8 S. Chapman — Kinetic Theory of Gases 



T is the absolute temperature, and R is the gas constant, while 

 A is a numerical quantity given by 



(A.2) A={5xJ2Y,}/8I,(w)r(4-^). 



The sum Uy^ is a number nearly equal to i, and depending 



only on the value of n, and on this only to a slight degree. 



Thus the dependence of the viscosity on the temperature is 

 according to the law 

 (A.3) KocT^ 



where 



(A4) ^ = i + _A_. 



Thus n may be inferred bv observing the variation of K with 

 respect to temperature. 



The distance (Tq) of closest approach between two molecules 

 moving towards one another in a direct line, each with the 

 mean molecular energy fRT, is given by 



3(n-i)RT j 



Expressed in terms of K and N, by means of (A.i), this 



becomes 



(A.6) To = 3-i/(n-i) A-^ (mo R T)i {WjKf = A^(Ni/K)^ 



The force Fo at this distance is given by 



(A.7) Fo = t./r« = 3 (71- i) R T/ro ^ AJ (K/N^)^ 



where 



(A.8) Ai=3(n-i)RT/A^ 



the force F at any other distance r is Fo (ro/r)^. 



It is convenient to tabulate log. A^, log. AJ,, for the 

 temperature o°C. or 273°* i absolute, using the values of l^in) 

 calculated in this paper : the value of Sv^ has been estimated 

 for the various values of n as follows, 



^= 3 5 7 9 II 15 



ijv^ = 1.01737 i.ooooo 1.00170 1.00400 1.00625 1.00815 



while 



mo= 1-651. io-24gm., R- 1-372.10-16, 



The results are 



^= 3 5 7 9 II 15 



log^- A ^ -= 1 1 .7068 10.2719 "10.3146 10.3292 10.3378 T0.3431 

 log.A^= 3.6450 3-3809 3-5144 2.6247 2.7130 2.8533 



