512 Mr. A. Ferguson on the Theoretical 



Also, as we have seen, 



q* = 2a 2 + ^{4-x/2} = 2a 2 (approx.). 



Substituting the exacter value of q in the important terms 

 of (vii.). and the more approximate value in the small term, 

 we obtain, after a few reductions, 



2a 2 (l - cos co) = P-^ + ~ < 4a 2 - k*% . (viii.) 



or or ■ v 



where &>, the angle of contact, is the supplement of fa. 

 Putting the approximate value 



k 2 = 2a 2 (1— cos &>) 



in the small term on the right-hand side of (viii.) we obtain 

 finally, 



P = 4aWf-^(l-cos'f) . . (ix.) 



which in form agrees exactly with Poisson's result, but, as 

 in the case of equation (ii. a), will give slightly different 

 numerical values, owing to the different interpretation of 

 the length r. 



We turn now to the explanation of a method which, while 

 rather more laborious, is, on some counts, preferable to those 

 which depend on the application of formulae (iii.)j (v.), and 

 (ix.) . It has further the advantage that the formulae deve- 

 loped can be applied either to large or small drops and 

 bubbles. A photograph of the drop or bubble is taken, and 

 its contour explored in a manner previously described by the 

 writer*. Taking the case of a pendent drop, and considering- 

 the equilibrium of the portion below the plane ABGD (fig. 2), 

 we have, resolving vertically, 



2.1'jT sin (f)=gp(li—y 1 ),v ] 2 + gp \ ardy. 

 Resolving horizontally for the portion BOCD, 



x dy — 2gp I xy dy = ±s. 



^o Jo 



Whence, eliminating gph between the above equations, we 

 obtain 



T=S p C 2Gx 1 ' + AB-Axfy l 1 ( , 



x x \ 2 A sin <j> + 2x^ cos (fy — x^s j ' 



* Ferguson, Phil. Mag. March 1912. 



