202 Mr. W. Sutherland on the Spontaneous 



Of course, Crookes in working his M'Leod gauge to get 

 the pressures just given, had no knowledge of Bohr's sub- 

 sequent discovery of the failure of Boyle's law in oxygen at 

 low pressures, so that the numbers given in the first row as 

 the pressures are not the true pressures; though starting 

 nearly true at 1000 they end up at 190, nearly twice as large 

 as Bohr's formula would give. But, as has been pointed out 

 in "Two New Pressure-Gauges''*, this erroneous yield of 

 pressures does not affect our application of them in onr for- 

 mulae for log. dec. and deflecting force, because in these 

 formulae p merely replaces 1/B, and what the M'Leod gauge 

 really gives is 1/B, whether Boyle's law holds or not ; if 

 Boyle's law holds the values of 1/B are given in such a unit 

 that they are equal to p, but if Boyle's law fails, though they 

 no longer give p, they give 1/B in an arbitrary unit. Thus, 

 for example, according to the formula for log. dec. 



{(L-^/G-^-l} 



is proportional to X, the mean free path, which is directly as 

 the volume B, so that 



(^-l)/B=2<A /B D, 



wherein Crookes's values of p may be taken as correct rela- 

 tive values of 1/B, so that we can form the products 



{(L-a.)/(Z-/*)-1}/B 



from the values of /, the log. dec. in the last table, taking L 

 as *1120 and //. as '004, and 1/B as given by p; thus for 

 2aX /B D we have the values 17, 21, 19'7, 20'6, 20*9, 17'3, 

 18*1, and 15*6, which for a pure gas ought all to be the same, 

 but as I is not very different from L at the higher pressures 

 we cannot expect accurate constancy, but can state that there 

 is no disturbance in 2a\ /B D at all comparable to the dis- 

 turbance in the deflecting force. To assure ourselves of this 

 we will trace the values of 2a\ /B D down to the lowest 

 pressures. 



p 171 110 82 70 48 31 28 22 16 12 4 1'6 -3 



10 4 I... 1033 988 940 912 840 744 724 670 621 585 433 348 302 

 149 153 164 168 164 165 16-2 157 13-8 11-8 7'0 4'0 -94 



These show that 2aA, /B D has an approximately constant 

 value at about 16 down to about a so-called pressure of 

 20/10 6 atmo, below which there is a rapid diminution. 



Being now in possession of the essential facts connected 

 * Supra, p. 83. 



