538 Royal Society : — 



ing to that stated for the ellipsoid in partial differentials of the 

 first order under the case of the first example denoted by (/3). 



Thus, in general, if Rj, R^ be the principal radii of curvature 

 at any point of a surface, resuming for a moment the conven- 

 tional notation, 



1 + J_= {l+qy-2pqs + {l-\-p'')t 



Ri Ra (1+^2^^2)1 



But for the ellipsoid, if P be the perpendicular on the tangent 

 plane, 



Hence, if any corresponding theorem exist, it should be deter- 

 mined by equating these two expressions, or by the form 



{l+qy-2pqs+{l +py= ^a^g^g 



(aH^V + cVA 

 an equation which has no singular solution, properly speaking, 

 and could have none, being linear in ?•, s, and t. 

 Again, in general we know that 



1 _ rt-s^ 

 n,n^-{l+p' + (/f' 

 and for the ellipsoid we know that 



Jl P^ 



R,R2~a56V 

 By identifying these expressions we obtain the equation 



but of this, again, there is no singular solution. 

 Trinity College, Dublin. 



LXVII. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



[Continued from p. 482.] 



June 18, 1857. — The Lord Wrottesley, President, in the Chair. 



1"^IIE following comnnuiications were read : — 

 "On the Thermal Effectsof Longitudinal Compression of Solids." 

 By J. P. Joule, Esq., F.R.S. ; and "On the Alterations of Tempe- 

 rature accompanying Changes of Pressure in Fluids." By Prof. W. 

 Thomson, F.R.S. 



In the further prosecution of the experiments of which an out- 



