Pressure- Gauges for the Highest Vacua. 8? 



the discrepancy in the last comparison entirely to the inade- 

 quacy of the indications of the gauge at these very low 

 pressures. 



In Crookes's measurements of the apparent repulsive force 

 of a candle on his torsion radiometer we have another means 

 of determining the pressure independently, and the torsion 

 radiometer thus used becomes our second form of pressure- 

 gauge. In " Thermal Transpiration and Radiometer Motion"" 

 it was shown that the deflecting force exercised by a source of 

 constant radiation on the vertical plate of the torsion radio- 

 meter is connected with the pressure of the gas by the 

 formula 



deflecting force = c'l(M'p + W" +l/p). . . . (26) 



But we must remember that this is derived from the equa- 

 tion (12), 



which, when n is large enough, reduces to 



dp 3R 2 _ dv 



dx Ar\ dx 



whence the deflecting force becomes proportional to \ — that 

 is, inversely proportional to the density. Hence, at a large 

 enough value of n, the deflecting force gives a measure only 

 of the density, just as the M'Le'od gauge and the viscosity- 

 meter gauge do ; and it is only by using Boyle's law that we 

 get the form of equation (26) given above, which, when p is 

 large enough, becomes 



deflecting force = c'jkl'p* 



Similarly it can be shown that when p becomes small enough 

 the equation really only gives a connexion between the mean 

 density and the difference of density at the front and back of 

 the plate, which passes into a connexion between deflecting 

 force and pressure only on the assumption of a law connecting 

 density and pressure. When this is Boyle's law, the complete 

 equation is (26) above. For Crookes's instrument with air 

 c' = 3'0, A" = -001, and B'" = -01 when the unit of pressure is 

 1/10 6 atmo and the unit of deflecting force arbitrary. Accord- 

 ingly, with the values of the deflecting force at low pressure, 

 we can calculate the pressures ; thus in the following table 

 we give the pressure as given by the M'Leod gauge with 

 Boyle's law, by the deflecting force with equation (26), and 

 by the log. dec. as given in the last table, and we add a row 



