•'- <- -C — Tsj — S-P *■— 3 O 3 7 3 3 ", — < ~> -.''J .j .7 c* " 7 ’> ■ £ 7 , .3 .3 ^ - —4 -~x •*» 3 * 3 "• ■7 3 — .3 3 3 '3 ‘3 -3 «• « * ••• ft • •«• • • • • • • • • r*, • ♦ » • . j j 3 3 .7 3 * "7 3 7 _7 £ D — .7 .4 7 ' 3 .j O O / 1 1 1 t \ 1 »

_- 7 “ -r. — *■«- *»-. 7 . 7. — 4,. 7 “s. i » • * , 4 « • ft • • • • • • ft 1 • • • • * ft ft —) . 3 7 ; — —* ':: ■ 3 3 • 3 0 0 .3 - - O

-. v _ .. - «--- - -» *-t* •H-\ 7 s, 7 - r - > - 7* 'N '7, £ : 'C ~ ,“S 7 , r. 7 s . ■r .n * 0 »••• 4 • » ft • • • •« • « » ft » • •••« « ft * r -r, >T v“ *•“ ** sT .7 ■C* V. * 7 vT *7 > 7 v T ■»7 < r •sT — — j — > — - -t --• •— — — ■ r~- ' - m. —<

•7 •7\ .7 . 7 '7. * 7 3 7 - ,-v. M O r.- < “V •¥% X > - • • ■ • • •••• ft « ft • ft ft ft •• •« • ft ft • r * 7 -N", C O v 7 — 4 V rv O O O ■** r\. O ro r g T\ > 7 s.? n N. -> •O -3 0 r*\ I 1 l 1 1 1 I 1 1 1 1 ) 1 1 1 1 I 1 1 1 1 1 \ 1

'vj 'O CsJ •“V rC. C r ~ rv *Ju’ £ } .3s C .n !\i N» 7 O ft » « • • • • ■ * « • « ft ft ••» • • « ft • • 4 *v. .7 <**» “'••J r. • v r“— 0 .7 :3 *C* rx. rv - ' 7s

•0 7 V ‘ -.: - - £> »v_ “ vl.‘ > - ■*'- v '» r^- O 2 ' j Tk. ~v s» VJ N >4 >7 *<7 7

_ .. 'T» — 4 7 f -i'S 3 7- ;C ■> < -7 s* ■C —* 7 * ♦ £ 7 ■ 3 3 O 4“ rf*> . ^ rO —4 ~* * *- •‘* 7 —V •V •v *•• “V -V •”> » > ;i» ?* 7. *>

I) “- r. -*s -> —1 •:■>,; ^ -r *" •0 .3 — f\. *•“• v7 . • r— •v. T-’ >-• •w N* V* «s». h- N- *v> •v. .mi o •r. T— «r. o *G ■*^- c. c* >- r~+- o rr* A pa4 IV • « • • • «* • • • • • • • 9 t • 9 • • • •• • • O o o o 7 n o r j o o 3 o o O a n a o O O o n 75

7 —1 9-* mm m* —* O "4 -H mm -H V ■' ■* 3 JV •M rvi m* trn*

* 0 r O O 0 o o a o o o o o o o • T O O o a in m »— »o o IJ «m«4 0 0 O D 3 o 3 3 3 o o o o r- .3 3 o o *•2 v o

»<> • > <"* V o o - n <*n V r— > 2 5 3 n 'A O O > r •V O — 1 •m*. : n V V* •a . V - n "■J V — 4 •*“*j •j* IV* V 1 < V V — j V sT 3 -—* -3 7 ~ * 3 -~s 3 '3 ' 3 ~ . > 3 n3 3 7 •"J *3 ■ 7 •"1 C l C 5 o o o 3 O b O O o O 3 )O C C v ' 3 b O •T5 • • • • t •• • • • • • • • p *•»••• « ••• ., _ a . «• . -, — y »x . , ,, — -* . » V . j - ■■*' 1 • * * _v ..j ■— ** -• - * i — ■ • m -- ' - —* > - «v*» mm «» mm > 7 '-■’1 <•"?» ' 3 rs*~ . 7 c : •Ml# V OO *7 * * n - f s T a.^ -a. 7 7 mm > • * 3 > - \ 3 * 7 3 ■77 7 K- A "Z — \ T's, .V 7 ..7 r'l 3 --« -— 3 r— —- 3 7 V O 7 7 •V » s 3 . j • 3 ' • - 7 3. 7: 7, " 7 7, 7 7. 7 7 .7 . 7 . ■3* • •• • • • •• • t 9 «• *• •••• • • • • • • < 7 7 7 7 0 Q • ■ V O OO f ' l O O < 3 ■ 3 rf; 0 ‘a * 7 O O O

I J V .«rO •n JV c n .3 ■•o 3 *0 n V >?“ ‘7* “xj —* V* n: •V —- xT* ■VV ‘ J— mm V ■*V '3 3 7 ‘j 3 3 s~*. 3 3 3 77 3* 7 ■7. ' 7 3 * ■ 3 3 7 0 V OO D C) .3 5 31 O ••s O a -m* b O O 7 c b 71 • •• t • • « • • • • « • «•• • •••• •• • “u • x -- 3 - -• - •*« _> -- - ■ j ‘7 - 3- 7' ■n --> >» **> — 7 , .3 - ■7* -.- n." '•O oc _ ) *3 — —» --4 >r — — z> j r“* V ■3 ^-1 0 '3 7 7. mm ’Z' 7 . 7 — — 7, ■7 —* • z> •3' 7 7 ■^. -3 »3 r 7 '_.■ 7 Jj ' * 7 7 *; 'j • -j 3 3 7 . 7 7 *7, 3 * •»* • • * • • • « •« 4 •• « •••••• 1 3 *7 3 3 3 '3 3 7 3 3 •^7, 3, 3 "~y :5 0 3 7 3 3 J 0 .3* O

• f ■ ~ * "■* ■* r sT r ^ a >r ""-- 4' v*“ s- 7 , I • • • • • • « 1 • * * « • 1 » 1 • • 1 i • • • • • 3 3 3 3 7 .,1 3 --' 3 0 3 3; 0 3 Zj O 3 3 0 3 O O OO

_ - ' ... “*. •* - •• * * . , - .« ' * * >» > — . i*,. ~r~ •v. 7, r X.T -V ' m m r\_. ^ 3 rv. :~- t-v •»%. u''. 7* ■0 O • • • • • 1 » 1 1 • 4 m • ¥ • • • • • • • 4 « • • *— r vr -r C C '/ c c ^ \ x -.? s4" •'*'N V' < r c _ ^ . — m ~ -- - — a — a— — . a- « — - ~U ^ a— a — 1 ,m mm mm ,.m* mrn mm» m m m m

V.. 0 3 r—• 7 r\. '-V n . — 2' 7, . > “'•.i A X i > • » • • • 9 9 • • 4 • • • •• • 9 9 9 9 * 9 • 9 • ,■»* 0 — 1 7 .7 7 - 9— CZ sT r~, s" «\ n A ,r“ 2t 0 7- O A O O r\ rv nT ■^a s» O n ■ . •» •*n -n r^» «.** V ■V ,-rv rO "■ 1 1 JV*% m m. ■V O s ’ O ■~r> r-T, - r-' O 1 _a* V O X « 9 • « • ••«••• 9 • • 9 • 9 • 9 9 9 9 9 9 • a— 0 7 /. O '0 V, ■n •ai* “K V V ■n »rt •*.* V 3 O 1 '-T •7 7 •*■ > ‘ b

✓ * 7 . 7 7 7 '.5 'V 2 “ + 7 7- ■7 .7 .7 7 ,a* 1- 0 . 7. 0 c 7 sT _ *

►- 7 7 - 7 >7 '. A '^- 7 3 .V *■ ’ •<* A ■ w >- •*i •> • -i 9-~ vT v.7 •s. ■ J >?■ • i ' -vT C 7 - r> r, .3 7 '.7 n a A. r v7 0 «-w/ *6 0 0 b ) **s '*\ 1 *r> > •- - - ’• ‘**. - > “* 3

— j , N ^ r . s- r*« ■r 3 9— T :n . A , *s n a ' A ■n *n .A O 2 O 'C 0 -3 '1? w' O A >* r^ r- ^ s- ,-s. *— 7- r^. N— ^- Sa r*- 7*_ >- -^- >• s* f^9 r** 7-. X_ f*X •*\: J* r+~ X • J vT c 3 A r? r.-*, 0 ~m* s\ £ f\) £T* T O' S. -7> • • ft • ft « ft t ft •• • • • • • • • • • •• • • • o o o O 3 o a o o a O o o o ' 3 o 3 3 a 3 3 3 3 O 3

— • a — 4 (M r-^i X r s i c m «M 4 r — ft *"4 - o r \ J C M • * ■ * 3 O O — ■

V r> x d o o o o o

P" O' >r A 3 O >r O o >» *NJ .A 7s o •T T» uP O Vj* ,*s p >- O >0 f\j i A r-« —H f\J ■3 -X -P rA 3 .;** 3 •. »• ~: 3 v^> 3 ,3 c> 3 O 3 CJ O • 3 • s '.'3 O X- O O O 6 3 o o. ■3 o O O o O ■_ • O Q o O O OO ••« * ft • • • •• • • ••••••• •• • • •• 3 3 ;7 ' ^ *•- 3 D -3 3 3 O O 3 ■n 3 >- X *P A V V^/ o >«. s O .A A- ■O o O UP f.P. r\ T 3 V X' r •.*» >- o A > >r • 0 r-- ,*x r*> fTs . ■"• *p f"\ a r-* T'h '.'W A. — 1— iN o •3 «“7 —* —. 3 :: X 3 Z :J o •3 3 w •3 3 •3' O O 3 h— •» ft • » ♦ » •» ••••« • • • •• • ••• • • o O 0 0 0 o .'3 0 O C c O c 0 0 o OO 0 O O 1 1 1 1 1 1 1 1 1 1 1 l 1 r 1 1 1 1 1 1 1 *

-U N» p . -w» — 3 , 3k o ‘X A *^s AJ A, p 'X P ■> ■s —* . ^ .r ‘•j —. *s . — w>4 Aj p, •w* rO M rP ^\j .3 3 o ;; o «x 3 3 o 3 o w J o O o O a O O X 3 o 3 3 •** 3 a o O •5 3 o 5 O o o 3 3 S '3 O O Z*m • • • * • • * •••• • •••• » •• «»••• • 3 3 - O 3 3 3 o a - • ■< •A o - o 3 .O O 3 O O O •x O A o >• Aj s» .*3 rr X- ■ A ■p. -P nT P- O % *— r*.j ■'Nj w — r^- 3 1 vT 3 A. o 3\ _< 3 CZ 0 ••• ft • •• •«• •••••••• • • • •» 9 • 3 ~z 3 3 7 j 3 3 •3 3 o o 3 O O o O .3 ■3 3 OOOO 0

|“s j 3 **• A ^ -X . A. •3 c p.- /V, p ' j ft • ft ft • • • ft • • « f—< 3 ..; - O ^ 3 3 3 —O 3 O O 13 O 0 3 O a I -S - -1 . • ------r* - •x. «. ;— 1 . - *>\ 3* n*' “i" c O .r ,£■ P. j • 1A X* - r 7s > • .3 P P 'J- p P > T » • • • • • • • ft ft »** ft « « ft ft • • « ft ft ft ft n-> ■n T x T vj .p s T

x — .A z 3 A — X A •%j 'A >- X -*s r - A or 0 A p. P ■X* >* ft ft • • ft ••• ft ft ■ • ««« ft • ••• • * • ft • XX •A, A ■J A _ P *c r>*. <* O 0 A P- A p - tp rp sC ■X O CO A CO r ^ t X X 1 — 1 A •x C lP vC 0 O' 0 X N- O •n sT rp 1 1 1 1 1 1 1 1

AJ O A rx. IP X '■s A •n TO O O A* k—ft A 'T rp A >< ft •• • • ft • ft • ft • • • • ft ft • • • ft ••• • • t~4 ..' X A '.T N. X*. A- •X P A v*. r - , r X) *>T ;P O s _ rP P •>4 O ' - 7. :; “2 - -J .j -- - —*— -* —

w A ■s^ C .p •‘X ;X A •— "P X <- **• '.3 -3 A 3 rP ftx. ps O < ,*W A A P- >- N* *x. fx *C- *C *;*> ■‘0 ’•* X ■v 3 Pg 3 .ps 3 'T' 5 O -T' 3 > 3 3 - "p •X, X, ;r. 7s 3 3 ' O p s •P-i

-N .7 7 ' "s —- ‘'vJ 3 T t.P • 0 X 3 ■ A •p - f iP 0 rx* • P *7' 0 P- •x. px x. r ~ . CO X aj X X XX X :o ps 7* CP O' 0 0 *x •x. ■x. A >• A A >■ p- r- p- p- p- >- P- •s. p. A ^ p» X rO •7 . *7 a j rv. K. i s •J2 .1* *> > r 7 Cl •.T *T •7 ' O' O (-7 c c O' • • • •• • * • # • »• » • • • • • •• « •••• -7 o o O o o 3 o o 3 3 7j 3 O 3 ."3 O •3 ■3 3 3 O 0 •*-4 O 3 •4 - O - - ul. 0 0 ,•**. a : O O *-7 o 3 r s n 3 o a 3 O O O O 0 3 O "5 0 3 •-J • f-a» —, u 0 7 T 0 o D o o o O w 3 O O n 3 O a 0 OOO 0 3

*0 , o — 4 r - r < “C — < «-* r-"* N- 3 f\J rsj 'J’ CvJ D (%J **■ ■ 4 wmU r%* — 4 fA. * r t - —• o Psj *7 •J- •7 ••» ■~s 0 J ", <*-* s~\ 5 c 0 O 6 6 0 O O • w 0 ■6 3 O •0 3 b ••••• • • • • • • • • • ••• •••• •« • •■> 3 .0 c O 3 ..’j _y 7* * ■.0 0 ■■- ** *•* > - < v S -O *0 C j .r. > r CC rA n.-* 1—* 3 O CvJ ;*• p, *.v •j*\ ’O 3 s* “7- x» -■*, ■ —. ^-1 —J— — 4 rvj — < — « — 1 Tvf — ro %l “VI 3 ,__ -7> r ; 3 ‘ O' 3 O' 3 0 *3 i m ••• • • • •• • • « • • • ♦ * * • • • • •• • «... y— . >•> ■-> .r-». •O O 0 O 0 O O 0 C -C i 1 T \ 1 1 1 1 r 1 1 1 i 1 1 1 1 1 1 T 1 1

CrC r A .01 a — r\. — 4 ~ -O f*J c O r\. ■*v 3 3 i \ i *■> r'v .— * S* rr- - 7 — 7 * 7 — —- —* —4 n7 . r * *T *— » .~S “I " 7 0 C* C*J ■7 . _5 '*•> 3 r o 0> 'j ..> . 3 3 j' ■ 0 0 JO 3 D O 3 J? O a 3 O 0 3 ’-y 3 '0 3 3 O 0 7 , • •• ••••••• • • • «• •• • • • •• • • _-j ." ■ j ' 0 Z j _ o :D 3 > v 0 3 -- -- •- 3 3 0 0 0

■Tk .7 -••k r\; •A, 7 - — r»"' r v C < v •k>- rA r—4 -.7 a c>. ■v. 1 ■*» • V -s % rA rW <\. .3 -7 .-r*. •7 , “7 •100> * 7 z > 0 * : 3 .0 3 3 w —.—1. -> - •' -y’ •' -•* - 3 3 3 3 Cj ••• • • » • • •• « * • •• ••••• •• • • • a ~ j '7 3 J ,7 . 0 : 7 0 ■3 o «/ 3 3 3 00 3 Ill I 1 I I I t I I 1 1 1 1 1 1

, ^ i»v ___ > .r — ■**• c <• 3, /J *v < r 1 » • • • • f ■ • •• •• *• •• •••••• __ .«.. . **\ ■_ J ■■j 3 • 4 - Tj *•4

.. r - _ _ . .• „ 3 '\i .7* 3 —. •"'w .O 3. v r s s7 * ' , y 7 v] c •a n7 r-* 'C' *>7 H ■n

v« - -> 3 . - :,- 0 v- JO 0 %r .a . 7y _-\ ■v” •^. * 'C .'j rS >- «••••••*•• 1 • • » *•• •• « t « • • 9 0 r\. r> S'' 3 . rv. ■r -O i w rr_- r? CC • • 4 r - O cc O' P>4 •«*v •A q * 4 -A 1 l 1 1 r"*' p-~ nT ■ 0. ,*** 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 I 1 1

, •«r 1% •r“( O'C r\ JT* ."O, tr> O O' '7 *.»y O' i.rv s <—< 0 y; •• «• ••• •* • •* •••• t • «« • * •• ■*k r -r —4 0 > .7 ■T* ■— t-*- -t s 7% ,7 "j . 3 — **- nT LO 3 —. — > — 4 ... -- —• -1 • -. r— — — r*‘> C1* r.i -4 <— ««4 —4 r*4 > -» —* _*4 — 4 -4

3 - 3 -— - 3 •7 3 :3 .* J L.,

C.'

%.• -7 *-^ *.* 3 . f— i -*^ 1 *«7 .0 —. r. .b -C ‘vj O *«4 N*t O J 3 O — ( — 1 .— • c \ 7 . C\J ru .*v rv> .-^l ,«A, 7 c -•T , *•• 1 **' —* 0 **: 3 0 1 - 0 3 J O “0 r * j 'j. 3 • ' \ ' j •.0’ ■ ^ 3 •3 .0 — 4 — 4 — 4 t "4 t— 4 >■ »4 •— ^4 i«4 —4 f^4 ^4 ^-4 >—1 r-4

-4 f\j .*A <- r- O ^ * * • 4 *A •7 .3 .J) 'C • O -** C\» - -c :0 v. jC‘ CC r> 'O -r" CD

<*

-■ •

*0 n 0 n *0 * i) • r. ■ 1 * V I 9 * 0 / 9 * 1 <_'/ 0 ] 0 9 0 *0 T 0 V I r.' 0 ‘ r' V r 0 0 * 0 f -10 o• r () • n - ■ / * V I 5 * 9 / 9 * 9 r VJ ■'11 ■■•’f *0 1 o c. 9100"' i l C :*0- V 100*0 r; (' r. i >• 0 J. ■ S.l ■ n • 9 1 f * 1 / f * f ■ . Z'OO | / £ « 0 0 * 0 1 Q 0 V I ! 10 * •*> 6*00*0- •/I 00*0 / * 0 1 * 0 - 7 1 * v f 9 * 0 V 0 * *7 ' I' 1 9 9 • ’ I 0 f P

* 71 _ f .g *0 T 0 0 5 I no * o f n f. • o - 0 F 0 0 * n '< T 0 o 9 " 0 o *v ; i * <7 *7 r>' z f 9 f t 1 9 £ 9 • 0 I 0 0 V 1 00 * 0 c *71 r. • u - V 100*0 */ ?! 0 0 * 0 f 1 s * f ! - ’ f. 1. f * t. /' O '" ” I V£ ! ro*o 1 0 o f100 * 0 Q(7' i • 0- f [n o *o / I /o • n j * o ■ */ • 9 i 0 * Or.' 1 * v . 0 f . c t i £ V 0 • o t 0 r Z I 0 * 0 t 00 9 * 0- £ I 0 0 * •' j i !'r * r» : V * S. I ■ ? ' 9 r! 9 * n .. o O M 0 £ o M * n 1 0 c oino*0 f 1 V!!*0- o t o o *0 f 1 *7 • r ! * <' - .' o * M 9 u7 • /. ‘ • .■ f' / 5 I 1 £ P

• o o n * 0 1 0 0 V T ' ‘0 / I o o* r j - I • •i i;'!:r>*T ;• * 1 : f * c I 0 * *7 c' 9 * :• . ' 9 9 'I O f 1 ^ ' 0 T 0 0 9*700 • rs 1 r ■ c.' ’ ‘ 0 - 9*7 0 0 * n t j • i ( ■ ' > • o • o < ' Z \ *7 * •« i 0 * I >: l- <. < : 1 MR • M 0 o. < ' l e * 0 1 0 p MOO V O 0 0 * 0 - 6 100* * i * 0 > t. * G ! * ( ; 1 6 * I l 9 I •••'

A V (1 N •>!V.q • 1 N 1 !T'! Jf:.; \«I ■ .If >J.-| ,0 - 1 /, A y V 0 1 1 o V I 1 149 LIST OF REFERENCES

Abt, H. 1957, Ap. J., 126, 138.

Abt, H., and Hunter, J. H. 1963. Ap. J., 136, 381.

Becker, W., and Stock, J. 1958, Z. f. Ap., 4£, 282.

Becker, W. 1963, Z. f. Ap., 11?.

Bidelman, W.'1962, A. J., 67, 64-5.

Binnendijk, L. 1946, Leider Ann., 25* Part 2.

Blaauw, A. 19^5, Galactic Structure, ed. A. Blaauw and M. Schmidt (Chicago: University of Chicago Press), 435.

Brown, D. 1958, RCA Data Reduction Tech. Report, No. 46.

Brown, D. 1965, U. S. Dept. Comm. Tech. Report No. AD609O69.

Bruggemann, H. 1935, Hamburg Abh., 4, 157.

Cherubim, R. 1929, Gottinen, Ver., No. 9*

Clasen, M. C. 1937, A. N.. 264, 33. de Jonge, A. K. J. 1966 (private communication).

Dieckvoss, W. 1955, A. N., 282, 25.

Eggen, 0. J. 1985, Galactic Structure, ed, A. Blaauw, and K. Schmidt (Chicago: University of Chicago Press), 111.

Eggen, 0. J. 1987, The Magnetic and Related Stars, ed. K. C. Cameron (Baltimore: Kene Book Corp.), 141.

Eichhom, H. K. i960, A. N., 28^, 233.

Fredrick, L. W. 1956, A. J., 61, 437.

Fricke, W. and Kopff, A. 1963, Ver. Astr. Rechen-Inst. Heidelberg, No. 10.

Graff, K. 1923, A. N., 219, 297.

Hardie, R. H. 1962, Astronomical Techniques, ed. W. A. Hiltner (Chicago: University of Chicago Press), 138.

Hershey, J. L. 1967, Pub. Leander McCormick Obs., 11, No. 25.

Hertzsprung, E. 1934, B. A. N., £, 187. 150 Hoag, A. A,, Priser, J. 3., Riddle, R. K., and Christy, J, W, 1967, Pub. U. S. Naval Obs., 20, Part 2.

Hudson, C. J. 1929, Pub. Allegheny Obs., 6 , 9.

Ianna, P. A. 1965* Vistas in Astronomy, ed. A. Beer (Oxford: Pergamon Press), 6 , 93-

Jaschek, M. and Jaschek, C. 1958, Z. f. Ap., 4£, 35.

Jaschek, C.# and Jaschek, M. 1967* The Magnetic and Related Stars, ed. R. C. Cameron (Baltimore: Mono Book Corp.), 381.

Jaschek, C. 1968 (private communication).

Johnson, H. L. 1952, Ap. J., 119, 184.

Johnson, H. L., and Iriarte, B. 1958, Lowell Obs. Bull., 4, 47.

Johnson, H. L. 1963, Basic Astronomical Data, ed. K. Aa. Strand (Chicago: University of Chicago Press), 204,

Hamper, C. 1968 (private communication).

Kotchlashvili, T. A. 1950, Bull. Ap. Obs. Abastumani, 11, 19.

Kraft, R. P. 1967, Ap. J., 2 M * 129.

Lippincott, S, L. 1957, A. J., 62, 55.

Mathews, R. T. 1963, Pub. Goodsell Obs., No. 14.

McDonald, J. K. 1948, J. R. A. S. Can., 220.

Meisel, D. D. 1966 (private communicatinn).

Miller, J. A. and Marriott, R. W. 1914, J. Franklin Inst., 178. No. 4.

Kitchie, R. W. 1964-, Ann. Rev. Astr. and Ap., ed. L. Goldberg (Palo Alto, Cal.: Annual Reviews), 2, 4-9.

Murray, C. A. 196TT. R. Obs, Bull., 41, 268.

Petrie, R. M. 1946, J. R. A. S. Can., 40, 325.

Petrie, R. M. 1962, Astronomical Techniques, ed. W. A. Hiltner (Chicago: University of Chicago Press), 63.

Petrie, R. M. 1964, M. N. R. A. S., 128, 245.

Pritchard, C. 1884, M. N. R. A. S., 44, 335.

Schilt, J., and Titus, J. 1938, A. J., 197.

Schlesinger, F. 1915, Proc. Nat. Acad. Sc., 1, 13. Schmidt, K. H. 1963, A. N . f 28£, 41. ^

Searle, L., and Sargent, W, L. W. 1967, The Magnetic and Related Stars ed, R, C, Cameron (Baltimore: Mono Book Corp.), 219.

Slettebak, A. 1968, Ap. J., ljjl, 1043.

Strand, K. Aa. 1958, Ap. J., 128, 14.

Strand, K. Aa. 1966, Vistas in Astronomy, ed. A. Beer and K. Aa. Strand (Oxford: Pergamon Press), 8, 9.

Taussky, 0. 1950. Math. Tables and Aids Comp., 4, 111.

Titus, J. 1938, A. J., 4£, 25.

Trumpler, R. J. 1914, A. N., 200, 217.

Trumpler, R. J. 1930, Lick Obs. Bull, 14, 154.

Trumpler, R. J.,and Weaver, K. F. 1953. Statistical Astronomy, (Berkeley: University of California Press), 265. van Bueren, H. G. 1952, B. A. N., 11, 385. van de Kamp, P. 1935. Ap. J., 81, 297. van Rhijn, R. J., and Klein-Wassink, W. J, 1924, Groningen Pub., No.35

Varga, R. S. 1962, Matrix Iterative Analysis (Englewood Cliffs, N. J.: Prentice-Hall, Inc.).

Vasilevskis, S., and Klemola, A., and Preston, G. 1958, A. J.,6^, 387.

Vasilevskis, S. 1962, A. J., 6 7 , 699.

Vyssotsky, A. N., and Janssen, E. N. 1951. A. J., jj6, 58. von Hoerner, S. 1957. Z. f. Ap., 42, 273*

Wachmann, A. A. 1939. Hamburg-Bergedorf Sp. D., Part 1.

Wilson, R. E. 1953. General Catalog of Stellar Radial Velocities, (Washington, D. C. : Carnegie Institution of Washington, D.C.).

Wolff, S. C. 1968, P. A. S. P., 80, 218.

Wright, R. R. 1967. (M. S. thesis submitted to The Ohio State University).

Young, D. M. 1954, Trans, Am. Math. Soc., 7 6 , 92.

Young, D. M. 1962, Notes on Num. Sol. Diff. Eq., Univ. N. Carolina.

Zug, R. S. 1933. Lick Obs. Bull., 16, 128.