508 



Mr. A. Ferguson on the Theoretical 



fig. 1, measured from the plane of greatest horizontal section 

 to the vertex of the bubble. For greater exactness, we 



Fiar. 1. 



assume that the bubble has a large but finite radius of cur- 

 vature /n, at the vertex 0. The march of the argument is 

 exactly as in the paper cited*, and the main steps therefore 

 only are given. 



At the point P, the differential equation to the surface is 



R L R 2 fju a 2 ' 



Substituting for Rx and R 2 , and transferring the origin to 

 0', we obtain 



dx r dx r v x y fi v M y /jut 



=y(l+jp»)*— ffi(l+l^)l (i.) 



Putting x equal to cc in (i.), and substituting the approximate 



value of a 2 ~r so obtained in the second term on the left- 

 dx 



hand side of (i.), we have, after a few reductions similar to 



those already given t, 



a 2 ]) dp <*>P 



2a 2 



(ii.) 



giving, when r is infinite, 



a 2 pdp 



(i+j^i 



Za- 



ffn= .'/ + - 



fi 



* Phil Maa\ Dec. 1912 (hereinafter referred to as I c). 

 t L. c. p. 841. 



