ASTRONOMISCHE NACHRICHTEN. NZ 2672.

On the latitude of Harvard College Observatory. By S. C ChandZer jr.

The principal object of this article is to give the stars situated between +so and -5" declination. In the result of a determination of the latitude of this observatory immediately following table are given the individual results recently made with the salmucantarc. On account of the of the separate observations of each star. The latitude novelty of the instrument and method it will perhaps be indicated is that of the almucantar pier, 80 English feet of interest to make a more detailed statement than would north of the centre of the large dome, which is the latitude ordinarily be deemed desirable, especially as the result reference-point of the observatory. The deviations in the confirms the fact, that the accepted value of the latitude column (C-0) are from the value +42O 22'48Y36 adopted requires a considerable correction. as the definitive result of this determination. 'The present determination is based on Berl. Jahrbuch i, Latitude of Almucantar Pier. Results of individual observations.

i Date 1 Observed q~ c-0 Star Observed q~ c-0 _-___ - R Aquilae W 1884Nov. 9 , 42O22'48f52 -0Y16 B Aquilae W j 1884 Nov. 8 42O 22'48Y22 +o:'r4 " >> 10 i 48 19 + 0.17 *I a9 48.07 + 0.29 4 Virginis W 1885Apr. 6 48.60 - 0.24 ,I 2 I0 47.93 + 0.43 " 29 47.92 + 0.43 W '9 48.1 7 +o 19 D Dec. 16 -- 0.22 E m6 49.02 - 0.66 48.58 33 Sextantis W 1885Apr. 6 48.60 - 0.24 D '9 48.93 - 0.57 W '9 48.8 I - 0.45 10 Monoc. E 1885Mar. 5 48.00 0.36 + E Febr. 23 48.99 - 0.63 W a6 0.49 47.87 + W Mar. 2 49.43 - 1.07 12 Ceti W 1884 Nov. 29 48.57 - 0.21 m Apr. I 49.04 - 0.68 2 1885 Jan. 2 47.86 + 0.50 W "9 49,3' - 0.95 a "5 48.26 + 0.10 D " I0 49.3 1 - 0.95 6 Sextantis W 1885 Febr. 23 48.82 - 0.46 a Aqiiarii W 1884 Nov. 29 47.98 + 0.38 n Dec. 3 0.41 W )> 2 5 48.2 I +0.15 ' 47.95 + Nov. 9 W Apr. 19 48.42 - 0.06 E 47.92 + 0.44 D 8 I0 0.41 E Febr. 2 5 48.85 - 0.49 47.95 + W Mar. 2 48-31 + 0.05 Aquarii W 1884 Dec. 3 48. I 6 + 0.20 B Apr. I 48.14 + 0.22. >> 29 48.37 -. 0.0 I E Nov. IC 48.89 - 0.53 Br. 1197 W 1885 Febr. 23 47.99 + 0.37 u Leonis W 1885 Apr. 6 + 0.06, W 25 48.34 + 0.02 48-30 W - 0.40 W Mar. 2 48.26 + 0.10 a 19 48.7 6 D '7 48.68 - 0.32 7 Virginis E 1885Apr. 10 47.73 + 0.63 W w 21 49.14 - 0.78 5 Virginis E 1885 Apr. 9 48.43 - 0.07 W Apr. I 48.60 - 0.24 W ~6 48.83 - 0.47 x Piscium E 1884 Nov. 8 48.40 - 0.04 W w9 49.07 -0.71 m "9 48.24 4-0.12 E Febr. I 7 48.57 - 0.2 I 2 w I0 48. I3 -k 0.23 >> " 29 48.47 - 0.31 y Aquarii W 1884Nov. 29 47.83 + 0.53 W Dec. 3 48.09 + 0.27 I o 9 Virginis E 1885 Apr. 19 48.69 - 0.33 E Orionis E 1885 Febr. KT 47-91 + 0.45 p Virginis E 1885 Febr. 25 47.84 + 0.52 W Mar. 2 47.97 + 0.39 2 Mar. 17 48-03 + 0.33 Bd. 112. 8 I 16 Ilj 267 2

~ - 0 Nr. of 01)s. Lat. or Star Date Observed (p c Date c-0 - Vest East Alrnuc. pier _- $ Virginis E 1885 Mar. 2 I 42' 22' 491'02 - oY66 m Apr. I o . 48.48 - 0.12 1884Nov. 8 I I 42O 22' 48:'31 -I- 01'0 j D '9 48.90 -- 0.54 n94 2 48 21 +o. I5 18 Monoc. W 1885 Febr. 25 41.90 4-0.46 )i I 0 4 3 48.29 +0.07 6 I 48.27 +om9 Q Mar. 6 41.61 +075 29 1) ec,.. 3 - 48. i4 +0.22 E Febr. I 5 48.1 I -t 0.25 3 > 16 I 48.58 - 0.22 > Mar. 2 47.53 + 0.83 1885 Jan. 2 2 I 48.04 +a32 rn D5 47.65 -t 0.71 I - 48.26 +O.lO 48.82 0.46 25 8 Hydrae W 1885 Febr.25 - Febr. I 5 __ I 48.1 I +0.25 1 Apr. 10 48.3 I + 0.05 - 2 48.24 +0.12 s >' 1 9 48.10 + 0.26 2 2 48.62 -0.2 6 48.06 E Mar. 6 + 0.30 4 3 48.3 8 -0.02 d Aquilae W 1884Apr. 9 48. I tl -k 0.17 2 4 48.25 +O.I 1 I 2 48.02 )) > I0 48.2 3 + 0.13 +0.34 P * 29 48.53 - 0.17 2 2 48.09 +0.27 I I 48.36 0.00 a Ceti W 1885 Mar. 2 48.00 0.36 + I I 49.08 -0.72 d Virginis E 1885 Febr.23 48.67 -- 0.31 I 2 48.58 --- 0.22 n 25 48.67 - 0.31 4 I 48.67 - 0.3 I n Apr. 10 47.97 + 0.39 I 2 48.93 -0.57 B '9 48.63 - 0.27 I 4 48.27 + 0.09 48.60 -0.24 6 Ophiuchi W 1884Nov. 9 48.35 + 0.01 5 4 Q n 10 48.73 - 0.3 7 From this table the observed values during different L Piscium W 1885 Jan. 2 48.2 I 0.15 + periods are: v Eridani W 1885Mar. 5 48.42 - 0.06 Nov.and Dec. 26 obs. 42'22'48Y26 $6 48.80 m - 0.44 Jan. D Febr. 17 > 48.43 March 17 R 48.27 From the preceding table we have April 25 48 17

47 obs. West (p = 42O 22' 481'35 There is manifested a slight tendency to system in the 38 B East 48.43 column C -- 0, which I note without comment. Whether Mean 42 22 48.39 f01'030 it is due to instrumental or personal causes, or is simply Reduction to Dome . -0.79 fortuitous, can be told only from more extended observation. Latitude of Dome 42 22 47.60 f0.030 I propose to continrie this series during the remainder of the current year. The residuals for 33 Sextantis and I 8 Monocerotis In regard to the accidental error pertaining to ob- show large systematic discordances. The places of these servations by this method we find from the first table stars are among the least certain of the Berl. Jahrbuch list. above, taking the stars observed four or more times each, The former does not belong to the 539 stars in the A. G. that the probable error of a single observation of is Publ. XIV, but is inserted provisionally from the 83 southern sp 0:)2 I. This is for a single observation of a star observed stars of Publ. XVII, for the purpose of filling an .incon- -+ either east or west. But what should properly be counted venient gap. The above observations indicate a needed as a single complete observation of is the result from correction of the adopted declinations, of -1y2 for 33 Sex- sp, one star observed both east and west, or from a pair of tantis, and of +1:12 for 18 Monocerotis. stars, one east and the other west, the observations in all Rejecting these two stars we have, cases being at moderate or small hour angles. The probable 43 obs. West sp = 42'22'48y36 error of such an observation is not over k01'15. 30 East 48.36 It will accordingly be seen that the precision attainable Mean 42 22 48.36+0!'028 with this instrument is of a high degree. With some obvious Reduction to Dome -0.79 and easily effected improvements in mechanical details, such as the illumination, more uniform azimuthal tangent motion Latitude of Dome 42 22 47.57 h0.028 etc , the accidental errors ought to be considerably further which is the value I adopt as the result of this determination. reduced. It may be of interest to give the results arranged The above value of sp (47:'57) accords nearly with according to the various nights of observation. that (47Y63) which I published in 1883 obtained with the 117 2b72 I I8 small Salmucantarc of inches aperture. It differs so Dr. Gould notes that the Bond-Peirce result above given materially from the heretofore accepted value (4811 as given would be considerably reduced by the substitution of new in the El. J. and N. A., and 4813 in the Am Ephem.) that star places, and also states that his own result is less by I have been led to examine former determinations with about 015. This latter inference, however, seems to be a some care. misapprehension as will appear from the following facts, First is the value obtained with a Transit in the which, of course, were unknown and inaccessible to Dr. Gould. Prime Vertical in 1844 and 1845, the observations by The value 48160 was for the old prime vertical piers. W. C. and G. P. Bond and Major J. D. Graham, the discussion When the present observatory was built these piers were of them by Prof. B. Peirce, in Vol. I1 of the memoirs of the demolished; but from the records they appear to have Am. Acad. Arts .and Sci., Boston. This determination rests been 20 feet north of the present prime vertical piers, on I 68 observations of five stars, a Lyrae, B Persei, y An- which in turn are 27 feet north of the centre of the large dromedae, 8 Can. Ven., and p Urs. Maj., all of which pass dome. Thus in reality Dr. Gould’s value (48!‘15) is nearly the prime vertical near the zenith of this observatory. The in exact accord with the older one (48160 -0147 = 48113). declinations employed by Prof. Peirce were deduced from On the other hand, since Dr. Gould’s determination, the the Greenwich, Oxford and Edinburgh observations for ten published data bearing on the places of the stars employed years up to I 845. If we compare them with A. G. Publ. XIV, by him have very greatly increased. All the additional it will be found that four of the five declinations are in material up to I 8 7 5 has been incorporated by Prof. Safford excess. For Persei the difference is surprisingly large, 2!’45. in his >Catalogue of 2018 stars#. ‘l’he systematic difference I give here the values of the latitude from the separate Auwers - Safford has been investigated by Prof. Rogers in stars, according to Prof. Peirce, and also reduced to Auwers’ his >Comparison of the H. C. 0. Catalogue with Safford, system. Ross and Newcomb.( Thus we have the means of referring Peirce Auw. Decl. Dr. Gould’s latitude to Auwers’ system. The following table gives for each pair of stars, the seconds of latitude as a Lyrae 35Il2 obs. 42’22’ 48157 42O12‘ 48:’18 deduced by Dr. Gould, the difference (Safford-Gould) of /IPersei 39‘12 2 48.47 46.02 (d+&), the systematic difference ( Auwers-Safford) and y Andromedae 63 ’ 48.95 48.17 finally the corrected value of the latitude reduced to 8 Can. Ven. ‘31+ 47.05 47.26 Auwers’ system. p Urs. maj. ___~-- 1611~ m 48.40 47.55 Mean 168 R 42 22 48.60 42 22 47.53 S---G 3yst. diff Red. to Dome Pair Corr. q~ -0.47 -0.47 Y 1I/*(&-& A-S Lat. of Dome 42 22 48.13 42 22 47.06 __- -_

I 401’79 +0!‘08 -0:1 I 42O 22’ 40:’76 In the last column the result for 8 Persei is 1151 I1 40.36 +a03 -0 I1 40.28 below the general mean. This discordance seems to be I11 41.83 -0.19 -0.16 4 I .48 altogether too large to be regarded as observation error. I v 41.06 -0.56 -0.0 I 40.49 I would suggest that the proper motion in declination v 39.86 --0.52 -0 01 39.33 (+O:’OIO) of Publ. XIV, based upon Bradley, is discordant VI 41.21 -- 1.09 -0.13 39.99 with d’Agelet, whose six observations joined with the most VII 40.65 -0.40 -0.1 5 40. I 0 recent observations indicate a pa= -0103, and also that VIII 41.48 -0.59 ---0.01 40.88 a proper motion of about this amount will accord better IX 40.8 I +o. I 6 -0. I 5 40.82 with Groombridge and with observations about I 845. Without X 40.69 +0.62 ---O.I5 41.26 closer scrutiny of the matter, which I leave to more com- XI 40.88 -0.41 -0.13 40.34 petent judgment, I am inclined to think that until the un- XI1 41.30 -0.2 7 -0.1 5 40.88 certainty attaching to the proper motion in declination of XI11 41.13 -0.56 -0.14 40.43 @ Persei can be removed, we are justified in discarding the XIV 41.78 -0.78 -0.15 40.85 star for our present purpose; which, being done, will give xv 41.3’ -1.08 -0.02 40.2 I the latitude cf the dome 471’53 instead of 47Y06. As there XVL 41.21 -1.1 I .- 0.03 40.07 may be two opinions about it, however, I place both values XVII 40.41 -0.80 0.00 39.61 in the synopsis hereafter given. XVIII 40.3 7 -- 0.39 -0.04 39.94 The next latitude determination available for comparison XIX 40.84 -0.69 --0.13 40.02 is that made in 1855 by Dr. Gould at the Cloverden Ob- servatory, by Talcott’s method, with a zenith telescope From ;he mean of the last colum we have (U. S. Coast Survey Report 1865). Referred trigonometri- cally to Harvard College Observatory it gives Lat. of Cloverden Obs. 4za 22’ 40:’4I f0708 Red. to H. C. 0. +7.20 Lat. of Harv.Col1. Obs. (Dome) 42 22 47.61 f0.08 Lat. of Cloverden Observatory 42O 22‘ 40:’95 Red. to H. C. 0. +7.20 which is in close accord with the almucantur determination Lat. of Harv. Coll. Obs. (Dome) 42 2 2 48. I 5 (47Y57 f0:‘03). 8% 2672 I20 I I9

Next in order comes an unpublished determination The telescope was then tapped to bring the bubble by Prof. Rogers in 1864 with a transit instrument in the near zero, the level read, and when the star entered the prime vertical. Of this I will here say nothing, as it is field, its times of transit were recorded on the chronograph his intention to make a re-discussion and publication in over the pair of horizontal threads which serve ordinarily the immediate future. to fix the centre of the field for transit observations. The Finally a determination which I made from a single level was again read, and the next star set for and ob- night's observations in 1883 with the portable broken served in the same manner. In this way fourteen stars of Herbst transit, deserves at least to be mentioned. A delicate Safford's catalogue were observed at both east and west cross level was firmly clamped perpendicular to the horizontal transits, about equally divided north and south, and at axis so that the bubble should play when the instrument azimuths not greater than say 40'. Without describing was raised on the reversing carriage and pointed to a further the obvious precautions taken, or the processes of zenith distance of 4O30', this being the greatest zenith reduction, which, except for the reference to the level-zero, distance at which the width of the shutter opening would are the same as for the ~Almucantarc, I will simply state permit observations being made at all azimuths. The that the resulting latitude of the transit pier which is approximate times and azimuths at which the various known exactly west of the centre of the dome, was stars to be employed crossed this almucantar circle, east qJ = 41022'48'159. and west, being computed, the instrument was turned on the reversing carriage to each in succession, by means of The reduction to Auwers' system is -0'114. Collecting, a cardboard azimuth setting circle attached to the base. now, the previous data, we have the following synopsis.

~ Number of Lat. of Dome Prob. Determination I Date INiehts IStarsl Obs. red.to Auw.syst.I error --1:'07 47:'06 Bond-Peirce; Prime Vertical Tr. 1844-45 r7 5 168 42O 22' 48:'60 -0147 42O22' c -0.60 47.53 Gould, Cloverden ; Zen. Tel. 1855 17 38 308 40.95 +7.20 -0.54 47.61 fo'108 Small >Almucantara (f3/,*inch.) 1883 4 9 18 48.42 -0.79 0.00 47.63 k0.12 Portable Transit 1883 I 14 28 Large BAlmucantaru (4 inch.) 1884-85 22 25 85

The double value given for the first determination depends on 42O22'47Y6, the retention or exclusion of @ Persei, as heretofore explained. I In conclusion, I propose for future adoption as the in place of the value 4813 given in the American Ephe- rounded tenth probably nearest the true value of the meris, and 48:" given in the Berl. Jahrbuch, Naut. Almanac latitude of the dome of Harvard College Observatory, and Connaissance des Temps. Cambridge, U. S. A,, 1885 May 5. S. C Chander j~.

Entwickliing der &orenden Krafte. Von Dr. N. Herz.

In dem 91. Bd. der Sitzungsberichte der Wiener Perihels vom Knoten und Linge des Perihels, (v) die Pro- Akademie der Wissenschaften erschien vor Kurzeni eine jektion des Radiusvectors auf seine ungestorte Bahneb ene, Abhandlung von mir: P Entwicklung der storenden Krafte z der senkrechte Abstand von derselfien, v die wahre nach Vielfachen der mittleren Anomalien in independenter Anomalie; haben ferner il, a,, a,,zl, (rl), a,, v1 dieselbe Form(, von welcher ich hier einen kurzen Auszug gebe. Bedeutung fur den storenden Himmelskorper [ (rl),z, be- Seien fur den gestorten Himmelskorper i, a,m, x, zogen auf die ungestorte Bahnebene des letzteren] und ist Neigung, Lange des aufsteigenden Knotens, Abstand des

[a]= -~sinl/,iJsin(m+v) sin(n,+v,-a) -2 sin1/ai12sin(ml+vl) sin(z+v-$&) + 4 sin i sin il sin(a+v) sin (ml +vl) [sin i sin i, cos (a-Ql)+ cos i cos ill [aa]= -sin zl sin (z+v-al) + sin i sin (cu+v) + 4 sin i sin il sin (m+v) [sin I/, i cos lizil cos (&-a1)- cos i sin ill lab] = - sin i sin (zl+vl-~) + sin i, sin (ml +vl) + 4 sin i sin I/, il sin (al+vl) [sin I/, il cos i cos (Q-&) - cos I/, il sin i]