On the relation of Pressure to Density. 401 



the thermometers are well fitted^ and the notch in the side of the 

 cork of R' closed by a fragment of bees^-wax, the apparatus may 

 be safely left for many hours without risk of the liquid absorbing 

 atmospheric air. 



In order to diminish the weight of the mercury without de- 

 creasing the amount of its acting surface, I have in some in- 

 stances formed the bulbs with fiat bottoms, and in other cases 

 have made them of the shape of a turnip, thereby diminishing 

 the weight of the liquid also. 



In attaching the india-rubber tube L, the bulbs should be held 

 by the tubes 1 and K only, because the apparatus is veiy fragile. 



Birmingham, May 9, 1859. 



LXVI. Theoretical Considerations respecting the relation of Pres- 

 sure to Density. By Professor Challis*. 



A THEORY of physical forces, such as that which I have 

 indicated in preceding communications, while it may be 

 proved to be false by a single contradictory fact, in the absence 

 of such proof receives confirmation by every additional fact, or 

 class of facts, which it explains. I have to a considerable extent 

 shown the consistency of the hypotheses of the theory with 

 phpenomena of light ; and in the Philosophical Magazine for last 

 March I gave the principles of an undulatory theory of heat 

 based on the same hypotheses. To this communication I pro- 

 pose now to revert, for the purpose of inquiring how far the 

 views there advocated are consistent with what is known by ex- 

 periment respecting the relations between pressure and density. 



The fundamental hypotheses above referred to are these 

 only : — The ultimate atoms of cognizable bodies are inert, hard, 

 and spherical, and act upon each other by the intervention of 

 the undulations of a continuous and highly elastic medium per- 

 vading space. In the article just cited, it was found on hydro- 

 dynamical principles that each atom is an origin of reflected un- 

 dulations, and that the velocity V and condensation a, at any 

 distance r from its centre on the prolongation of a given radius, 

 and at any time t, are given generally to the first approximation 

 by the equations 



^_f{r—Kat + c) f{r—Kat-\-c) 



V A , 



r r' 



flr—Kat + c) 



Ka<r = •'-^— ~ . 



r 



Further, it was shown that the central velocity expressed by the 



* Communicated by the Author. 

 I'hil. May. S. k Vol. 17. N.). 1 IG. June 18.59. 2 E 



