486 Mr. W. Sutherland on Thermal 



of the gas becomes comparable with the linear dimensions of 

 the containing vessels ; they did this by pushing the rare- 

 faction of the gas so high in a vibrating-disk apparatus for 

 measuring viscosity that the logarithmic decrement diminished 

 measurably — for example, with air and a distance of \11 cm. 

 between the fixed and moving plates the log. dec. at 1 atmo 

 was *132, at '01 atmo it was *129, and at -0008 atmo it was 

 •111 ; now at 20° 0. and at these pressures the mean free 

 path in air is about '00001 cm., '001 cm., and *012 cm. 

 respectively, this last value is nearly 1/10- of the distance 

 between the plates, so that when the distance between the 

 plates is only 10 free paths the log. dec. diminishes by 16 

 per cent, of its limiting value when the distance is a large 

 number of free paths. Thus we see how the measurements 

 made by Crookes of the log. dec. in his apparatus give 

 valuable information as to the relation between the free 

 path of the gas and the distance from the edge of his mica 

 plate to the glass bulb. In the following table the first 

 row contains the pressures of dry air at 15° C. in terms 

 of the atmo as unit, the second gives 10 4 times the log. dec, 

 the limiting value of which at higher pressures is 1000, and 

 the third contains the deflecting force of the candle in an 

 arbitrary unit : — 



prerfs 736 495 300 100 72 39 



10 l log. dec 975 966 952 876 824 710 



def for rexp * •'• 3 ' 5 5 ' 5 10 '° 27 '° 32 ' 9 41 ' 4 



leal. ... 4-0 5-9 9-6 25 313 39-7 



presB 36 29 19 13 11 



10 4 log. dec 695 657 577 500 460 



def for ( ex l 3 - - 42 " 5 42 " 6 388 30 ' 9 27 ' 1 

 leal. ... 407 40-8 36-8 30-0 26-8 



Thus at a pressure between 36 and 29 millionths of an 

 atmo the repulsion rises to a maximum, say at 30 millionths, 

 at which the mean free path is *00001 x 10 6 /30, that is one- 

 third of a centimetre. The actual distance between the edge 

 of the mica plate and the bulb is not given by Crookes, but 

 from the figure he gives one would imagine that the distance 

 might be between '5 cm. and 1 cm., and thus the experi- 

 mental result corresponds to our theoretical one that the 

 maximum effect is to be expected when D = 2X ; before the 

 maximum is reached the repulsive effect ought, according to 

 (27), to vary inversely as the pressure, so that the products 

 of the numbers in the first and third rows above ought to be 

 approximately constant, and the first four products are 2600, 



