536 Mr. W. Sutherland on a 



Now both these formulae for g are derived by combining a 

 theoretical equation with empirical formulae, and in the theo- 

 retical equation molecular attraction is supposed not to exist. 

 But the effect of molecular attraction on viscosity will partly 

 account for the apparent shrinkage of molecules, because 

 slowly moving molecules coming near to one another without 

 actually colliding are swung round their common centre of 

 mass by the action of molecular force, and are affected as 

 regards their subsequent paths, as if they had suffered a col- 

 lision. At high velocities two molecules, which pass close to 

 one another without actual collision, shoot past one another 

 with only a slight mutual deflexion ; thus the molecules 

 behave as if they had larger volumes at lower temperatures. 

 This effect of molecular force on the temperature-variation of 

 viscosity is a difficult problem in the kinetic theory of gases, 

 which remains yet to be worked out. Steps towards its solu- 

 tion have been taken by Maxwell (Phil. Trans. 1867) and by 

 L. Natanson (Kinetische Theorie unvollkommener Gase), but 

 no definite enough result has yet been reached to give a 

 quantitative estimate of the importance of molecular force in 

 viscosity of gases. Yet from a general point of view we may 

 feel pretty sure that in the case of hydrogen the large appa- 

 rent shrinkage of the molecules cannot be traced entirely to 

 the- effect of molecular force, and must be regarded as a true 

 phenomenon. If we take our deduction from Barus's expe- 

 riments, 



a m /o- e =(6/273y% 



we notice that, although 6 ranges from 273° to 1489°, yet 



T ^ ranges only from 1*60 to 1*84 ; and thus, while the for- 

 mula for cr, if supposed to hold down to absolute zero, would 

 give the impossible result of a being infinite at zero, this 

 impossible result is merely the consequence of trying to 

 extrapolate with an empirical formula over a range seven 

 times as great as that covered by experiment. 



Accordingly, we can get no definite assistance from the 

 present state of the theory of viscosity of gases, but only a 

 general assurance that molecules shrink with rising tempera- 

 ture. For the law of shrinkage of the molecules of solids I 

 will take the expression E = E o /(l+6'0), which, up to the 

 melting-point, may more conveniently be used in the form 

 E = E o (l-6'0), so that £-E = E (5 + 6')6>. 



The steps in the differentiation for finding the bulk-modulus 

 are not affected by the variability of E with temperature : as 

 before, we have (6), 



