ii6 Report S.A.A. Advancement of Science. 



One of the problems that presented itself to the writer several 

 years ago, when the first star of this type was discovered, was : is it 

 possible to ascertain the shape of the stars continually eclipsing one 

 another ? 



A first investigation proved that to deal with this problem with 

 any hope of even partial success, necessitated observations of great 

 refinement. A new telescope was, therefore constructed with the 

 sole purpose of obtaining measurements as accurate as human skill 

 could .secure. 



Lately, also, there has been added to this telescopic equipment 

 the photometers used by Professor Prichard at Oxford. England. 



But even with the most favourable conditions of seeing and 

 measuring, I question whether we will be able, with our present 

 limitations, to secure observations refined enough to respond to the 

 exacting demands of the problem. 



For to deal with the whole problem fully would mean our being 

 able not only to distinguish but to measure the change in the amount 

 of light given out by a candle at loo feet distant, as compared with 

 the same candle at loi feet. It is unnecessary to say that the eye 

 can with difficultv distinguish differences soi minute as this. 



But although the problem does not admit of an ab.solute 

 solution, it admits of a solution so nearly absolute that it is of im- 

 portance to indicate what has been accomplished in this direction. 



If two stars revolve round one another in contact the stress 

 and strain of their mutual attraction will produce considerable 

 deformation in both stars. They Avill no longer be spherical in 

 figure, but will be egg-shaped masses with their narrower ends in 

 contact. 



For the exact figure of equilibrium which rotating masses of 

 fluid would take under the combined influence of attraction, tidal 

 action and rotation, the curious are referred to Professor Darwin's 

 classical investigations. (Phil. Trans., Vol. 178, Plates 12. 23.) 



We have already indicated that it is impossible to secure 

 observation refined enough to enable us to determine rigorously the 

 exact form which a close binary star, say RR Centauri, assumes 

 just when separation has taken or is taking place. The furthest 

 we can go without the risk of making our equations indeterminate 

 is to assume a spheroidal figure for the twin stars. That is, we 

 postulate tivo unequal axes for each star. 



Interpreting the light changes of RR Centauri into orbital 

 movement, with this limitation, we find that the system is composed 

 of two stars, spheroidal in figure, with their major axes lying along 

 the line joining their centres. A sectional representation of the 

 system is given in Fig. 3. 



In Fig. 4 are given the figures of equilibrium which two rotating 

 masses of fluid would assume when nearly in contact. The figures 

 are copied from Professor Darwin's masterly work. 



The similarity between the figures determined from pure obser- 

 vation alone, and the theoretical figures derived from a consideration 



