2G4 PROFESSOT^ G. H. DARAVTX OX THE STABILITY OF THE PEAR-SHAPED 
Subtracting this from ^JJ as given in (12), 
il /2 
0/ J 
But the latter factor was found in ( 11 ) as equal to — ^e^(cro)h The term 
only contributes a constant to the whole energy and may therefore he dropped. 
Accordingly 
. 1/2 
\jj - (JR)' = f - p,'Q,>) y'(a.y-} 
(13). 
For the other portion {JJj) ' we have 
/If n-\z 
Then by means of ( 10 ) 
(JR)" = \ U"p,h = 3 ^(1)“' P,>Q ,>\jp ,h 
= I P.'Q.' {e-h + S(/')Y' + - 2e%} 
(14). 
In the terms of the fourth order we may put (/f/^’q)® equal to unity. Therefore 
combining (13) and (14) 
i./j-- .77?=- f {.««[- (\mo - +6P,'Q.'u 
/. Q \/. / /un 
(/Wd) (15). 
§ 6 . Swface Density of Concentration C; Energy (77?. 
The region 7? being filled with positive volume density p, is concentrated along 
orthogonal tubes on to J, and there gives surface density S. 
To the first order, 1)y (5), 
(Iv 
(It 
— pfa- 
Ci7s2 P cOs2 7 
Adr7 
1 
Integrating with respect to r from the pear to we have as far as scpiares of 
small quantities 
8 = - 
Pop 
eS, + + jf - e) (.%)= 
