The density of double-star systems 561 



The period of fi Lyrae is relatively long', being 12' 1 21 h 47 m , the 

 orbit is sensibly eccentric, and the two spheroids are not so much 

 elongated as was the case with RR Centauri. The mass of the system 

 is enormous, one of the two stars being 10 times and the other 

 21 times as heavy as our sun. 



Further illustrations of this subject might be given, but enough 

 has been said to explain the nature of the conclusions which have 

 been drawn fi-om this class of observation. 



In my account of these remarkable systems the consideration of 

 one very important conclusion has been purposely deferred. Since 

 the light-curve is explicable by eclipses, it follows that the sizes of 

 the two stars are determinable relatively to the distance between 

 them. The period of their orbital motion is known, being identical 

 with the complete period of the variability of their light, and an easy 

 application of Kepler's law of periodic times enables us to compute 

 the sum of the masses of the two stars divided by the cube of the 

 distance between their centres. Now the sizes of the bodies being 

 known, the mean density of the whole system may be calculated. In 

 every case that density has been found to be much less than the sun's, 

 and indeed the average of a number of mean densities which have 

 been determined only amounts to one-eighth of that of the sun. 

 In some cases the density is extremely small, and in no case is it 

 quite so great as half the solar density. 



It would be absurd to suppose that these stars can be uniform in 

 density throughout, and from all that is known of celestial bodies it 

 is probable that they are gaseous in their external parts with great 

 condensation towards their centres. This conclusion is confirmed by 

 arguments drawn from the theory of rotating masses of liquid 1 . 



Although, as already explained, a good deal is known about the 

 shapes and the stability of figures consisting of homogeneous incom- 

 pressible liquid in rotation, yet comparatively little has hitherto been 

 discovered about the equilibrium of rotating gaseous stars. The figures 

 calculated for homogeneous liquid can obviously only be taken to 

 afford a general indication of the kind of figure which we might 

 expect to find in the stellar universe. Thus the dotted curve in 

 Fig. 5, which exhibits one of the figures which I calculated, has 

 some interest when placed alongside the figures of the stars in 

 RR Centauri, as computed from the observations, but it must not be 

 accepted as the calculated form of such a system. I have more- 

 over proved more recently that such a figure of homogeneous liquid 

 is unstable. Notwithstanding this instability it does not necessarily 



1 See J. H. Jeans, " On the density of Algol variables," Astrophysical Journ. Vol. xxn. 

 (1905), p. 97. 



D. 36 



