on the Physical Properties of Gases. 409 



collisions of a molecule and atom with a blow > c 



=±xys/irs\\J ^-e ^e 



= the number of molecules destroyed. The number of colli- 

 sions of two atoms with a blow < c 



=8yv 7r ,-u/^(i-r% 



V m 



Hence the whole gain of molecules in a unit of time is 



& 



rlr c - 3c ' 2 ° 2 AwJ 



^={2/^2(1-6 ^)-xys\s/\e & - x 2 s 2 e~^}U / — 

 at 2 V in 



dx 

 When the temperature is constant -=- must = 0, which condi- 

 tion, with 2(x+y) = N, gives us equations to find x. Putting 



y ?? 4m °' 

 the condition becomes 



f+f.Vi(j 1 )V^2V2.(f)%»-«~^)=0; 



say 



f= ± v d 2 + b — a. 



12. The negative root has no meaning, whence . we must 

 take the positive root. But before we can assert that this 

 value of f gives the actual proportion, we must see whether 

 the state of the gas would be stable. The condition for this 



is clearly that, if x be increased, -j- must be negative, and vice 



versa. Writing 



dx , r . N 



dt = A x >V)> x +y=~, 



we have when x is increased to x + h, and therefore y to y — h, 



J-jw**<£-©-(£-3). 



we must therefore have — — -j- = negative quantity. In this 

 eft?? ft y 



particular case 



f(xy) = X(by 2 -2axy-x 2 ), 



where \, a, & are positive. The condition for stability, there- 



