Prof. Challis on Hydrodynamics, 33 



of Professor Rankine as to the true capacity of bodies for heat. 

 Professor Rankine considers that the true capacity for heat of 

 the same body can have different values when the states of 

 aggregation of the body are different ; whereas I, on the other 

 hand, have given my reasons for supposing that the true capa- 

 city of a body for heat must be the same in all states of aggre- 

 gation*. 



M. de Saint-Robert now makes this same supposition, that 

 the capacity of a body for heat is the same under all states, and 

 consequently that the quantity of heat which a body contains is 

 proportional to its absolute temperature ; but instead of referring 

 to the reasons which had led me to this conclusion, he merely 

 says (page 83), " The temperature / being the outward mani- 

 festation of the quantity of heat H contained in a body under 

 its original form of heat, it follows that whenever a body has the 

 same temperature, it must have the same quantity of internal 

 heat." 



I cannot think that this argument will be regarded as con- 

 clusive. It does not appear to me directly evident that the out- 

 ward manifestation of the heat must be the same in the different 

 states of aggregation. If the conclusion in question could be 

 deduced in so simple a manner, so quick-sighted a philosopher as 

 Dr. Rankine would assuredly not maintain the opposite opinion. 



V. Supplementary Researches in Hydrodynamics. — Part III. 

 By Professor Challis, M.A., F.R.S., F.R.A.S.-f 



THE Hydrodynamical Researches communicated in the Num- 

 bers of the Philosophical Magazine for September and 

 October 1865, which were mainly devoted to the consideration 

 of the problem of the motions of a small sphere acted upon by 

 the undulations of an elastic fluid, carried the solution of it so 

 far as to evolve expressions for the acceleration of the sphere 

 containing two undetermined arbitrary constants m x and m\. It 

 will be my endeavour, in continuing the Researches, to complete 

 the solution by ascertaining the composition and values of these 

 quantities. Having found, in the course of revising for this 

 purpose the reasoning in the previous researches, that it re- 

 quires some modifications, I shall commence with pointing these 

 out. The novelty and the difficulty of the mathematical investi- 

 gations involved in the treatment of this problem may be alleged 

 as sufficiently explaining why I am obliged to proceed by slow 

 and tentative steps. My reasons for considering the solution of 



* [Professor Rankine' s remarks on these observations will be found at 

 p. 407 of the preceding Number. — Ed.] 

 f Communicated by the Author. 

 Phil. Mag. S. 4. Vol. 31. No. 206. Jan. 1866. D 



