54 



KNOWLEDGE. 



[March 2, 1891. 



intervals, moving the telescope in right ascension by the 



width of its own field, while the plate was simultaneously 

 shifted ^O" or 30" in declination. A series of parallel 

 trails would result, exhibiting with absolute fidelity the 

 gradations of loss or gain of light by which an Algol star 

 traversed a critical stage of its minimum. Although ex- 

 posures covering the whole of any one minimum could 

 rarely be obtained, the comparison of trail-pictures of 

 various sections of successive minima would be almost 

 equally instructive. The realization of this plan would 

 seem to be of considerable importance for the study of 

 variable stars, and may safely be left to the ingenuity of 

 celestial photographers. 



The eclipse-theory of stellar Ught-ehange possesses little 

 elasticity. Its explanatory powers are well defined, and 

 incapable of extension. In the first place, the progress of 

 the variations which it can account for must be along a 

 smooth curve. There can be no stoppages or interrup- 

 tions. Again, the amount of change must be invariable. 

 High and low minima might, indeed, very well alternate 

 in the same star, although they have not yet been found 

 to do so ; but capricious deviations from the assigned 

 measure of obscuration are inadmissible. They seem, 

 nevertheless, occasionally to occur. S Cancri and U 

 Ophiuchi have each been once observed to lose far more 

 than the usual proportion of their light ; and M. Duner 

 recorded, at Upsala, November 2-5 and December 7, 1890, 

 two abortive minima (as they might be called) of Y Cygni, 

 when the star dropped to the extent of scarcely five, 

 instead of eight tenths of a magnitude.* 



Besides these anomalies in the measure, there are 

 anomalies in the mode of change, which are equally per- 

 plexing and more persistent. The curves graphically 

 representing it are unsymmetrical in at least seven of the 

 Algol stars.! Their light, in other words, varies at a dif- 

 ferent rate before and after minimum. This is obviously 

 incompatible with the progress of an eclipse by a body 

 mo\lng in an approximately circular orbit. And marked 

 ellipticities are impossible (as Professor Pickering long 

 ago pointed out in the case of Algol) where the conjoined 

 stars are in such proximity as to leave no room for con- 

 siderable oscillations about a mean distance already 

 perilously small. 



But indeed no amount of eccentricity in the paths tra- 

 versed could satisfactorily account for the observed pecu- 

 liarity. To begin with, the retardation does not advance 

 continuously ; in three or four of the stars a pause is indi- 

 cated, followed by a resumption of progress. Moreover, 

 the observed irregularities are of an invariable type ; they 

 take the form of a delay in recovery after minimum. It 



* The exceptional minima of all these three stars have been re- 

 corded on excellent authority. TJ Ophiuchi is No. G, 1G2 of Schjel- 

 lerup's Copenhagen Catalogue, and was suspected by him of 

 variability, on tile ground of his careful observation of it, June 9, 

 1863, as of 7'7 magnitude, while Lalande had put it at G, Bessel at 

 7 magnitude. The regular course of change of the star, since ascer- 

 tained by Mr. Sawyer, is from G'O to G-7 magnitude once in every 20'3 

 hours. Of S Cancri the usual range is from 8-2 to 9 '8 magnitude. 

 Nevertheless, Schmidt observed it at Athens, April 14, 1882, to 

 remain stationary for a whole hour at 11-7 magnitude (Aslr. Nach., 

 No. 2,491^. In his determinations of Y Cygni, Duner used 

 Ch.andler's comparison-star /), of 7-8 magnitude in the Durch- 

 musteruny, and exempt from any suspicion of change. At all the 

 minima oi)served by Chandler and Yendell. T Cygni sank decidedly 

 lower than this star ; but on the two occasions mentioned in the text 

 Dunc'r found it to remain two steps (about one-fifth of a magnitude) 

 brighter, and concluded, on apparently strong evidence, its phases to 

 be inconstant {Astr. Nach. No. 3,011). 



t These are: Algol, S Cancri, 8 Libnc, X Tauri, U Cephei, 

 U Ophiuchi, and U Coronac. S Antli.-c will probably be added to 

 the list ; and we are unacquainted with particulars as to the phases 

 of Y Cygni and R Canis Majoris. 



is always the ascending branch of the curve which is 

 lengthened.; In order to explain this remarkable circum- 

 stance on gravitational principles, we should need the 

 wholly unwarrantable assumption that nil the stars in 

 question passed periastron before falling under ecUpse. 

 Such a concurrence of coincidences is of course highly 

 improbable. 



Look, besides, at the minimum curve of U Ophiuchi de 

 picted in Fig. 1, from the mean of 295 observations by 

 Mr. Chandler. 



haq 



T-7-1 1 1 1 i 1 1 1 r 



0^ / Z J ^ s- 



Fig. 1. — MiNiMDM of U Ophiuchi. From 295 Observations by 

 Mr. S. C. Chandler. 



The singular inflection of its ascending line is vouched 

 for, as an objective reality, by the independent determina- 

 tions of Messrs. Chandler and Sawyer {Astninumk-al 

 Journal, No. 177), and often appeared more conspicuous 

 in individual phases than as it emerged from the average 

 of many. The possibility of regarding it as an effect of 

 orbital retardation is at once excluded by the fact that, on 

 the whole, there is no delay. Accelerated progress before 

 and after the pause is so exactly compensatory that the 

 duration of recovery just equals the duration of decline, 

 notwithstanding irregularities in the rate of one as com- 

 pared with the rate of the other. 



Here, then, evidently, we have a physical cause of 

 obscuration co-active with the geometrical one, and tra- 

 velling in its train. Conjectures as to its natiu-e hence 

 naturally associate themselves with the enormous tidal 

 strains necessarily prevalent in systems of such peculiar 

 construction as those of Algol and its congeners. From 

 these extensive deformations of figure must result in both 

 members of each revolving pair ; but the effects upon 

 light-change are not easily unravelled, and, indeed, depend 

 to some extent upon what we know nothing about, the 

 mode of axial rotation of the stars concerned. On this 

 point the simplest, and perhaps most probable, hypothesis 

 is that they have none relatively to each other. If this 

 be so, they move as if spitted together ; there is no tra- 

 velling tidal wave, but each body has the permanent form 

 of an elhpsoid with three unequal axes, the longest cen- 

 trally directed towards the companion-star. The widest 

 expanse of luminous surface would, under these circum- 

 stances, be presented to our vision a quarter of a revolution 

 before, and a quarter of a revolution after each eclipse, 

 when slight maxima should occur, with corresponding 

 intermediate minima. And the matching of these theo- 

 retical by actual effects in X Tauri, and perhaps also in 

 Algol, is suggested by some recent observations of il. 

 Plassmanu, needing, however, to be confirmed before 



J Although the curve of U Cephei (.see Fig. 2) shows a slight 

 pause heforc minimum, the whole time of recovery considerably 

 exceeds that occupied by the decline in light. 



