322, 323] Diffusion 269 



Since, by equation (264), 



and since p and h are constant throughout the gas, it follows that 



i/j + y 2 = constant ........................... (619). 



This, in fact, is nothing more than a re-statement of Avogadro's Law 

 (S 128). 



323. The number of molecules of the first kind, which cross the plane 

 z = z {} per unit area per unit time in the direction of z increasing, is 



(620), 



in which the limits are from GO to + oo as regards u and v, and from to oo 

 as regards w. 



These, however, do not all come from the same point, and v 1 must, in 

 accordance with the principles already explained, be evaluated at the point 

 from which they started after their last collision. Those which move so as 

 to make an angle 6 with the axis of z may be supposed, on the average, to 

 come from a point of which the z coordinate is Z Q X cos 6, and at this point 

 the value of v l may be taken to be 



*i = v l (*) - \ cos ( d -) ........................ (621). 



\oz/ Z(I 



If, then, we wish to go as far as the first order of small quantities we 

 divide the integral (620) into two integrals corresponding to the two terms of 

 the right-hand of equation (621). 



We obtain as the value of the first 



/&* 



7T 



where w = w w 



f+ao 

 J -ao 



TH.'-oo 



e- to ' w2 (w + Odw ............ (622). 



Now 



I X e- to ' w2 (w + Od 



J Wo 



! +Q e- hm ^du= ! +X e- hm * v *dv .-=y ^, 



