132 Mr. A. Ferguson on the Shape of the 



be treated as hemispherical, putting rj = r 2 and V=§irr 2 3 , 

 (xiii.) becomes 



2a 2 = (h 1 -h 2 )r 2 -^ y .... (xiv.) 



Here again we note that it is only logically justifiable to 

 assume the drop to be hemispherical when 77 is negligible in 

 comparison with h x — h 2 , that is, when the effects of gravity 

 on the capillary surface are negligible in comparison with 

 the effects due to the surface-forces; under which circum- 

 stances the !asc term in (xiv.) is quite negligible. In his 

 later experiments M. Mentis uses equation (xiii.), but treats 

 the outline of the drop below CD as a semi-ellipse, so that Y 

 becomes the semi-volume of a spheroid of semi-axes r 2 , t) r 

 and r 2 . 



But now let us apply to the problem the formulae already 

 developed. Considering fig. 2 a, we have 



2T 

 Pressure in liquid at Oi = II— =p-, 



2T 



•>■) 55 •>-> T> ^2 = A-L + tJ~ , 



where II is the atmospheric pressure, and R x and R 2 are 

 the principal radii of curvature at O x and 2 respectively.. 

 Henc^, subtracting 



or 



From fig. 2 b we similarly obtain 



and therefore 7 , 2a 2 



But, substituting the value of R 2 from (xi.), (xv.) becomes 



i j 2a 2 2a 2 



/ti— h 2 — 5— = — + 



r 2 



So that, finally, 9 „ 2 _ a , * r 2 2 .< 



Za =(/ii — h 2 )r 2 —-±- (xvi.) 



But this equation is identical with (xiv.). Thus we see 



