304 
STAFF COMMANDER EVANS AND ME. A. SMITH ON THE MAGNETIC 
ON THE EFFECT ON THE COMPASS OF PAETICULAB MASSES OF SOFT IRON IN A SHIP*. 
The form of the general equations for the effect of the soft iron of a ship on the 
compass does not, as we have seen, depend on the form, position, or inductive capacity of 
the iron. They involve, it is true, nine coefficients which depend on these particulars, 
but the data of the problem are in general not these particulars, but the effects which 
they cause in certain definite positions of the ship. This is fortunate, because, while the 
form of the general equations is obtained at once from very simple physical considera- 
tions, and while the special formulae required are deduced from these by simple trigono- 
metrical operations, and the coefficients are then deduced from the observations by a 
simple arithmetical operation, the a priori determination of the effect on the compass 
of given masses of iron is, in all but the very simplest cases, a matter of great and gene- 
rally insuperable difficulty. 
It is however in all cases interesting, and in some cases important, to be able to form 
an approximate estimate of the nature and amount of the effects on the compass of 
particular masses of iron, and although the precise cases of masses of iron in which the 
problem admits of an exact solution may not often occur, yet cases frequently occur of 
masses of iron sufficiently resembling them to have much light thrown on their effects 
by the knowledge of the effect of the simpler bodies which they most nearly resemble. 
The most general case for which the problem can be solved is that of ellipsoids and 
ellipsoidal shells, including the forms into which these degenerate, as spheres, spheroids, 
plates, cylinders, &c., but the general solution is so extremely unmanageable, in its 
practical application, that it is more convenient to consider the simpler cases indepen- 
dently. The cases which we shall consider are — 
1. Infinitely thin rods of finite or infinitesimal length. 
2. Infinitely thin plates of finite dimensions magnetized longitudinally. 
3. Infinite plates of finite thickness magnetized perpendicularly. 
4. Spheres. 
5. Spherical shells. 
6. Infinitely long cylinders magnetized perpendicularly. 
7. Infinitely long cylindrical shells magnetized perpendicularly. 
A little consideration will show that there is hardly any arrangement of iron in a ship 
which does not bear more or less resemblance to one or other of these cases. 
The physical theory of Coulomb, on which Poisson’s mathematical theory is based, 
supposes, as is well known, that there is no separation of two kinds of magnetism except 
within infinitely small elements of the iron ; but on this theory, if the iron be homoge- 
* I beg to express my obligations to Professor W. Thomson for much of what is contained in this part of the 
paper, and at the same time to express my hope that he may be induced to complete the promised Treatise on 
the Mathematical Theory of Magnetism, part of which was published in the Phil. Trans. 1851. — A. S. 
