216 Lord Kayleigh on the 



and 



z=U${Sf(p-)dp-TLf?}- h dp (15) 



It is possible that a graphical process would be found suitable. 

 Equation (14) determines the curvature at any point of the 

 curve representing the relation between p and z in terms of 

 the coordinates and the slope. 



When the relation between p and z is known, the calcula- 

 tion of the surface-tension is a matter of quadratures. Probably 

 the simplest way of considering the question is to regard the 

 free surface as spherical (liquid within and vapour without), 

 and to calculate the difference of pressures. 



We have from (1), 



p 2 _ i , 1= [ /3 y]-r (2) V^ = 2K( / a/-p 1 2 )-r (2) Y^^ . (16) 



J(l) J(l) a ~ 



z being measured outwards along the radius. The question is 

 thus reduced to the determination of V at the various points 



Fig. 3. 



of the layer of transition, for all of which ^ = R approximately. 

 Let P (fig. 3) be a point at which V is to be estimated, 

 so that OP = 0, and let A Q B be a spherical shell of radius 

 £— ?, of thickness <if, and of density p' . We have first to 

 estimate the potential dY of this shell at P. 

 The element of mass at Q is 



p'.iir sin 0dd{z-Z) 2 d£. 



If, as before, <£(/) express the ultimate law of attraction, and 



w)=JV)#, 



we have to multiply the above element of mass by II(/). 

 Now 



f2 = YQ^ = z^ + ( z -^-2z(z-i) cos 6, 

 so that 



—a COSC/— y — ^r-. 



