372 Lord Rayleigh on the Momentum and 



Maxwell concluded that all statical theories are to be rejected. 

 It is to be remarked, however, that our calculations involve 

 the law of pressure only as far as the term involving the 

 square of the variation of density, and that a law agreeing 

 with Boyle's to this degree of approximation may perhaps 

 not be inconsistent with a statical Boscovitchian theory"*. 

 Passing over this point, we find in general from (30) 



£S™TP=i (ft-fld'-itfj (p-Po)dxdy dz . (32), 



whenever the character of the motion is such that the mean 

 pressure Q J i) * s the same at all points of the walls of the 

 chamber. Further, as before, 



and finally, regard being paid to (9) as extended to three 

 dimensions, 



(Pi~-Po> = (g + ^Q^) x to" energy . (33). 



In the case of Boyle's law f ;/ = 0, and we see that the 

 mean pressure upon the walls of the chamber is measured by 

 one-third of the volume-density of the total energy. 



For the adiabatic law (12), (13) gives 



/l y — 1\ 

 (Pi ~Po) v = (j + — 2~ J x total energy. . (34) . 



In the case of certain gases called monatomic, 7 = 1 J, and 

 (34) becomes 



(Pi -po) v = § X total energy . . . (35) . 



Thirdly, in the case of the law (15) for the relation 

 between pressure and density, 



(Pi—Po)v = — § x total energy . . . (36) , 



the mean pressure upon the walls being less than if there 

 were no motion. 



So far we have treated the question on the usual hydro- 

 dynamical basis, reckoning the energy of compression or 



* I think the difficulty may be turned by supposing the force, inversely 

 as the distance, to operate only between particles whose mutual distance 

 is small, and that outside a certain small distance the force is zero. 

 All that is necessary is that a pair of particles once within the range 

 of the force should always remain within it — a condition easily satisfied 

 so long as small disturbances alone are considered. 



