1887 .] Sir W. Thomson on Doctrme of Extraneous Pressure. 31 
C-i(S.l) . 
.i(2S-i);M.i(2S-L)iN.l(2S-l) . 
where 
1/1 1 
+ 7S + 
3\a /I y/ 
Next, to find G, H, I ; by (38), (44), and (45), we have 
G + H + I = l(L + M + N) = f/tS = |A:(Ni + -) . . 
whence by (38) and (44), 
20. Using (43) and (47) in (19), we have 
Sa2 8^2 § 2 .J„2 S 2 ■, 
(43) , 
(44) , 
(45) . 
(46) , 
(47) . 
(48) . 
•/32 
Now we have, by (2) log {a^y) = 0. Hence taking the variation of 
this as far as terms of the second order. 
P y 
which reduces (48) to 
Remembering that cubes and higher powers are to be neglected, we 
see that (50) is equivalent to 
3E = JA:8(1 + ^ + 1) (51). 
Hence if we take k constant, we have 
)• • • • • 
and it is clear that h must be stationary (that is to say 3/i; = 0) for 
any particular values of a, /I, y for which (51) holds; and if (51) 
holds for all values, Ic must be constant for all values of a, /?, y. 
