484 Mr. W. Sutherland on Thermal 



one of which was larnpblacked. For all the experimental 

 niceties reference must be made to the original paper (Phil. 

 Trans, clxxii.) 



It is obvious from the description of this apparatus that it 

 does not comply with the conditions under which (25) was 

 established, as the mica plate is probably only a fraction of a 

 millimetre in thickness and between 5 and 10 millim. from 

 the glass bulb where it is nearest, so that the length of the 

 region in which thermal transpiration occurs is much less 

 than its width, whereas in (25) the contrary is supposed to 

 be the case. The chief effect of the difference in these con- 

 ditions will be that thermal transpiration, instead of going on 

 over the whole distance between edge of plate and bulb, will 

 extend to a distance from the edge of the plate which will 

 depend on the conductivity of the gas ; in fact, if we move 

 along the shortest distance between plate and bulb we shall 

 find the fall of temperature across that line grow less as we 

 leave the plate and become negligible before we reach the bulb ; 

 but the better the conductivity of the gas the farther will the 

 dominating influence of the edge of the plate extend ; there- 

 fore in our formulae, when applied to Crookes's experiments 

 with the torsion radiometer, D must be interpreted as a 

 function of conductivity k' . Then b being the length of the 

 edge of the black half of the plate, the area S over which 

 thermal transpiration is effective may be taken to be bT), over 

 which at the front and the back of the plate there is an 

 average difference of pressure p^—p^ which, however, will 

 not be maintained over the whole front and back of the plate, 

 because there is so much facility of escape for the gas, but 

 only near the edge, so that probably E varies as bD ; thus 

 (E + $)b/s will be replaced by 6K, where K is a function of 

 kf. Another effect of the fact that thermal transpiration 

 occurs only to a certain distance from the edge of the plate 

 will be to reduce the effect of slipping, seeing that the velocity 

 of transpiration dies away to zero in the gas. To indicate 

 that slipping has not its full theoretical effect we had better 

 change B' to B", and to remind ourselves that in A! and B' 

 the symbol I) or 2R now means a function of A/, we will 

 change A! to A" and B" to W f and put 



bK(v 2 — vi)/(v 2 + v 1 )=e r , 

 then (25) becomes 



deflecting force = c7(A"p + B'"+l/p). . . (27) 



There is no need to take account of molecular force in 

 altering density at edge of plate because so small a fraction 

 of the free path lies in the condensed gas. 



