27 MAXWELL'S LAW 



55 



simple form that is equally true for all gases, viz. (see 19 

 of the Mathematical Appendices) : _ 



* v \^ i ^"* j ^ -^-~ 



= 0-9213 a, ^ tt 



which, with extreme approximation, may be written 



Joule and Clausius' values are therefore greater than 

 the arithmetic means of the molecular speeds by about a 

 twelfth part. 



The latter may just as easily as the former be calculated 

 from the value of the pressure ; for the formula for the 

 pressure p given by Joule and Clausius (13), viz. 



where p denotes the density of the gas, may be replaced by 



p = ^Tr/ofl 2 , 



from which the arithmetic mean values fl of the molecular 

 speed for different gases may be calculated, as has already 

 been done in a Latin dissertation 1 that I published in 

 1866. 



Further, for the calculation of the most probable value 

 W of. the speed, according to Maxwell's theory, we have 

 the formula 



the value W is, therefore, smaller than both the others, and 

 stands to them in a ratio which is the same for all gases. 



Closely related to this most probable value is a third 

 mean value of the speed, which is called the value of 

 mean probability, or, more shortly, the mean probable value. 

 The signification of this value, which I denote by in 19* 

 of the mathematical theory, is that there are as many particles 

 with speed less than as there are particles with speed 

 greater than 0. Its value lies between W and fl, and we 

 have 



= 1-09 W = 0-96 H. 



1 Inaugural dissertation, De Gasorum Theoria, Vratislaviae 1866. 



