94 PROFESSOR TAIT ON THE 



This expression is obtained by noting that none of those leaving the first 

 plane can pass the second plane unless they have 



*-C09-/3>2a Ta; - 



All of the integrals contained in these expressions are exact, and can therefore 

 give no trouble. The two reckonings of the number of particles, when com- 

 pared, give 



rfU 1 dn 1 dh 



dx ~n dx 2hdx ^ '' 



From (1) and (2) together we find, first 



— -o 



dx~ ' 



which is the condition of uniform temperature ; and again 



Avhich is the usual relation between density and potential. 



[In obtaining (2) above it was assumed that, with sufficient accuracy, 



To justify this : — note that in oxygen, at ordinary temperatures and under 

 gravity, 



3 



^t = 1550 2 in foot-second units, 



™- 32 



dx " 



so that, even if a = 1 inch, we have approximately 



** ~. dx "300,000 J 



It is easy to see that exactly similar reasoning may be applied when U is a 

 function of x, y, z ; so that we have, generally, 



where h is an absolute constant. And it is obvious that similar results may be 

 obtained for each separate set of spheres in a mixture, with the additional 

 proviso from Maxwell's Theorem (§§ 20, 21) that P/A has the same value in 

 each of the sets. 



