Shape of Large Bubbles and Drops. 511 



Poissoir's formula have interpreted r' as being the radius of 

 the bubble in the plane of greatest horizontal section. Their 

 results, therefore, happen to be in accordance with equation 

 (iii.) of the present paper, but would differ slightly from 

 results computed on the basis of Poisson's formula. 



We now proceed to formulate in a similar manner the 

 expressions which give the total depth (k) of a large bubble 

 or drop in terms of its capillary constants. 



Let fig. 1 inverted represent a large drop of mercury 

 lying on a horizontal surface. The differential equation to 

 the surface at P, a point on the meridional curve between 

 the plane of greatest horizontal section and the surface on 

 which the drop is sessile, will be 



1 + x - h ~y. 



Hi P2 a " 



Proceeding as in the formation of equation (i.), putting 

 r=co in the resulting equation, and substituting in the small 

 terms as before, we obtain 



a*P dp + a 2 p__ _ 

 (l+p 2 )Vdz rx/l+p 2 "*'' ' ' [Y1 ' } 



where zis put for k — y. 



Put r = oo in (vi.) and integrate, when 



z 2 = 2a 2 ( 



1 + 



Vl + p 2 )' 



remembering that z 2 = q 2 = 2a 2 when p=co. Hence we 

 obtain 



P _ = z\/±a 2 -z 2 

 \/l+p 2 2a 2 ' 



which, substituting in the small terms of (vi.) and integrating, 



gives 



determining the integration constant from the fact that 

 z = q when p = co . 



When ?/ = 0, i. e. when z = k,p= tan <j> ly giving 



2a 2 cos <j> 1 = k 2 -q 2 + I (4a 9 -**)*- 1 (±a 2 -q 2 )%, (vii.) 



o# or 



