Page:Proceedings of the Royal Society of London Vol 4.djvu/166

Rh the stern, corresponding to a small real change in one particular position, the former change being 97°, whereas the latter was only 23°, and the small amount of disturbance indicated ])y the compass near the bow.

After giving the observations for the determination of the influ- ence of the ship on the horizontal intensity of a needle suspended at each of the stations, in four different positions of the ship's head, and the disturbances of the dipping needle at three of these stations, the author enters upon the theoretical investigation.

The fundamental supposition of the theory of induced magnetism, on which Mr. Airy states his calculations to rest, is, that, by the ac- tion of terrestrial magnetism, every particle of iron is converted into a magnet, whose direction is parallel to that of the dipping needle, and whose intensity is proportional to that of terrestrial magnetism, the upper end having the property of attracting the north end of the needle, and the lower end that of repelling it.

The attractive and repulsive forces of a particle on the north end of the needle, in the directions of rectangular axes towards north, towards east, and vertically downwards, and of which the compass is taken as the origin, are first determined on this supposition in terms of the co-ordinates ; and thence the true disturbing forces of the particle in these directions. The disturbing forces produced by the whole of the iron of the ship are the sums of the expressions for every particle. Expressing this summation by the letter S, and transforming the rectangular into polar co-ordinates, Mr. Airy gives to the expressions for the disturbing forces the simpHfications which they admit of, on the supposition that the compass is in the vertical plane passing through the ship's keel, and that the iron is symme- trically disposed on both sides of that plane. He thus deduces for the disturbing forces acting on the north or marked end of the needle,

— I cos ^. M -f I cos L P cos 2 A -f- I sin ^. N cos A, towards the magnetic north ;

I cos d. P sin 2 A -!- I sin N sin A, towards magnetic east ;

— I sin ^. Q + I cos L N cos A, vertically downwards :

Where I represents the intensity of terrestrial magnetism ; d the dip ; A the azimuth of the ship's head ; and M, N, P, Q, constants depending solely on the construction of the ship, and not changing with any variations of terrestrial localities or magnetic dip or intensity.

From the consideration of these expressions for the disturbing forces is deduced the following simple rule for the correction of a compass disturbed by the induced magnetism only of the iron in a ship.

1 . Determine the position of Barlow's plate with regard to the compass, which will produce the same effect as the iron in the ship.

2. Fix Barlow's plate at the distance and depression determined by the last experiment, but in the opposite azimuth.

3. Mount another mass of iron at the same level as the compass, but on the starboard or larboard side, and determine its position so