116 il/r Todd, A partictdar case of a theorem of Dirichlet 

 hence the area of the section made by the F-plane will be 

 27r V(l + «^ + ^-)/3nV3 F. 



Now the perpendicular distance between two near F-planes, 

 r and r + ST, is 8r/V(l + >i^ + ^-), and so the element of volume 

 enclosed by these two planes and the surface A = 1 will be, to the 

 first order, 



27r ST 

 3nV3'^' 



Integrating this between the limits F = 7^+^ and F = 7^' (i.e. the 

 F-planes of any two consecutive integral points), we find that the 

 volume of the space enclosed is 27r log 7/3/1^3 ; and since this is 

 independent of the integer p, our proposition is proved. 



a 



