Kinetic Theory of Solids. 535 



about 65 times as large as the actual, and latent heats about 

 4- 7 5 times as large. 



3. Testing of Equations on the supposition that the Mole- 

 cules alter somewhat with Change of Temperature. — The next 

 step is to ascertain what modification in the assumptions so 

 far made would bring theory and experiment into accord. If 

 we return to the approximate expressions 



((3) £=-2D/9<?(>-E) 2 



and 



(9) \ = 2D{vo-v l )/3e 2 (e-E), 



we see at once that if E, which represents the linear dimen- 

 sions of the molecule, were to diminish with rising tempera- 

 ture, then theory and experiment could be brought to better 

 accord. Now the shrinking of molecules with rising tempe- 

 rature is a result required by the kinetic theory of gases, for 

 the variation of the viscosity of gases with temperature is 

 such as can be accounted for satisfactorily only by shrinkage 

 of molecules with rising temperature. 



Holman (Phil. Mag. 5th ser. vol. xxi.) has made a thorough 

 comparison of the results of all the best measurements of the 

 effect of temperature on the viscosity of air, including his 

 own, and his series of curves shows that up to 250° C. the 

 viscosity of air at any temperature is best given in terms of 

 that at zero C. by the exponential formula 



Vt = Vo (l + 0-0036Jt)™ or *=W0/273)**, 



where 6 is absolute temperature. Now, according to the 

 kinetic theory of gases, assuming the molecules to be spheres 

 of sectional area <r d 2 , and ignoring molecular attraction, we 

 have 



Ve = V2rMiBH 2 W27B)i y 

 and hence 



(<r m /o- e y=(d/273y 26 ; 



that is to say, the molecules shrink with rising temperature. 

 Now Barus (Amer. Journ. Sci. 3rd ser. vol. cxxxv.) has 

 given weighty support to this idea of molecular shrinking by 

 pushing the study of the viscosity of air and hydrogen up 

 to 1200° C, and showing that up to that temperature the 

 viscosity of both gases is well represented by 



2 



^ = ^273 (0/2 73) F , 

 according to which 



(<r m /<r 9 ) 2 =(0/my- 



