that the compass points correctly when the ship's head is N.E., S.E., S.W. or N.W. ; then the compass will be correct in all positions of the ship's head, and in all magnetic latitudes.
When the disturbing iron of the ship is at the same level as the compass, the correction is stated to be much more simple, it being then only necessary to introduce a single mass of iron at the star- board or larboard side, and at the same level as the compass.
It is farther remarked that if one mass of iron is placed exactly opposite another equal mass, both in azimuth and in elevation, it doubles its disturbing effect : if one mass be placed opposite the other in azimuth, but with elevation instead of depression, or vice versa, it destroys that term of the disturban'^e which depends on sin A, and doubles that which depends on sin 2 A : and if one mass be placed at the same level as the compass, its effects may be de- stroyed by placing another mass at the same level, in an azimuth differing 90° on either side. If a disturbance, from whatever cause arising, follow the law of + sin 2 A, (changing sign in the success- ive quadrants, and positive when the ship's head is between N. and E.), it may be destroyed by placing a mass of iron on the starboard or larboard side at the same level as the compass ; if it follow the law of — sin 2 A, the mass of iron must be on the fore or aft side.
From the consideration of the expression for the disturbing forces produced by the ship, it is farther inferred, that both in the con- struction of the ship and in the fixing of correctors, no large mass of iron should be placed below the compass.
The expressions for the disturbing forces towards north and east, being transformed into forces towards the ship's head and towards the starboard side, give
I cos ^. (— M + P) cos A + I sin ^. N, for the former, and
I cos ^. (M + P), for the latter.
The author next proceeds to investigate the effects which result from the combination of induced magnetism with permanent mag- netism. Calling H, S and V the new forces arising from the latter, and directed towards the ship's head, its starboard side, and verti- cally downwards, the whole disturbing force towards the ship's head becomes
H + Icosc\(-M + P)cosA + Isin^.N; and the whole disturbing force towards the starboard side, S 4- I cos d. (M + P) sin A.
The manner in which the numerical values of these quantities may be found from experiment is then pointed out, and being determined from the observations on board the Rainbow, at Station I., a compa- rison is made between the observed disturbances of the needles, and those which would result from the action of the ship as a permanent magnet. From this comparison it appears that almost the whole disturbance is accounted for by the permanent magnetism, and that the residual part follows with sufficient approximation the law of changing signs at the successive quadrants. For the complete veri- fication of the theory it remained only to effect an actual correction of the compass. This was done by placing below^ the compass, in a
