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To Identify Irregularities in O-Cdiagrams with VOL. 23, 1937 ASTRONOMY: STERNE AND CAMPBELL 115 CHANGES OF PERIOD IN VARIABLE STARS OF LONG PERIOD By T. E. STERNE AND L. CAMPBELL THE HARVARD COLLEGE OBSERVATORY Communicated December 23, 1936 One of us has investigated elsewhere' the mathematical theory of the accuracy of periods determined from dates of maximum, or minimum, or mth magnitude increasing or diminishing, of a variable star. The existence of cumulative errors2 in the periods of long-period variables was shown to provide a simple explanation for the major part of their observed irregu- larities of period, as revealed for instance by O-C diagrams,3 and plots of cycles against epoch number. The existence of cumulative errors was shown to be in itself sufficient to cause an erratic behavior in O-C diagrams, so that such diagrams did not by themselves furnish safe evidence for changes of true, or mean, period. Further, it was shown that a value of the mean period, obtained from observations extending over any finite interval of time, would be liable to errors of sampling, so that the mere existence of a scatter among' values of the mean period obtained from differing intervals of time was not in itself evidence for a changing true or mean period. Before the appearance of the previously mentioned investigations, it had been the common practice among workers in the field of variable stars to identify irregularities in O-C diagrams with "changes of period" in the stars. Thus, of the 566 variables with known long periods listed4 in the Katalog der Elemente des Lichtwechsels fur 1687 verdnderliche Sterne, sine terms were assigned to 85. Many of the reported "changes of period" were possibly of the nature of mere statistical fluctuations among cycles having a natural dispersion. It therefore became eminently desirable that the matter of changes of period should be reexamined at length, in an impartial and systematic fashion. The authors have examined systematically, for changes of true (or mean) period, 377 variable stars with periods usually in excess of 100 days. The stars include nearly all of the best-observed long-period variables. Ap- parent "changes" of period, that can reasonably be ascribed entirely to statistical fluctuations, have been carefully distinguished from systematic changes of period, here called changes of true or mean period. The material examined was obtained from (1) observations by members of the American and French variable star associations, and (2) earlier observations, referred to in (a) the extensive card catalogue bibliography of variable stars, compiled by Miss A. J. Cannon at Harvard, Downloaded by guest on September 30, 2021 116 ASTRONOMY: STERNE AND CAMPBELL PROC. N. A. S. and in (b) the bibliography contained in the Geschichte und Literatur des Lichtwechsels, edited by the Astronomische Gesellschaft. The method of study employed the x2 test of Karl Pearson. More complete details will be published in the Annals of the Harvard College Observatory. We have obtained the following results. 1. The SS Cygni type stars, SS Cygni, U Geminorum and SS Aurigae, are found to have sinuously changing true periods. 2. The Z Camelopardalis type stars, RX Andromedae and Z Camel- opardalis, show evidence of change in the true periods of the 12mO in- creasing phases, but show no good evidence of change in the true periods of the 12m0 decreasing phases. The existence of sinuous changes in the widths of maxima would constitute a possible explanation of the difference between the results obtained from the two phases. 3. Twenty of the 372 remaining variables are "suspected" of having changing true or mean periods, but of these only about five can be stated with any high degree of assurance, on the evidence, to have changing true periods. Although it is not certain which five these are, the most reason- able choices are R Hydrae, R Aquilae, R Cancri, U Bo6tis and S Serpentis. The first two have probably had diminishing true periods, the remaining three sinuously changing true periods. 4. The small percentage of the stars which can now be stated with assurance to have changing true periods arises probably in part from the insufficient duration and number of observations. However, among 52 of the stars, not of the SS Cygni or Z Camelopardalis types, observed since before J. D. 2,400,000 and therefore longest observed, only about four can be stated with assurance to have changing periods. These 52 stars have been observed, on the average, for over ninety-four years. 5. Most of the previously reported "changes of period" among long- period variables can be reasonably interpreted as mere statistical fluctua- tions. 6. There is no good evidence for any secular increase or diminution of period, of an evolutionary nature, among the long-period variables as a whole. 7. We have obtained an accurate list of periods. In closing, the authors wish clearly to point out that no conclusions as to the proportion of variables with changing periods, reached by this or any other investigation, can be regarded as final. An increase in the interval of time covered by the observations, and in their number, must render any tests more sensitive to continuing changes of period. All that we have been able to do has been to find out how many of the 377 variables which we have studied may be said with assurance, on the basis of observa- tional material now available, to have changed their periods in a manner which cannot be entirely attributed to mere statistical fluctuations. Downloaded by guest on September 30, 2021 VOL. 23, 1937 CHEMISTRY: ADELSON AND BOGERT 117 1 T. E. Sterne, Harvard Circular Nos. 386, 387 (1934); Popular Astronomy, 42, 558 (1934). 2 The existence of cumulative errors in long-period variables had previously been inferred by Eddington and Plakidis, Monthly Notices, 90,65 (1929). See also Plakidis, Ibid., 92, 460 (1932); 93, 373 (1933). 3 O-C diagrams are plots, against epoch number, of the difference, observed date minus computed date, of the phase selected for study. 4 Geschichte und Literatur des Lichtwechsels, 3 (1922). THE SYNTHESIS OF GAMMA-METHYL-5,6-CYCLOPENTENO- RETENE, A COMPOUND STRUCTURALL YRELA TED TO "DIELS' HYDROCARBON"' By DAVID E. ADELSON2 AND MARSTON TAYLOR BOGERT ORGANIC LABORATORIES, DEPT. OF CHEMISTRY, COLUMBI UNIVERSITY Communicated January 12, 1937 By fusion with selenium, the so-called "Diels' Hydrocarbon" (I) (gamma- methyl-1,2-cyclopentenophenanthrene) has been obtained from such interesting biologically and chemically important compounds as cho- lesterol, ergosterol, lumisterol, isopyrovitamin, pyrocalciferol, cholic acid, strophanthidin, gitogenin, anhydro-uzarigenin, sarsasapogenin and pseudo- bufotalin. Retene (II), likewise a phenanthrene derivative, is formed in the de- structive distillation of coniferous woods, or of rosin, due to the breakdown of the abietic acid present, and is found in large amount in the higher boiling fraction of the resultant tar. When abietic acid itself is heated with either sulfur or selenium, retene is the chief product. Further, retene carries the methyl and isopropyl groups, two radicals which are frequently found associated in natural products (cymene, terpenes, cam- phors, etc.), and which seem to have some significant function in nature. The attachment of the isopropyl group in the retene molecule, for example, exhibits the same carbon skeleton as is found in that important natural building unit isoprene, viz.: C- C I \C C / It seemed to us, therefore, desirable to attempt the synthesis from retene of products akin to the Diels' hydrocarbon and related compounds, Downloaded by guest on September 30, 2021.
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