37 MAXWELL'S LAW 83 



we can express it as a multiple of 8 ; for if 



AH = ( v - 1)8 and AJ = v $, 

 where v is an integer lying between 1 and q, then 



. 



We have then to find the sum 



.=.,- 



for all values of v from 1 to q ; but we have 



S.(2v-l) = g-fe + l)-gr- 



so that 



2.rS = i, 



and we have the simple expression 



for the number of particles of a gas at rest as a whole which 

 in unit time hit an area F of the containing vessel. If for 

 F we understand, as at first, the area of an orifice in the 

 side of the vessel, the expression we have found represents 

 the number of particles which in unit time get to the 

 orifice from the vessel. 



The formula is deduced on the assumption that all the 

 particles have the same speed fl. But it is easy to see 

 that the formula also holds good if fl denotes the mean of 

 all the speeds that occur; it holds good, therefore, as is 

 shown in 41* of the Mathematical Appendices, even if the 

 different values of the molecular speed are distributed accord- 

 ing to Maxwell's law ; it depends only on there being no 

 difference in the distribution in different directions. 



The number of particles getting into the orifice is not, 

 indeed, the same as that which pass through it ; for a 

 portion will be pushed back by collisions with others. But 

 the formula shows us that the speed of efflux of a gas must 

 be simply proportional to the speed of its molecular motion. 



The full meaning of this proposition comes out quite 

 clearly only when we compare two different gases with each 

 other. In both gases the speed of efflux must be determined 

 in the same fashion by the mean molecular speed, since 



G 2 



