CHAEACTEE OF THE AEMOUE-PLATED SHIPS OF THE EOYAL NAVY. 271 
?+- H tan 6 =93 H, 
^+1 H' tan ^=S5 , H' 
are the equations for determining c and P separately when S3 has been determined in 
two different latitudes ; 
(St-dg 
A i—i' ' i—i' ’ 
7 =SSH— tan 6 
K A A 
are equations for determining c and P separately when observations have been made 
in one geographical position, but on two different angles of heel ; 
®= i^cos£-(l + ©)cos£, 
©= sin £'+(!-$) sin £ 
are equations for determining SB and (5 by observations of deviation and horizontal force 
on one azimuth of the ship’s head, X and 3) being known or, estimated. 
There is a physical representation of Poisson’s fundamental equations so simple, and 
which gives us so great a power of estimating the effect on the compass of different 
arrangements of iron in a ship, as well as of tracing to their cause any peculiarities in 
the observed deviation, that it seems desirable, before entering on the peculiarities of 
structure and deviation in armour-plated ships, to explain this representation, and to 
show how it explains the phenomena of deviation. 
If an infinitely thin straight rod of soft iron be magnetized by the induction of the 
earth, the effect will be the same as if each end became a pole having an intensity pro- 
portional to the component of the earth’s force resolved in the direction of the rod, and 
to the section and capacity for induction of the rod. 
Let us now suppose nine soft iron rods placed as Plate X. It will be seen that for 
each rod we must distinguish the two cases, that in which its coefficient is +, and that 
in which it is — . It will also be seen that in the three cases, viz. —a, — e, —k, in 
which the rod passes through the compass, we may consider both ends as acting, but 
that in other cases it is convenient to consider only the action of the near end, and that 
the far end is at an infinite distance. 
The rod a, it will be observed, can only be magnetized by the component X, b only 
by Y, and c only by Z ; and if we call aX, bY, and cZ the force with which these rods 
attract the north end of the needle, and if we suppose, as we are at liberty to do, the 
mdccclxv. 2 p 
