260 PROCEEDINGS OF THE AMERICAN ACADEMY 



edge of the constitution of the stars it would seem extremely unlikely 

 that certain of them would lose half their light at regular intervals of 

 from one to twelve days. If it can be shown that the hypothesis sat- 

 isfies the observed facts, it seems unreasonable to deny it until some 

 more probable explanation can be offered. The difference in bright- 

 ness of the two sides of a star may be due to spots like those of our 

 sun, to large dark patches, or to a difference in temperature. In the 

 latter case, observations of the distribution in light in the spectrum at 

 the maxima and minima might show a greater variation in the blue 

 than in the red portions. If the body had the form of an oblate 

 ellipsoid rotating around one of its longer axes, its condition of equi- 

 librium would be unstable. If, however, it was a prolate ellipsoid it 

 would be in stable equilibrium, and if sufficiently rigid might revolve 

 in this way indefinitely. If, like our sun, it was in a fluid condition, 

 we might anticipate a return to the form of a solid of revolution. 

 Jacobi h;is however shown * that a fluid ellipsoid having three unequal 

 axes may be in equilibrium when revolving around its shortest axis. 

 An analogous case is found in Plateau's experiment, where a globule of 

 oil suspended in alcohol and water is made to revolve. "With a suffi- 

 cient velocity the globule, if slightly eccentric, elongates before throw- 

 ing off a satellite. We may also assume the existence of two nuclei, 

 or that the two components of a binary star are so close together that 

 both ai"e enveloped in the incandescent gas or photosphere. 



Another equation of condition would thus be furnished which might 

 serve to determine the absolute diameter of the star in miles. Thus 

 the observations discussed below give the relative dimensions of two 

 of the axes, and the condition that the body shall be in equilibrium 

 will determine the relative length of the axis of revolution. If the 

 star was an ellipsoid of revolution we could compute the flattening at 

 the poles from the diameter and the time of revolution ; we could also 

 compute the diameter if the other two constants were given. Although 

 the problem is more complex, evidently the same principle may be 

 applied to an ellipsoid with three unequal axes. 



Four of these stars, t, Geminoriim, fS Lyrce^ TjAquiliS, and 8 Cephei, 

 have been observed with great care, so that their variations are known 

 with much precision. Each will therefore be discussed in turn, accord- 

 ing to the following method. As the variation is periodic, it will be 

 convenient to denote the time by an angle, v, such that 360° shall corre- 

 spond to one period or revolution of the star. We now wish the light 



* Poggeiidorff's Aniialcn, xxxiii 220; see also Jourii Frank. Inst. ex. 217. 



