178 



Mr. N. D. C. Hodges on the Mean 



which molecules impinging on p come, are than those above, 

 from which particles come to p. 



If Bp is the obstruction met by a molecule in passing verti- 

 cally upward through a single layer, — *-? will be that met in 

 a direction at an angle (f> with the vertical. The integral 



J pi 



dp 



cos</> 



gives the obstruction met with by the molecule from 



one end to the other of its path. This integral must be con- 

 stant ; for the length of path is independent of the direction. 

 As the differential of the obstruction is the same as the differ- 

 ential of the density, 



cos Ho cos< £ 



where p is the density at the point p, and p x that at the other 



end of the path. As — — ~ =k, the numerator p x — p must 

 r cos 9 



be proportional to cos $. The pressure on p is proportional 



to this difference, and the resultant component in the upward 



direction to cos 2 <£. 



