1887.] Figures of Equilibrium of Rotating Masses of Fluid. 359 



lias been reached where further exhaustion does not affect the radia- 

 tion observed. In this way a condition seems to be reached asympto- 

 tically, in which the radiation is independent of anything removable 

 by the Sprengel pump. The value of the radiation found is, for the 

 particular bright platinum wire used : — 



At 408° C 378'8 x 10 -4 gram water centigrade units 



per square centim. per sec. 



„ 505° C 726*1 X 10 -4 gram water centigrade units 



per square centim. per sec. 



the temperature of the envelope being about 15° C. 



Comparatively little has been done up to the present as to radia- 

 tion from the same body with the surface in different conditions. The 

 important results of Mr. Mortimer Evans, 'Boy. Soc. Proc.,' 1886, as 

 to the energy required to maintain a given candle power in incan- 

 descent lamps, with dull and with polished filaments, have been con- 

 firmed. It is proposed to carry out further experiments on the 

 influence of the surface of radiating bodies. 



VI. " On Figures of Equilibrium of Rotating Masses of Fluid." 

 By G-. H. Dab-win, M.A., LL.D., F.R.S., Fellow of Trinity 

 College and Plumian Professor in the University of 

 Cambridge. Received April 28, 1887. 



(Abstract.) 



The intention of this paper is, first, to investigate the forms which 

 two masses of fluid assume when they revolve in close proximity 

 about one another, without relative motion of their parts ; and 

 secondly, to obtain a representation of the single form of equilibrium 

 which must exist when the two masses approach so near to one 

 another as just to coalesce into a single mass. 



When the two masses are far apart the solution of the problem is 

 simply that of the equilibrium theory of the tides. Each mass may, 

 as far as the action on the other is concerned, be treated as spherical. 

 When they are brought nearer to one another this approximation 

 ceases to be sufficient, and the departure from sphericity of each 

 mass begins to exercise a sensible deforming influence on the other. 



The actual figure assumed by either mass may be regarded as a 

 deformation due to the influence of the other considered as a sphere, 

 on which is superposed the sum of an infinite series of deformations 

 of each due to the deformation of the other and of itself. 



But each mass is deformed, not only by the tidal action of the 

 other, but also by its own rotation about an axis perpendicular to its 



