FOUNDATIONS OF THE KINETIC THEORY OF GASES. 263 



The terms in e ' are found to have cancelled one another, a result which greatly 

 simplifies the investigation. 



Had we complicated matters by introducing a + a ',z in place of a, the term 

 in a ' (which, if it exist at all, is at least very small) would have been divided 

 on integration twice by e , a quantity whose value is, on the average, of the 

 order 5 . 10 5 (to an inch as unit of length). 



The expression now becomes 



T/yM^+T) 3 ^'"'-)** 9 - 



We have omitted the zero suffixes, as no longer required ; and, as the plane 

 jc = is arbitrary, the expression is quite general. 



Omitting the product of the two small terms, and integrating with respect 

 to 0, we have 



The corresponding expression for the number of particles which pass through 

 the plane from the negative side is, of course, to be obtained by simply chang- 

 ing the signs of the two last terms. Thus, by (c) of § 38, we have 



/i 



or 



H£4)*)=°< 



40. The pressure at the plane x = 0, taken as the whole momentum (parallel 

 to jd) which crosses it per unit area per second, is to be found by introducing 

 into our first integrand the additional factor 



P(w COS Q — ot), 



where P is the mass of a particle. There results 



V 3 — +S+7> 2 / 46 )- 



2" I nv\fl 



We must take the sum of this, and of the same with the signs of the two last 

 terms changed ; so that the pressure (which is constant throughout, by (b) of 

 § 38) is 





■2h 

 Thus n/h is constant throughout the gas. 



p r x Tn 



P = ~3 I nvv2== oT • ( 2 -) 



