formed by Contact of a Liquid with a Cylinder. 843 

 If we neglect the term involving — 2 on the right-hand side 

 of the above equation, we then have 



ydy= sin— .dc, .... (xv.) 



giving on integration 



c = r cos : * .. „ 



Substituting in (xiii.), we obtain 



and when ?/ = 0, <i> = 7r, giving 



^J L = cos(<£ + ^) = cos^tan-V+f)- (xvi.) 



As before, when y = h, p=— cot i, and therefore 



2a 2 - /i 2 . /. , A\ , ... 



~2?- = sm ( z+ r7 ' * ' (XV110 



a convenient equation to determine i. 



Equations (xvii.) and (xi.) represent approximations of 

 different orders of accuracy, of which (xi.) is the closer. The 



neglect of the term involving —^ in forming equation (xv.) is 



evidently of a lower order of accuracy than the processes 



which result in equation (xi.) . The difference between the 



two results can readily be shown by computing the value of 



2 a 2 — li 2 



— 9~2~ as gi yen ^ or the two equations. 



If we take, for simplicity, a liquid of zero contact-angle, 

 a simple calculation shows that 



i 2a 2 -li 2 \ _/ 2a 2 -h 2 \ 

 \ 2a 2 ~ Avii \ 2a 2 U 



a small difference which becomes less important as r increases. 

 The preliminary experiments which have been carried out 

 are in agreement with this result. The approximation of 

 equation (xvii.) is specially convenient, as a knowledge of the 



