of Gases and Molecular Force, 529 



Integrating first with respect to b, we get 



"mil 7 ' 2 ^ [{1 + ^W/V 1 }*- (1 + W(Vr)/V*- V*/r*}*\ 



~^?L {1 + 2m/(l/r)/V 2 p+ {1 + 2iw/(l/r)/V»-0*/r*}* 

 D-2a 



; 2«p^ r 1 H 



Vj 2a 2aL{l + 2m/(lA0/V 2 }*+{l + 2m/(l/r)/V 2 -^/^}^ 2 J 



We could proceed no farther without a knowledge of the 

 law of force, but if it is that of the inverse fourth power, 



f(l/r) = A/A 



Even with this substitution the handling of the last integral 

 in a general way would occupy too much space, and for 

 present purposes we shall be better served by a consideration 

 of its values in particular typical cases, say those of hydrogen, 

 oxvgen, or nitrogen at particular temperatures : 2mf(l/r)/Y 2 

 takes the form (2a) a C/i*T, and Z/ 2 =(2«) 2 (l + 0/T). For 

 hydrogen C = 79, and taking T as 173, 273, 373, 473, and co , 

 we get by approximation the following numerical values of 

 the last integral, assuming 1/D = : — 



T 173° 273° 373° 473° oo 



Integral . . . -1647 '1652 '1658 '1664 -1666 



I do not guarantee the fourth figure of these values to be 

 accurate, but the main result is clear enough, namely, that 

 for hydrogen as a gas the integral is almost independent of 

 V 2 or temperature ; and as the integral has for nitrogen 

 (C = 109) the above values at temperatures 239°, 377°, 515°, 

 653°, and oo , and for oxygen at 278°, 439°, 600°, 760°, and 

 co , we can say that for the element gases the value of the 

 integral is 1/6, and thus 



-_ D-2a 2a 

 l ~ V + 3V ? 



which, of course, is the result also for forceless molecules, as it 

 is exactly true when Y = go , in which case finite force becomes 

 negligible. Accordingly it has been shown that the effect 

 which curvature of path and acceleration due to molecular 

 force have on the time between two encounters or on the 

 number of encounters may be neglected, and the number v for 

 attracting molecules is 



2 |m^(i + ^^ ( 4^)v{i-is^4 



Phil Mag. S. 5. Vol. 36. No. 223. Dec. 1893. 2 N 



