of Edinburgh, Session 1879 - 80 . 
453 
the cylindric interface. Denoting by a the radius of this cylinder 
we have 
T = (or , where r<a j 
> • • ( 45 )- 
» r>a 
r ! 
and 
rp Cl 
1 = Cl) 
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 ir/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), 
dw , 2io) 
n |— - + — w 
dr r 
] 
internal 
4oj 2 - (ioj - nf 
external 
dw\ 
dr )r=a 
(46): 
and from this and the equality of io on the two sides we have 
4 co 2 - (io) - n) 2 
/ dw \ external 
--(£)« ■ < 47 >- 
The condition that the liquid extends to infinity all round makes 
io = 0 when r=oo. Hence the proper integral of (24) is of the 
form IE; : and the condition of undisturbed continuity through the 
axis shows that the proper integral of (13) is of the form J { . 
Hence 
w = CJ) ( vr ) for r < a ) 
w = Clf (mr) „ r>a j 
and 
by which (47) becomes 
08 ); 
J i(va) 
] 
4o> 2 - (iw - ny 
- ?nTi(ma) 
I i(ma) 
(49); 
J,'(g) i _ - I [(ma) 
gJj(g) g 2 A maii(ma) 
or by (15), 
( 50 ), 
