The Vortex Ring Theory of Gases. 



35 



established round them moving about in water, and striking against 

 a grating immersed in it. The momentum of the anchor ring will 

 consist of two parts, one due to the circulation, the other due to the 

 translational velocity of the ring. If the grating is so fine that the 

 openings are only a small fraction of the whole area, then the 

 momentum communicated to the grating will be the whole momen- 

 tum ; if, however, the grating is a coarse one, so that the openings 

 form the larger portion of the area, then the momentum communi- 

 cated to the grating will only be the momentum of the ring itself. 

 And this seems to correspond to the case of vortex motion. 



Thus if a be the velocity of the gas resolved along the normal to 

 the boundary surface, the pressure on the surface per unit of area or 

 the momentum communicated to it per unit of time is — 



using the same notation as before. 



¥ ow, the number of molecules which have the quantities a. and /3 

 between «, j8 and x+dx, fi + dfi is proportional to — 



-A(a+j3) 3p-2 3p-16 



e x 2 (3 * dad ft. 



so that if N be the number of molecules- 



r 



/(§£ 



2/3 *V 4 J 1 3p-12 



where T(n) is written for 



J e~ x x n ~ l dx 



and the molecule is supposed to be so complex that we may, without 

 sensible error, suppose the limits of a. and /3 to be zero and infinity. 



We may take Ijh as proportional to the temperature of the gas, 

 since it is the same for each of two gases which are in contact 

 with each other, and is also proportional to the mean kinetic energy 

 of the rings themselves. 



Substituting the above value for e/3, we see that the pressure equals 



and thus varies as ~NG. 



d 2 



