15" MAXWELL'S LAW 381 



of which the first term is equal to zero and the second to 

 af dre- kmr * =a/B. 



J oo 



We finally obtain the value of k by calculating the mean value 

 of the kinetic energy of a molecule, which is given by the first 

 equation in 12*, thus : 



E = Am " f (" du 



\" f (" 



oo J oo J oo 



/OO pOO poo tmfr 2 4- 2 -v/ z ^ 



\Am drdsdt{(r + a) 2 + (s + b) 2 + (t + c)*}e * 



J _oo J oo J oo 



c=). 



The meaning of the constant k is, therefore, according to the 

 equation 



? = E - >(a 2 + Z> 2 + c 2 ), 

 4/j 



determined by that part of the kinetic energy which is present in 

 the system independently of its translatory motion as a whole, 

 that is, by the energy of its heat-motion. 



16*. Law of the Distribution of Speeds 



As the values of all the constants in the expression for the 

 probability have been found, we can sum up the result of our 

 investigation in the following way : 



In a gas which streams with a velocity whose components are 

 a, b, c, and whose particles are in a state of heat-motion of mean 

 energy 3/4& when the equilibrium stpfge has been reached, out of 

 every N molecules there are 



n = Mr-*kmyb-*l*-++*-*+'-*}du<bdu 



whose components of velocity lie between the limits u and u + du, 

 v and v + dv, w and w + dw. 



If we assume that the gas has no progressive motion as a 

 whole, but possesses only the internal heat-motion in all directions 

 equally and with equal strength, and so put 

 a = b c = 0, 



we obtain the simpler expression 



km{u * + * + ""du dv dw 



