On the Viscosity of Argon as affected hy Temijerature. 69 



-1 + 3 



perature, varies as v^-'^, a formula which includes the cases {n^b, 

 71 = 00 ) already specified. If we assume the law already discussed 

 — that /X is independent of density — this conclusion may be arrived at 

 very simply by the method of " dimensions." 



In order to see this we note that the only cjuantities (besides the 

 density) on Avhich /x can depend are m the mass of a particle, v the 

 velocity of mean square, and k the repulsive force at unit distance. 

 The dimensions of these quantities are as follows : — 



/X = (mass)i (length)"! (time)"^, 

 m = (mass)i, 



V = (length)! (time)"!, 



k = (mass)! (length)'*"^! (time)"^. 



Thus, if we assume 



ixocm^.vy.h^ (1), 



we have 1 = x-i-z, -- 1 = y + {n+l)z, -1 = -y-2Zj 



1 n + 1 //. + 3 2 



whence x = ? // — 



V - I ' li - 1 n - 1 



n + 8 _ 2 



Accordingly ix = a., nr'^-^ . v'-'~^.h (^)' 



where a is a purely numerical coefficient. For a given kind of mole- 

 cule, m and k are constant. Thus 



- (+3 -1 + 3 



[X oc y'~! oc 0'^-i-2 (3)^ 



The case of sudden impacts (?6 = go ) gives, as already remarked, 

 ju. oc y oc OK Hence k disappears, and the consideration of dimensions 

 shows that ft qc d~^, where d is the diameter of the particles. 



The best experiments on air show that, so far as a formula of this 

 kind can represent the facts, /x oc 0'^'". It may be observed that 

 n = S corresponds to /x oc 0^"'-\ 



When we remember that the principal gases, such as oxygen, 

 hydrogen, and nitrogen, are regarded as diatomic, we may be inclined 

 to attribute the want of simplicity in the law connecting viscosity and 

 temperature to the complication introduced by the want of symmetry 

 in the molecules and consequent diversities of presentation in an 

 encounter. It was with this idea that I thought it would be interest- 

 ing to examine the influence of temperature upon the viscosity of 

 argon, which in the matter of specific heat behaves as if composed of 



