Theory of Surf ace Forces, 



459 



in the figure. The value of the potential, corresponding to a 

 given infinitely small range of/, is then proportional to 



i 



sin 6 d0= 1 + cos 0=1 + z/f. 



If now we effect first the integration with respect to z, 

 have as the element of the final integral, 



2,rn(/)/V/{ f ( 1+2 //) ffc+.j'" 8 *}' 



we 



or 



27rnC/)/^/(2z-i/); 



and thus, on the whole, 



r v P d*=z . 4tt r W)/ ? #-*■ r n (/)/• df 



Jo Jo Jo 



= s.2K-2T, as before. 



An application of this result to a calculation of the pressure 

 operative between the two halves of an isolated sphere will 

 lead us to another interpretation of T. The pressure in the 

 interior is K + 2T/r, r being the radius ; and this may be 

 regarded as prevailing over the whole of the diametral dividing 

 plane, subject to a correction for the circumferential parts 

 which are near the surface of the fluid. If the radius r 

 increase without limit, the correction will be the same per 

 unit of length as that investigated for a plane surface. The 

 whole pressure between the two infinite hemispheres is thus 



7rr 2 (K + 2T/V)-2T.27rr, 

 or 



7n» 2 K-T.2<7rr. (40) 



This expression measures equally the attraction between the 



2 K2 



