Pressure-Gauges for the Highest Vacua. 85 



Now, as was first shown by Kundt and Warburg, and as 

 has been shown in " Thermal Transpiration and Radiometer 

 Motion," the effect of slipping of gas on the influence of 

 viscosity is to replace the viscosity tj by 97/(1 + 2£/D), where 

 f is the coefficient of slipping and equal to a\ } where a is a 

 fraction which is probably nearly the same for most gases, 

 and \ is the mean free path of a molecule of the gas near the 

 solid surface, D being distance between moving and resting 

 solid surfaces ; for a given gas, \ is nearly proportional to X, 

 the mean free path of a molecule far from the surface, and as 

 X is inversely proportional to the density, we have the result 

 that f varies inversely as the density of the gas. Thus a mea- 

 surement of slipping furnishes a means of measuring density, 

 and therefore, if the law connecting density and pressure is 

 known, of measuring pressure. 



If Boyle's law holds, then A.=Xqpo/P> where X is the mean 

 free .path at some standard pressure p ; thus tj is replaced by 

 r)/(l + 2dk p /Dp). When p is large enough, this is indis- 

 tinguishable from 7j, as we saw to bo the case in Crookes's 

 experiments with air from 47 mm. to 4 mm., through which 

 range the log. dec. retained a constant value which we may 

 denote by L. Then, if I is the log. dec. at lower pressures, 

 li/l gives 1 + 2a\ p /Dp, whence we can get values of 2a\ p /D 

 which ought to be all the same. But there is first one little 

 correction to make, namely that for the viscosity of the torsion 

 fibre, because a small constant portion of the log. dec. is due 

 to its small viscosity ; it is the value of the log. dec. for the 

 apparatus if an absolute vacuum were attained in it. Call 

 this part of the log. dec. yu-, then 



(j^-^P = 2a\,iVD. . . . (34) 



At the higher values of p we can neglect fi and obtain at 

 once a mean value of the constant 2a\ p /D, and then with this 

 as a known quantity solve for /a at the lower pressures. In 

 this wslj, from the data already given for air, 2a\ Q p /D appears 

 to be 15 and fi to be '004. With these values and that for L, 

 namely '1000, the last equation becomes one for obtaining p 

 by a measurement of I ; and to show how it works, we give 

 the values of p obtained by it from Crookes's values of / 

 already given : — 



p by gauge 1000 495 300 100 53 24 13 8 



p from log. dec 1153 406 283 101 49 23 138 86 



Now it is obvious that the new method of finding the 



