1881.] Note on the Reduction of Mr. Crookess Experiments. 459 



altogether liad tlie moment of inertia of the vibrating body been 

 sufficient to make the time of vibration sensibly independent of the 

 gas, as was approximately the case, the condition of similarity is that 

 the densities shall be as the log decrements of the arc of vibration, 

 and the conclusion from theory is that when that condition is satisfied, 

 then the viscosities are in the same ratio. Pressures which satisfy 

 the condition of similarity are said to " correspond." 



It was found that on omitting the high exhaustions, the experiments 

 led to the following law : — 



The ratios of the viscosities of the different gases are the same for 

 any two groups of corresponding pressures. In other words, if the 

 ratios of the viscosities of a set of gases are found (they are given by 

 the ratios of the log decrements) for one set of corresponding pres- 

 sures, these pressures may be changed in any given ratio without dis- 

 turbing the ratios of the viscosities. 



This law follows of course at once from Maxwell's law, according to 

 which the viscosity of a gas is independent of the pressure. It does 

 not, however, by itself alone prove Maxwell's law, and might be 

 satisfied even were Maxwell's law not true. The constancy, however, 

 of the log decrement, when the circumstances are such that the molar 

 inertia of the gas may presumably be neglected, proves that at any 

 rate when the density is not too great that law is true ; and the varia- 

 bility of the log decrement at the higher pressures in all but the very 

 light gas hydrogen is in no way opposed to it, though Mr. Crookes's 

 experiments do not enable us to test it directly, but merely establish a 

 more general law, which embraces Maxwell's as a particular case. 



The viscosities referred to air as unity which came out from Mr. 

 Crookes's experiments were as follows : — 



Oxygen 1 "117 



Nitrogen and carbonic oxide 0*970 



Carbonic anhydride '823 



Hydrogen '500 



The viscosity of kerosoline vapour could not be accurately deduced 

 from the experiments, as the substance is a mixture, and the vapour 

 density therefore unknown. Assuming the relative viscosity to Le 

 0*0380, the vapour density required to make the experiments fit came 

 out 3*408 referred to air, or 49'16 referred to hydrogen. 



When once the density is sufficiently small, the log decrement may 

 be taken as a measure of the viscosity. Mr. Crookes's tables show 

 how completely Maxwell's law breaks down at the high exhaustions, 

 as Maxwell himself foresaw must be the case. Not only so, but if we 

 take pressures at those high exhaustions which are in the same ratios 

 as "corresponding" pressures, the log decrements in the different 

 gases are by no means in the ratios of the densities. 



