498 Royal Society. 



23°, and the small amount of disturbance indicated by 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, Avhose 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 atti-active 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 

 tlie 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 simplifications 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 h. M + I cos ^. P cos 2 A -f I sin 2. N cos A, towards the 

 magnetic north ; 



I cos 0. P sin 2 A -i- I sin c. N sin A, towards magnetic east ; 



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



Where I represents the intensity of terrestrial magnetism ; Z 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 inten- 

 sity. 



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 

 sliip. 



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 

 that the compass points correctly when the ship's head is N.E,, S.E., 



