236 Messrs. Lodge and Clark on Dusty Air in the 



so some other component must be less. The horizontal com- 

 ponent of velocity parallel to the surface we naturally assume 

 to be simply the average. The component normal to the sur- 

 face must therefore be less than the average. In other words, 

 though the total pressure is the same in all directions, its 

 vertical component in the case of up- or down-streaming air is 

 greater, and hence the normal component is less; and the 

 amount by which the normal component of the pressure is less 

 than the average at any given distance from the body depends 

 upon the velocity of the convection-current at that place. 



But the current- velocity increases as we go from the body 

 to a maximum, and then decreases : consequently the normal 

 component of the pressure, starting from its average value 

 close to the surface, decreases as far as the maximum-velocity 

 layer, where it reaches a minimum, and then increases. It 

 is this differential normal pressure from the surface which 

 the dust-particles feel, and they are driven back towards the 

 maximum-velocity layer. They may not, indeed, be driven 

 quite to it, because there must be a compromise between the 

 rate at which dust is carried past the surface and the distance 

 to which the differential bombardment has time to drive them 

 through the air. 



It is easy to see that any differential bombardment will be 

 simply proportional to the volume of the particles, provided 

 their thickness is small ; hence the behaviour of big particles 

 relatively to small ones will be like their settling behaviour 

 under gravitation. 



Putting the matter in symbols, let us call the plane 

 of the solid yz, y being vertical ; and let u, v, w be 

 the three component velocities along a, y, z respec- 

 tively, and T the absolute temperature; and let = 

 signify proportion only when convenient : then 



u 2 + v 2 + w 2 = 3T. 



But at a distance x from the surface let the convection up- 

 streaming velocity be </>, and let the velocity along z be the 

 average: then 



8 t„ 2 =T, 



and 



v 2 = w 2 + (j) 2 ; 

 so 



u 2 = T-cf> 2 . 



Hence u decreases as </> increases, and there is accordingly 



