840 Mr. A. Ferguson on Shape of Capillary Surface 

 Referred to parallel axes through 0' as origin, (ii.) becomes 



«%^)J-"Ml+/) = (.*-%(l+P 2 ) 3/2 , • (iii.) 



or 



- 1 ~ a 't - ? (1 + ^ = ? (1 +^) 3/3 -Ki +jW (iv.; 



r rtA' «,« r r 



giving when r = oo 



« 2 J=i/(l+/) 3/2 ; (v.) 



or ?/ 1 



a 2 ~~ R x 



which is obviously the correct equation to the capillary 

 surface in contact with a plane wall. 



To obtain an approximate solution of (iv.) on the assump- 

 tion that r is large take the value of -f- in (v.) — which is 



dx v 



exactly true when r is infinite — and substitute in the first 

 term on the left-hand side of (iv.), which is a small term. 

 We thus obtain 



a2 <to .^ (1+jo2)=y(1+p2)3/ 2 5 



tilt/ If 



... dp dp 



or putting s -p. ^, 



dp , 1+^ 0+/) 3/2 , -, 



-/-+ — = §-^ — y (vi.) 



Again, if r be infinite, (vi.) becomes 

 dp '(1 + p 3 ) 3 / 2 



7 — 2 '/, 



giving on integration, 



^^?) • • • • (viL) 



the inte oration constant beino; obtained from the fact that 

 y and p vanish together. 



