510 Mr. A. Ferguson on the Theoretical 



Neglecting the term involving -~ and integrating, we have 



f = 2a 2 (l- cos -Y 



Substitute this approximate value of y in the small second 

 term on the right-hand side of (iv.) and integrate, when we 

 obtain 



y 2 -—2a 2 ( 1— cos- ) + -o- — — cos ;r 1— q cos o )• 

 u \ r ) 5r r lr\ 6 2rJ 



When , 7r , c y ir q 



y = g,<t>=j,md r == $ + 'r = 2 + r ? 



which values, substituted in the above equation, give, after 

 a few reductions, 





8 i/2a 8 



3r ' 



assuming that ■— is small compared with unity. So that, 

 finally, putting q 2 = 2a 2 in the small terms, we have 



<f = 2a 2 + -^— _ — ( a/2-1). 



Putting, as before, a 1 2 = 2a 2 , this becomes 



ai 2 = 4 2 — 609^- (v.) 



in good agreement with equation (iii.)« Poisson's analysis 

 results in 



a i 2 = q 2 -'606 Ci -\. 



r', however, is not the greatest radius of the bubble, but is 

 given by 



r' = r+(v / 2-l)a 1 *. 



The difference is small but appreciable. E. g m<i Poisson 

 gives, in a calculation referring to the depth of a large drop 

 of mercury t, 



r = 50 mm., r' = 51*083 mm. 



It is a curious fact that some experimenters who have used 



* Nouvelle Theorie, p. 216. 

 t Ibid. p. 219. 



