314 STAFF COMMANDER EVANS AND ME. A. SMITH ON THE MAGNETIC 
Thin Plate magnetized in its plane. 
If the compass be above or below the centre of a rectangular plate, which may repre- 
sent the iron deck of a ship, lx being the length, 2 y the breadth, n the thickness, z the 
height of the compass above it, r the distance from the compass to one corner, and v the 
volume of the plate, 
4 xnxy xv 1 
4 xnxy xv 1 
r.(y 2 + £ 2 ) - V y* + z*' 
1 
2r\y+z 2 a> 2 + 2- 2 J 
or such a plate will always produce a diminution of the directive force, and if x>y, or 
if its length be in the fore-and-aft direction, a positive quadrantal deviation. 
A vertical thin plate, such as a transverse bulkhead, may, as regards transverse 
induction, be considered as a series of thin horizontal beams giving a — e, diminishing X 
and increasing 3). As regards vertical induction, it may be considered as a series of 
•vertical rods giving a -\-c if before the compass, a — c if abaft, and a -f- k or — 1c according 
nearly as the centres of the supposed vertical rods are within or without the cone 
we have described. There would be no difficulty in computing the effect of such a 
bulkhead of given position and thickness if k were known. 
Thick Plate magnetized perpendicularly . 
If the length and breadth of the plate be infinite or very great compared to the 
distance of the compass, such a plate will produce no effect on the compass, the effect 
of one surface being exactly neutralized by that of the other. 
When the dimensions of the plate are finite we may arrive at an approximate result, 
by supposing lines drawn from the compass to every point on the edge of the further 
surface. The parts of the two surfaces within the pyramid bounded by these lines will 
neutralize each other, leaving only a margin of the nearer surface to act on the compass. 
The effect of this may be easily computed, by computing the effect of four such red or 
blue lines, as the case may be, the free magnetism in a unit of length being 
F 
— X breadth of margin. 
From these considerations we see that the effect of even a thick armour-plating, 
magnetized perpendicularly, will not be great. 
The effect of a thick transverse armour bulkhead, on a compass immediately above 
and near it, will be to produce a — a, which maybe easily computed, as we may suppose 
the dimensions of the plate in every direction below its upper surface to be infinite. 
If l be the thickness of the bulkhead, n the height of the compass above its centre, 
