of Edinburgh, Session 1879 - 80 . 
453 
the cylindric interface. Denoting by a the radius of this cylinder 
we have 
T = wr , where r < a 
a 2 
and T — co — „ r>a 
r 
Hence (13), (14) hold for r<a, and (23), (24) for r>a. 
Going back to the form of assumption (6) we see that it suits the 
condition of rigid boundary planes if 0 z be perpendicular to them, 
0 in one of them, and the distance between them tv I'm. 
The conditions to be fulfilled at the interface between core and 
surrounding liquid are that g and w must have the same values on 
the two sides of it : it is easily proved that this implies also equal 
values of r on the two sides. The equality of g on the two sides of 
the interface gives, by (13) and (23), 
and from this and the equality of iv on the two sides we have 
(i<o - n'j 
D 
^ id) - n\ 
/ dw\ 
\wdr) 
internal 2io)"~\ 
r=a u : 
4m 2 - 
{id) - n ) 2 
dlQ \ external 
wdr/ t = a 
(47). 
The condition that the liquid extends to infinity all round makes 
w = 0 when r— go. Hence the proper integral of (24) is of the 
form 3E { : and the condition of undisturbed continuity through the 
axis shows that the proper integral of (13) is of the form J;. 
Hence 
w = C J; (yr) for r<a 1 
and w = C$i (mr) „ r > a ) 
08 ); 
by which (47) becomes 
(i 
or by (15), 
io) - n) J^( 
id) — n) 
vJ [(yd) 
J iiyci) 
] 
4o> 2 - (id) - nf 
- mEiima) 
I i(ma) 
Jj(g) + 
gJi(g) g' 2 A, maliijna) 
(49) ; 
(50) , 
