﻿152 Mr. J. Rice on the Form of a 



This equation shows that the curvatures at points equi- 

 distant from the level CX', above or below, are equal. The 

 symmetry with respect to this level is an obvious consequence 

 of the assumed uniformity of the density gradient. 



It is not difficult to show that an ellipse of small eccen- 

 tricity is a possible form of meridianal section. 



For this to be so it is necessary according to the previous 

 equation that 



ab ± = 2±, l> 2 -y 2 

 b' 3 ab' a 2 the 2 ' 



where a = CA, 



6 = 00, 

 and // = the semidiameter conjugate to OP. 



If </> is the eccentric angle of P, this reduces to 



(l-* 2 cos-»* (l-^cos 2 <£)* i 2hc- 



a 2 \ 



L e., to 



If 



(i + 1)* 2 c ° s2 * + (if + ly cos ' * + &( 



a 2 b 2 

 ., a?b _ 3 x volume of drop 



and if also e were so small that £ 4 , ^ 6 , &c. could be neglected 

 in comparison with e 2 , the above equation would be approxi- 

 mately satisfied. 



It is clear that for a similar order of approximation, a 

 larger drop is possible, the greater the values of h and c. 



The method employed by Lord Rayleigh, in which the 

 differentials of the coordinates with respect to the arc are 

 used, does not, unfortunately, lead to an equation so readily 

 integrable as the one preceding equation (3) of his paper. 

 Still some headway may be made, although the approxima- 

 tions, if pushed very far, would become excessively laborious. 



E.g., the equation (1) becomes in these terms, 



(-') 



