88 Mr. W. Sutherland on two New 



for the ratio of pressure from log. dec. to pressure from 



deflecting force. 



Def. for 30-9 22 3 20-2 17 131 115 85 



p by gauge 13 8 7*2 5'9 44 34 2-6 



p from def. for.... 13'5 8-6 7'6 6-2 4*7 4-0 2-9 



j> from log. dec.... 13-8 8-6 79 67 5"0 44 36 



1-0 10 1-0 14 14 11 12 



Def. for 74 4'2 21 2-0 17 14 1-0 7 '5 



p by gauge 1"9 1'3 l'O "55 46 -22 44 -06 -02 



p from def . for. ... 24 14 70 -67 '57 47 '33 -23 47 



^ from log. dec. ... 3-0 2-5 22 1-8 165 1-33 1-25 -95 -53 



1-2 1-8 34 27 2-9 28 38 44 31 



At first sight these numbers seem to show that the pres- 

 sures given by the deflecting force are in much better 

 harmony with those given by the gauge than are those given 

 by log. dec, but we shall show that this is due to a defect in 

 Crookes's torsion radiometer when made to do duty as a 

 pressure-gauge, a defect which could be avoided in a suitable 

 design ; for a study of the row of ratios shows that while the 

 value increases slowly from 1*0 to 1°2 there is a sudden tran- 

 sition to a value about 3*0, and the theoretical reason for 

 expecting such a change of ratio was pointed out in " Thermal 

 Transpiration and Radiometer Motion/' as it was stated that 

 iii Crookes's instrument the formula would represent the 

 relation between deflecting force and pressure as long as the 

 vertical plate was able to control the fall of temperature in 

 the gas near its edge, but that it would cease to do this as 

 soon as the mean path of the molecules became nearly equal 

 to the radius of the bulb, for then the great surface of the 

 bulb compared to the thickness of the plate w 7 ould enable it 

 to swamp the influence of the plate, even in the plate's own 

 neighbourhood ; thus there should be a change from the 

 limiting relation def. force = c f p for the plate, to def. force 

 = c"p for the bulb. Now the above change of ratio is estab- 

 lished at a pressure about 2*5/10 6 atmo as given by log. dec, 

 when the mean free path of a molecule of air ought to be 

 about 10 6 x , 00001-r-2 - 5 centim. or 4 centim., which is about 

 the radius of the bulb. The approximate constancy of the 

 new r ratio at about 3 should increase our confidence in the 

 pressures derived from the log. dec. as continuously fairly 

 reliable down to the lowest pressure of half-a-millionth of an 

 atmo, whereas the M'Leod gauge gives pressures only half 

 as large as they ought to be at about 2/10 6 atmo and about 

 1/26 as large as they ought to be at # 5/10 6 atmo. 



