in the Kinetic Theory of Gases. 305 



This may be put in the form 



I dYY* f^Trsinaf dKirs^pW rf^Slog(F/)(Ey-F/j, 



where a is the angle made by OC with a given line — or, 

 changing the order of integration, -=- = 



f dVY*( dR7rs 2 pwCd*2Trsma J \dS\og(Ff)(Wf / -Ff). 



9. In case of finite forces acting between the molecules, we 

 have no such simple expression as irs 2 p to denote the number 

 per unit of time of encounters between two molecules with 

 relative velocity p. We might define an encounter to be a 

 case in which the relative velocity of two molecules is turned 

 by their mutual action through an angle exceeding a certain 

 limit, reckoning from the time when mutual action begins, to 

 a time when it has ceased, to be appreciable. If with that 

 definition we denote by irs 2 p the number of encounters per 

 unit of time, s is generally a function of p or of R. We 

 might use irs^p in this sense for any medium in which the 

 coincidence of two or more encounters for the same molecule 

 simultaneously is so rare as to be negligible. 



10. The equation 



F P / p = F pi / p 

 is satisfied by 



where C, C are constants, because if PCp, QCg be two 

 diameters of the spherical shells, 



M . OP 2 + mOf = M . OQ 2 + mOg 2 . 



It is also satisfied by 



Fp = Ce -AM(0p2+M2-2M ° p cos ^ 



f —Qf € —hm(Op2+u2-2uOpcosp') 



where u is a constant line measured in any direction, and 

 /3, j3t are the angles made by OP and Op with that direction, 

 because M . OP cos /3 + m . Op cos ft' has the same value for all 

 directions of PCp. These are the values of Fpand/^ when 

 both sets of molecules, M and m, have the same velocity, u, 

 combined with the velocities required by the kinetic theory 

 for a gas at rest. 



A motion of this description is called by Professor Tait 



