HOGG. — FRICTION AND FORCE DDE TO TRANSPIRATION. 123 



In that case equation (I) becomes, 



where 



I is the total decrement at a lower gas pressure, and the other 

 quantities have the same significance as before. 

 Now, on dividing (I) by (II), 



X-K _ D + 2p 

 l-K~ D 



P 



since /? is inversely proportional to jy. This equation may be written 

 in the form 



This equation is deduced by Sutherland ; and it is also of the form of 

 that used by Kundt and Warburg in their investigation to verify their 

 theoretical conclusion that the coefficient of slip varies inversely as the 

 pressure. As has been said, however, they were unable to measure 

 the lower pressures, and so the law was not submitted to a test at very 

 low pressures. 



The relation between pressure and logarithmic decrement expressed 

 here is the one utilized by Sutherland ^^ to determine p after the con- 

 stants in the foregoing equation have been determined. The data for 

 this purpose he found in Crookes' paper on ' Viscosity of Gases at very 

 High Exhaustions.' There the logarithmic decrement of a vane of mica, 

 suspended with its plane vertical, and performing oscillations about a 

 vertical diameter, is given for pressures ranging from that of an atmos- 

 phere to 0.02 million ths of an atmosphere. The pressure was measured 

 by a McLeod gauge. Sutherland's formula applied to these results 

 gave very good agreement from about 0.2 mm. to about 0.01 mm. in 

 the pressure as measured by the gauge, and the pressure as calculated 

 from the formula. Below 0.01 mm. the agreement was not good. 



Stokes 13 has shown that, in this apparatus, the coefficient of viscosity 

 is not proportional to the logarithmic decrement, and therefore, as 



" Phil. Mag., [5], 43, 1897. 



" Note added to Crookes* paper. 



