Intelligence and Miscellaneous Articles, 319 



portional to the number of molecules impinging upon the unit of sur- 

 face in equal times ; that is, it must, on the one hand, be propor- 

 tional to the molecules present in it in a given moment (because 

 these, when in motion, impinge simultaneously upon it), and, on the 

 other, proportional to the number of molecules in the unit of length 

 (for the surface will be the more frequently struck the smaller the 

 distance of the molecules, or, in a certain sense, of the molecular 

 layers). Hence the pressures at any time are 



p -fl _ 



wi)vv 



v 



P ^ / m rz\* 3 /" =T~V 



(v£)v v T 



(2) 



From equation (2) we get also ±— = — • — = — , As this ratio '" l 



n V w, » .1 • ...», 

 P v n n 2 

 of the molecules contained in the unit of volume is equal to the ratio 



71 



-j^r of the number of molecules contained in equal volumes v =V, we 

 have for equal volumes 



If, then, both the volumes and the molecular numbers are differ- 

 ent, we get, by combining equations (2) and (3), 



P Nv W 



By combining equations (4) and (1) we have, further, 



L= L- (5) 



2 



From Mariotte and Gay-Lussac's law we have, for the same gas at 

 constant volume, 



£ =!!l 273 + f 1 __n 1 T 1 (6) 



p 2 n 2 '273 + t 2 nX 



in which the ratio of the numbers n x and n 2 of the molecules contained 

 in equal volumes represents at the same time the ratio of the den- 

 sities. T\ and T 2 denote what are called the absolute temperatures, 

 counted from —273° C. 



But if, for equal volumes of the same gas, c Y and c 2 denote the 

 velocities corresponding to the absolute temperatures T 1 and T 2 , 



