612 Prof. Rankine and Mr. Smith on Molecular Dimensions 



values, viz., 0'943 xlO -4 C.GKS. units (in brackets in 

 Table V.), in conjunction with our value at 100° C, and 

 calculated therefrom Sutherland's Constant which is given 

 in brackets in Table V. It is recognized that, in view of 

 the mode of calculation, this value for C, viz. 370, is only 

 tentative, but it is noteworthy that Vogel quotes in his 

 paper the value 352, although he does not give his authority. 



Calculation of the Molecular Dimensions. 



We now proceed to the calculation of the molecular 

 dimensions of these gases. The basis of this calculation is 

 Chapman's formula * 



47TO- — 



_ 0-491(1 + <=„)/> V 



2H(l+£) 



where cr = radius of the molecule treated as an attracting 

 elastic sphere, 

 p = density of the gas, 

 V = mean molecular velocity, 

 v= number of molecules per cm. 3 , 

 7] = viscosity, 



C = Sutherland's Constant, 

 T = absolute temperature. 



The factor (1 -f e a ) depends upon the ratio C/T, but is 

 practically equal to unity in all cases under present con- 

 sideration. 



The quantity which we have calculated is 7rcr 2 , or rather 

 its equivalent in cases where the molecule is not spherical. 

 As already indicated f we may regard ira 2 in the above 

 formula as the mean area presented for mutual collision by 

 the molecules, and we will denote it by A. 



The number of molecules per cm. 3 has been taken as 

 2-705 XlO 19 at N.T.P. (as recently given by Millikan), and 

 the densities have been calculated on the basis of the 

 molecular weights, taking the density of oxygen at N.T.P. 

 as 1*429 x 10 ~ 3 gm. per cm. 3 



* Chapman, Phil. Trails. A. vol. ccxvi. p. 347. 



Note. — Chapman's formula, as given in his paper, Las been amended 

 by the inclusion of the initial factor 4 which Chapman had inadvertently 

 omitted. 



f A, O. Rankine, Proc. Roy. Soc. A. vol. xcviii. p. 360. 



