232 Free Path Phenomena [OH. xi 



282. If we change the suffix 2 into 1 wherever it occurs, we obtain an 

 expression u for the chance per unit time that a molecule of the first 

 kind moving with velocity c shall collide with another molecule of the same 

 kind. 



By addition, the total chance per unit time that a molecule of the first 

 kind moving with velocity c shall collide at all with a molecule of any 



kind is 



2@ 1 , = e il + <H) ]2 + <H) 13 + ........................... (536). 



In unit time the molecule we are considering describes a distance c, 

 hence the chance of collision per unit length of path, for a molecule moving 

 with velocity c, is 



c = ^2e is ................................. (537), 



c 



and the mean free path \ c , for molecules of the first kind moving with 

 velocity c, is accordingly 



1 c 

 Xc = - = ~ ................................ (538) " 



Tait's Free Path. 



283. When there is only one kind of gas, this assumes the form 

 _^_ hmc 2 



/v c p: .-^ . ........................ (OOt?). 



^7TV<T^ ( C */hm) 



and from this formula we can without difficulty calculate Tait's expression for 

 the mean free path defined as explained in 30. For, in a single gas, there 

 is at any instant a fraction 



v/~? 



7T 3 



of the whole number of molecules moving with velocity c, and therefore, on 



^ 



the average, starting to describe distances ^ each before collision. Hence 



(HI 



Tait's mean free path (\ T ) is given by 



ATI = 



= f 



7TVO- 2 J o 



7T 3 



^^P- (540). 



Y W 



This integral can only be evaluated by quadrature. The evaluation has 

 been performed by Tait* and Boltzmannf, who agree in assigning to it the 

 value 0'677, leading to the value for \ T which has already been given in 30. 



* Edin. Trans, xxxm. p. 74 (1886). 



t Wiener Sitz. xcvi. p. 305 (1887) ; Gastheorie, i. p. 73. 



