84:2 Mr. A. Ferguson on Shape of Capillary Surface 



h 4 

 jj-4 and higher powers ; the expansion is legitimate, as A 2 is 



always less than 2a 2 for acute angles of contact. This gives 

 at once 



2a%l- sinz) = /* 2 (l+^Y 



or, if h Q be the height to which the liquid rises against a 

 plane wall, then, very approximately, 



A 2 



=v(i-J). 



Equation (xi.) should, however, always be used in com- 

 puting sin i from numerical data. 



A solution of (vi.) in a different form can be obtained in 

 the following manner. 



Putting £>=tan<£, substituting, and taking, for reasons 

 similar to those already given, the negative sign in extracting 

 the square root of sec 6 </>, (vi.) becomes 



d4 1_ 4 



dy + r~ a 2 ~sin<£ (*"•) 



Putting the right-hand side of (xii.) equal to zero, and 

 integrating, 



r(j)= -y + c. (xiii.) 



Assuming c to be a function of y, as in the ordinary method 

 of variation of parameters, 



d<j> 1 dc 1 



-j- = ~~ j - — _ ? ( xiv. ) 



ay r ay r v 7 



substituting in (xii.) the values of c and -=£ given by (xiii.) 

 and (xiv.) we have a V 



1 dc y 



r dii „ . c — «/' 



17 a 2 sin — ^ 



r 



J -= sin — '-dc, 



r r 



,2 



(a c a c \ 

 — sin- —^o cos- )de. 

 r r r z rj 



