CHARACTER OF THE ARMOUR-PLATED SHIPS OF THE ROYAL NAVY. 311 
Internal surface (blue at North), 
I'=*F- 
1 + 4tx + 4 tt 2 x 2 
I 1 "?) 
Hence for an external particle the coefficient will be J^I'^. 
/ o 2 \ (l + 2wx)/l— 
2 5 r(I-I^)=2 5 r*F « — LL 
' P ' 1 + 4irx 4- 4tt 5 x 2 / 1 — - 
'H) 
_ 2irxF p 
~ 2ttx+1 £ 1 
J9 + 2^ 
nearly, when * is large and 1 — ^ small. 
In the interior of the cylinder the coefficient is 
2 TTX 
= — 2t*F. 
H) 
1 + 4?rx -f 4 tt 2 ; 
= -F. 
1-2+J- 
p 2nx 
nearly, if x be large and 1 — ^ be small ; or whole force in interior 
1 + 
2™^1-| 
Application to particular cases. 
As we know from the general equations that the effect of any masses of soft iron may 
be represented by means of the coefficients a, b, c, d, e, f, g, h, k, and as we are in possession 
of formulae which give the different parts of the deviation in terms of these coefficients, 
by far the most convenient mode of expressing the effect of any given mass of soft iron 
is to find the a, b, c , d , e,f, g , h , Jc to which it gives rise; and in what follows we shall 
suppose the formulae involving these quantities and connecting them with the deviation- 
coefficients to be known. 
Thus from the expressions we have given for the effect of a finite or infinite rod, we 
at once derive the coefficients a, b, c, they being the factors of X, Y, Z in the expres- 
sions for the force towards x, and so of the others. From these we might derive the 
coefficients 9(, SB, (S, T>, ($, K, x ; but there would be no interest in the general solution, 
as the rods we have to deal with in practice are always parallel to one of the principal 
axes, and these we shall therefore consider separately. 
mdccclxv. 2 u 
