The Specific Heat of Saturated Vapours. 501 



These gravitation potentials satisfy Einstein's equations ; 



2m 



and, in fact, if ry=l— — , which appears to be a natural 



assumption to make for approximately elliptic motion, a must 



be r— and 8= if these equations are to be satisfied. 



. '2 in u 2 1 



r 



It may be worth mentioning that the above method of 

 finding the path of a particle in a central gravitational field 

 is the same as the application of Hamilton's Principle if 



d» 



j- multiplied by any constant is substituted for T + U, 

 ai 



where T is the kinetic energy and U the force function. 

 Thus, reverting to ordinary units, we may write 



t + u = - m c = fi - 2 ": i!_ - ™ 2 l ' , 



L ,,- t , (l _ S) , J 



or, neglecting small quantities, 



= m (ffr + r 2 ) - M (c 2 - ~ ) , 

 c being the velocity of light. 



LVII. The Specific Heat of Saturated Vapours and the 

 Entropy- Temperature Diagrams of certain Fluids. 



To the Editors of the Philosophical Magazine. 



Gentlemen, — 



N thanking Dr. A. W. Porter for his comments (p. 211) 

 on my paper in the June number of the Philosophical 

 Magazine (vol. xxxix. p. 633), and for his reference to the 

 interesting work of Mathias on Sulphurous Acid, which 1 

 had overlooked, T should like to explain cue point which 

 was put too briefly in my paper. The entropy of the liquid. 



6 , is of course I l ° ( , as follows from one of the relations 



Tit' 1 rp 



there mentioned, namely, K„ — ". But we have in 



d 1 



I 



general no direct experimental knowledge of K w , whereas 

 in certain fluids we know (approximately and through a 



