Clearing the Compass. 379 



f \/ {} -\- ss): which reduced to the direction of the magnetic 

 meridian, becomes /\/(l + ss) -yZ-j — /Vll — ss) and 



2 s s 



to the transverse direction f J i\ + ss) k/ -rz f J 2, s. 



J -w \ ' ^ \ + ss ^ 



The joint force in the direction ofthe meridian will therefore 



be always (1 +/) >/ (1 — ss) and the transverse force s/ 2./s : 



consequently, the tangent of the angle of disturbance will be 



V2/ s , . , . . , , 



— — '■—. — — - — ,, which is proportional to the taneent of 

 1 +y a/(1-ss) 



the dip, and to that of the magnetic latitude. 



19. Hence it appears that the tangent of the angular dis- 

 turbance produced by the induced magnetism of a mass of 

 iron so situated, when the ship's head is E. or W., will vary 

 as the tangent of the dip. It will also be in opposite direc- 

 tions on opposite sides of the magnetic equator. The dis- 

 turbance on board the Isabella, in latitude 86°, if deiived from 

 this cause, would amount to 21" 19'; and it is remarkable, 

 that conclusions, so nearly agreeing, should be derived from 

 suppositions so totally different. 



20. It is not improbable that the soft or conducting iron 

 about a ship may often be so arranged as to produce effects 

 considerably resembling those of a sphere or shell situated 

 before the compass, and as much below it as is here supposed ; 

 but the proposition cannot be generally maintained that a sphere 

 may alivays be so placed as to produce effects equivalent to 

 those of the ship's magnetism, however the guns and ballast 

 may be arranged. Supposing, indeed, the guns to constitute 

 the principal part of the iron concerned, the deviation should 

 vary initially in a ratio nearly approaching to that of the square 

 of the sine of the apparent distance of the ship's head from the 

 magnetic meridian, amounting to half of the maximum at 

 about 45°, instead of about 30°, as it commonly appears to 

 do ; since the intensity of the induced magnetism of the guns 

 would vary nearly as the simple sine of the distance, and its 

 effect on the compass again as the same sine. The deviation 

 produced by the sphere would follow a very different law, but 



