September 1, 1898.] 



KNOWLEDGE. 



167 



That extraordinary star, S Antlia?, on th3 other hand, is 

 certainly made up, like fi Aurig^^, of twin suns, for it 

 undergoes, once in seven hours and three-quarters, phases 

 lasting five hours ; and since an echpse longer than half 

 the time of revolution is a patent absurdity, there can 

 be no hesitation in admitting (with Mr. Backhouse) that 

 the stars occult each other twice while they traverse their 

 orbits once. Nor is any systematic difference perceptible 

 between successive phases. The effect is the same whether 

 number one occults number two, or number two occults 

 number one. The connected stars are hence probably 

 alike in size and brilliancy, although their eclipses can 

 only be partial, the loss of light being less than one-half. 



There is another Algol star, however, in which the loss 

 of light is exactly one-half. This in itself suggests alter- 

 nating occultations by two equal stars, revolving in twice 

 the period of variability. The presumption has been 

 accurately verified. 



Y Cygni was detected as an Algol variable by Dr. S. C. 

 Chandler on December 9th, 1886. Its phases, carrying it 

 from 7'1 to 7'9 magnitude and back once in about thirty- 

 six hours, had a duration assigned to them of eight hours, 

 equally divided between decline and recovery. But their 

 recurrences were soon found to be subject to enormous 

 u-regularities. Towards the middle of 1888 they were no 

 less than seven hours behind their calculated times, which 

 soon after began to be largely anticipated. Never before 

 had perturbations on such a scale been betrayed by the 

 light-changes of an eclipsing binary ; still. Dr. Chandler 

 thought that, hke those of Algol, they might prove to be 

 dependent upon the varying length of the journeys of light 

 in travelling hither from different parts of a large orbit 

 described by Y C3'gni round an unseen primary. The 

 possibly undulating line of its proper motion might even, 

 it was hoped, serve to make these hypothetical revolutions 

 directly measurable. 



The problem has, however, received a different solution. 

 M. Duner, ' director of the Upsala observatory, took the 

 star in hand in April, 1891, and observed its minima 

 steadily until April, 1802. But when he came to discuss 

 the results, and compare them with those obtained else- 

 where in Europe and America, he was at once struck with 

 a persistent discrepancy between the odd and even sets of 

 minima. The first, third, fifth, seventh, and so on, from 

 a given epoch, obeyed a law quite distinct from that con- 

 formed to by numbers two, four, six, eight, etc. The 

 lapse of time, in fact, from an even to an odd minimum 

 proved to exceed, in November, 1891, the lapse of time 

 from an odd to an even minimum by the startling amoimt 

 of 9 hours 42 minutes 55 seconds ! Not these discrepant 

 intervals, then, but their appreciably constant sum, repre- 

 sents the circulatory period of the mutually eclipsing stars. 

 Since, moreover, they run through corresponding phases 

 twice in each revolution, they must stand at practically 

 the same level as regards light-giving ; while the marked 

 inequahty with which the phases divide the period 

 amounts to a demonstration that the path pursued is an 

 ellipse, the major axis of which, although lying in the 

 same plane, makes an angle with the line of sight. The 

 disclosure of these peculiarities has been much hampered 

 by the circumstance that successive minima, being 

 separated by a mean interval of a day and a half, cannot, 

 as a rule, be watched by the same observer. The various 

 sets of data refer, accordingly, to odd or even series, the 

 strict comparison of which could alone show the true 

 character of the star. 



* Astr, Sack., Xo. 3091; ''Sur les elements tie I'etoile Tariable 

 Y Cvgni," eommimicated to tLe Academy of Sciences of Stockholm, 

 September 14tli, 1892. 



The amplitude of each phase is three-quarters of a 

 magnitude. In other words, just half the light is tem- 

 porarily cut off'. This is as much as to say that the 

 eclipses are total. For if they were partial (as are 

 probably those of S Anthfe), we should still receive the 

 full light of the eclipsing body plus a fraction of its com- 

 panion's light ; so that their combined rays would be 

 diminished each time by less than one-half. And the 

 identical character of successive eclipses implies, not only 

 the agreement of the stars in lustre, colour and bulk, but 

 the exact coincidence of the plane of their orbits with the 

 line of sight from the earth. 



These orbits are perfectly similar elhpses traced out in 

 opposite directions round a common focus, also necessarily 

 the common centre of gra\ity of the moving bodies, which 

 are presumably twins, as in other respects, so also as 

 regards mass. If this be so, the elhpses they traverse 

 agree not in shape only, but also in size. Now it is 

 scarcely necessary to explain that stars forming an un- 

 disturbed binary combination are always two right angles 

 apart. They are situated at oj^posite ends of a right line 

 passing through the centre of gravity, and at distances 

 from it inversely as their masses. But this line, unless it 

 should happen to coincide with the major axes, divides the 

 orbital ellipses unsymmetrically. The section on the peri- 

 astron side is both smaller, and is traversed at a more 

 rapid rate, than the apastron section. Thus, if the stars 

 occult one another (as viewed from the earth) a short time 

 (say) after their nearest approach, they cannot again faU 

 in with our visual ray imtil they have slowly wended their 

 way round the far sides of their orbits. Alternating 

 phases are thus anticipated and retarded, the disparate 

 intervals taken together representing a single period of 

 revolution a little short of three days in length. I 



But while their sum is constant, their diff'erence is very 

 far from being so. It amounted in 1886 to about three 

 hours and a half; it reached, in November 1891, nearly 

 nine hours and three-quarters. The rapid growth of the 

 inequality is thus positively ascertained, and it may well 

 be that the inchned balance is by this time in course of 

 restoration. M. Duner's explanation of these changes, 

 although given under reserve, and needing confirmation, 

 is of great interest and promise. He supposes that the 

 line of apsides of the eclipsing stars revolves under the 

 influence of an invisible perturbing body, just as the lunar 

 apogee progresses through the distm-bing action of the 

 Sim. Obviously, when the line in question is pointed 

 towards the earth, there can be no discrepancy between 

 the light-periods, the eclipses taking place symmetrically 

 at apastron and at periastron. This condition prevailed, 

 according to M. Duner's calculations, a short time before 

 the recognition in 1886 of the star's variabiUty in light. 

 The inequality so fruitfully discussed by him then began 

 to develop, and seemed likely to reach a maximum in 

 seven or eight years. This should occur when the 

 parameter of the two orbits coincides with the line of 

 sight — when the stars, that is to say, come to be eclipsed at 

 opposite ends of a line di-awn through the common focus 

 at right angles to the major axis. This arrangement gives 

 the greatest possible diversity of minimum-epochs, because 

 the stars, in order to reach the points of eclipse, traverse 

 by turns the entire periastron, and the entire apastron 

 sides of their orbits. Or, putting it otherwise, we may 

 say that the period of revolution is divided into two equal 

 periods when the ellipses traversed lie lengthwise towards 

 the earth, but into two unequal periods when they are any 



t The precise diu'ation is 2 days, 23 hours, 54 minutes, 43'26 

 seconds (Dimer). 



