310 Mr. W. Sutherland on the 



force parallel to T exerted by a ring of radius r about N, 

 and of thickness dl on an element dz of the rod, we get, 

 if ON = ZandOZ=^, 



„ . _2 ^^ '^^ ^Trr- dr z—l 



Integrate with respect to r from NR to NS = C the radius of 

 the tube, with respect to z from OQ to a limit which we 

 may indicate by the symbol oo , and with respect to I from the 

 limit A, which is the distance from the plane AB up to R, 

 which is OP the radius of the surface, and we have the 

 desired expression 



S^r^ „, ^Jz — l)dzdlrdr 



xJh Jr+wv 



The integral evaluated becomes 



+ log ^-±X^^^^=^'\ . 



Expanded in powers of h as far as 1st, and with s put for 

 R— /t, this becomes 



27rAap^riog ^ + ^1 -"4+ ^ ] ■ 



'^L^5+^/25R <^c R R(s+V2^R) -* -" 



Let us call the angle of contact of meniscus-surface with 

 tube 6. We know, from the usual theory of capillarity 

 verified by experiment, that 6 is constant ; and this result 

 holds in the same manner for the law of the inverse fourth 

 power, so that, in the above expression, c/R, which = cos 6, 

 s/H, which =1— sin^, are both constant ; and therefore the 

 first term is independent of the curvature of the meniscus, 

 while the coefficient of e may be written 



^ n/ 2(1 - sin 5')+ sin 6' -^(1- sin ^)? 

 Rcos6> ~ R "^ R { 1 - sin 6' + '^2(1 - siir^ ^ 



We leave out of count the constant term as not entering into 

 the question of capillary action, and compare our last ex- 

 pression with the expression which we get for the capillary 

 pressure on the column QT, due to a tension a per unit width 



27rAap2 f 



