284-286] Calculation of Mean Free Path 



Meyer's Kinetic Theory of Gases (p. 429), gives the ratio of A, c to Maxwell's 

 mean free path A, for different values of c, from c = to c = oo . 



Probability of a given Free Path. 



286. A further problem which is of importance is the probability that a 

 molecule shall describe a free path of given length. 



If f(l) is the probability that a molecule shall describe a path at least 

 equal to I, then/( + dl), the probability that a molecule has already described 

 a path I and shall describe a further distance dl, will be the product of 

 f(l) and a second factor, this second factor expressing the probability of no 

 collision occurring within the length dl. This factor is, however, known 

 to be 1 B c dl, where B c is given by equation (537). Hence we have the 

 equation 



or, what is the same thing, 

 of which the solution is 



= -#c/(0, 



, 

 ot> 



f(l) = e~ cl (548), 



the arbitrary constant of the integration being determined by the condition 

 that /(O) = 1. 



The probability of a molecule moving with velocity c describing a free 

 path X, of length intermediate between I and I + dl, is therefore 



(549). 



