THE KINETIC THEORY OF MATTER. 



151 



Fio. 81. 



But near the edges this compensation will not be complete. For a 

 distance inwards comparable with the M.F.P. the lines of flow of heat 

 will diverge from each other as shown in Fig. 80, and the temperature 

 falls at an increasing rate from the hot plate outwards. The density at 

 the average distance from which we 

 may suppose the molecules to come 

 to the plane is greater than well 

 inside the edge, and the change in 

 temperature and in velocity of the 

 molecules at their impacts is greater. 

 This results in a greater pressure 

 against the area near the edge on the 

 hot side, which continues as long as 

 that side is hotter. On the cold 

 side there will be a similar edge 

 effect, for the hotter molecules will 

 to some extent come round the edge 

 and carry heat into the cold surface. 

 The temperature at the average dis- 

 tance from which we may suppose the 

 molecules to come will be higher and 

 the density less than well inside the 

 edge on the cold side. There results 

 a defect of pressure near the edge. 



Reynolds and Maxwell both showed that the excess of normal pressure 

 on the surface is proportional to 



rate of increase of temperature slope outwards 

 pressure. 



Hence, since the temperature slope with a plane decreases outwards 

 only near the edges, and for a width of surface comparable with the 

 M.F.P., both the numerator and denominator contribute to make the 

 total force greater the less the pressure of the gas ; hence the necessity 

 for the very high vacua with vanes of the ordinary size. 



If the vanes are curved, as in Fig. 81, the convex side being hot, the 

 lines of flow are somewhat as represented in Fig. 79, and the divergence 

 on the hot side is more marked, while it is hardly noticeable on the cold 

 side. In this case the excess of pressure on the hot side will be greater 

 than with a plane surface. 



At ordinary pressures the edge acted on by the pressure excess is 

 exceedingly narrow of the order of the M.F.P., which, as we have seen, 

 is comparable with 10" 5 cm., while the pressure excess can be shown by 

 the theory to be inversely as the pressure. Hence the total force is very 

 minute. But if the body acted on is reduced to exceedingly narrow 

 dimensions, and its mass correspondingly reduced, the effect may still be 

 noticeable at ordinary pressures. This was pointed out by Reynolds, 

 and he succeeded in detecting the action on spider lines and silk fibres 

 at pressures comparable to the atmospheric pressure, one side of the fibre 

 being exposed to radiation (I.e., p. 768). 



We have, perhaps, an example of the action, which we may call 



