216 PHENOMENA DEPENDENT ON MOLECULAR PATHS 85 



as a factor into the formula for the coefficient of viscosity, 

 increases with the temperature at nearly the same rate for 

 all gases ; and it is not unreasonable to expect the same also 

 with respect to the free path. 



As a fact, the earlier of the more accurate measures 

 made on the increase of the coefficient of viscosity with the 

 temperature seemed to result in a simple relation to the 

 coefficient of expansion, and therefore to a magnitude which 

 has nearly the same value for all gases. Maxwell 1 first 

 drew from his observations that the coefficient of viscosity 

 of air increases in the same ratio as the absolute tempera- 

 ture, and thus proportionally to 



1 + a$, 



where 3 is the temperature measured from freezing-point, 

 and a is the coefficient of expansion. It was, indeed, 

 proved by the later experiments of other observers 2 that 

 the viscosity, at least of atmospheric air, does not increase 

 with the temperature so rapidly as Maxwell had believed ; 

 but it was conclusively shown that it rises more rapidly 

 than the square root of the absolute temperature, i.e. faster 

 than the magnitude 



There can therefore be no further doubt that, in the 

 formula for the coefficient of viscosity ( 78) 

 97 = 0-30967 pl/n, 



not only does the speed ft, which is proportional to that 

 square root, increase with the temperature, but so also does 

 the free path L. 



The endeavour was then made at first to express the 

 dependence of the coefficient of viscosity on the temperature 

 by a factor of the form 



i + aBr, 



1 Phil. Trans. 1866, clvi. p. 249 ; Scientific Papers, ii. p. 1. 



2 0. E. Meyer, Pogg. Ann. 1873, cxlviii. p. 203. Puluj, Wiener 

 Sitzungsber. Abth. 2, 1874, Ixix. p. 287 ; Ixx. p. 243 ; 1876, Ixxiii. p. 589. von 

 Obermayer, ibid. Abtb. 2, 1875, Ixxi. p. 281; 1876, Ixxiii. p. 433 ; Carl's 

 Eepert. 1876, xii. p. 13 ; 1877, xiii. p. 130. Warburg, Pogg. Ann. 1876, clix. 

 p. 403. 



