\64s 



KNOWLEDGE 



[July 1, 1898. 



nitude of the partly eclipsed globe is 1-22, based on the 

 light ratio, 2-512. It is supposed that the distance of 

 the bodies from us is so great that the telescope would 

 only show them (even if both bright) as a single star. 



In this way the five systems have been treated, and 

 a series of points plotted as in Fig. 2. The abscissa 

 represents a unit of time, i.e., the period occupied Uy B 



in advancing one-tenth of the diameter of A. The motion 

 is supposed uniform and transverse to the line of sight. 

 The ordinates are star magnitudes divided into tenths, so 

 that the length representing one-tenth of a magnitude 

 equals that representing a unit of time. A curve is then 

 drawn through the points, which we may call the theoretical 

 light curve. 



It should be noted here that the shape of the light curve 

 may be altered indefinitely by changing the ratio of time 

 to " magnitude." But the light curves of different stars are 

 strictly comparable provided the same ratio is maintained 

 for all. For this reason the shape of the Algol curve, as 

 given by Prof. Pickering in Fig. 3, differs widely from the 

 theoretical curve in Fig. 2, simply because the above ratio 

 adopted in the two cases is different. 



In System I. the diameter of the dark globe is one-tenth 

 less than that of the bright one. This is pretty nearly 

 the proportion as given by Vogel for the system of Algol. 

 Hence a very considerable diminution or drop in light of 

 A results, owing to so much of its face being obscured by 

 the dark globe when central. 



In System II. the diameter of B is assumed seven as 

 against ten of A. Hence the light curve is not so deep, 

 and the central flat is longer ; lor, the occulting globe 

 being smaller than in I., and supposing it to travel at 

 same rate as before, it is, for a relatively longer time, 

 wholly contained visually within the globe or projected 

 superficies of A. While so contained the light of A is 

 reduced to a minimum and theoretically does not change. 



In in. the small globe is half the diameter of the large 

 one. Here the resulting light change is so small (only 

 0-13 of a magnitude) that it would be practically unnoticed 

 and undiscoverable by a method of visual observation such 

 as Argelander's. Hence it would seem that any companion 

 or planet smaller in diameter than -5 of the larger could 

 never be discovered by present methods of visual observa- 

 tion. If all the planets of our system could be seen 

 projected on the sun, as seen from a star, the resulting 

 diminution in his light would be absolutely unnoticeable. 



IV. Suppose now that globe B is bright — in fact, just 

 the same brightness, surface for surface, as A. Then we 

 have a binary system like many known ones, except that 

 we are supposing the distance from us so great that it is 

 beyond the power of any telescope to " split " the pair. In 



this case we regard the normal light as that of globe A 

 plus globe B. Any portion of H projected on A makes no 

 difference, seeing that any light obscured is replaced by 

 a similar quantity. The quantity of light, therefore, 

 outside the central globe — that is, the lune D G F H— 

 must be calculated and result added to that of A. This 

 has been done for the various positions when a 1, 2, 3, 

 etc., and the fourth light curve results. 



In System V. the diameter of B is still regarded as nine, 

 against ten of A, but the albedo, or light-reflecting power, 

 only half that of A, surface for surface. In this case the 

 total light when the globes are separated is that of A plus 

 that of B. When in transit, as in Fig. 1, the total light 

 is proportional to area of A, plus half area of B, minus 

 area of lune D E F G. This has been worked out for 

 different positions, and the fifth light curve obtained. 



All these five curves are similar in character, and the 

 light curves of all possible varieties of binary systems can 

 be thus represented. The amplitude of the curve will 

 vary according as the size of the occulting body is varied. 

 Again, the speed of the occulting body may vary, and the 

 transit be accordingly fast or slow ; also it may occupy all 

 positions when in mid-transit, from being exactly concentric 

 with A to just touching it externally. 



With regard to the smaller globe passing behind the 

 larger, if B is perfectly opaque and dark, the light of A 

 is not affected. If B is luminous, and of same albedo as A, 

 then the total light of the system will be diminished by 

 B passing behind, exactly to the same amount as when B 

 transits in front of A. If the albedo, as in Case V., is 

 half that of A, then when B is partially behind A (Fig. 1) 

 we get the total light proportionate to area of A plus 'half 

 area of D G F H (the portion of B outside A). Hence 

 with an albedo of B differing from A we get a different 

 light curve for a transit of B in front from a transit 

 behind A. In the latter case the light at minimum is 



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-Theoretical Li^lit Curves of Different Binary Systems. 



simply that of globe A ; in the former it is A-B + ^B : 

 that is, area of A minus half area of B. Hence the light 

 curve for a back transit is not so deep as for a front transit. 

 The question now arises, Is it possible to observe and 

 record the light changes in a star with sufficient accuracy 

 to mark the distinguishing features of the curves as given 

 above ? All observers of variable stars know the great 

 difficulties and sources of error attendant on visual obser- 



