on the Mariner's Compass. 455 



directions arising from the part of the force which is parallel to 

 a', will be a^ cos a', a ' cos a ', and a ' cos a' ; and so on : whence 

 the theorem is evident. 



If it is wished to apply this theorem to practice, it will be con- 

 venient to assume the axes a and a' in the horizontal plane; in 

 this case assuming e for the angle made by the projection of the 

 needle in that plane with the axe a, we shall have cos e. sin a"= 

 cos a; and sin e. sin a''= cos a'; whence it follows that the 

 horizontal forces, estimated at right angles to the deflected 

 needle, are respectively, 



\ c^ cos e + Og'. sine + a^'' cot a''l .sin a", sin (e — o) 



5 o^ cose^-fl' sin e + a^"cota"[ . sin a", cos (e— 5). 



Whence may be readily derived an expression for the deviation 5; 

 which however for want of room I must omit. We may however 

 observe, that this expression applied to the experiment detailed 

 in page 60 of the Essay on Magnetic Attractions, will show very 

 clearly the reason of the results there obtained agreeing so nearly 

 with those deduced from the formula employed, (which is the 

 same as our 8th,) although that expression is not generally ap- 

 plicable to the attractions of irregular masses. 



From the preceding expression we are also enabled to calcu- 

 late what would be the deviation produced by the attraction of 

 the iron in a vessel, at any place, and with the ship's head di- 

 rected to any point of the compass; provided we know the in- 

 tensity of magnetism ; and the angle of the dip at that place ; 

 and the effect produced by the same mass, in three different po- 

 sitions of the vessel's head, at any other place. 



But one of the principal uses of the last theorem will be found 

 to consist in the easy demonstration it affords of Mr. Barlow's 

 very simple practical method of determining the attraction of the 

 iron in ships; a point which it is of much importance to establish, 

 and the more so as its truth has hitherto been allowed to rest 

 wholly on analogy ; the only attempt at proof being derived from 

 tiie manifest fact, that both the iron in the vessel, and the plate 

 employed to ascertain its effect, must have a resultant of for* e : 

 hut no sufficieiit evidonce has been adduced to show that the re- 

 sultants of these differently-shaped masses will continue the same 

 fur all directions of the meridian and dip* ; a point which was 

 indispensably requisite, (in that mode of demonstration,) to prove 



* That no sufficient proof is derived from the experiment witli the t«"cnVy- 

 /our pounder we have already seen ; and the example of the sittrnctioiis ini 

 board the Isabella is manifestly too restricted ; since the dip, which was 

 from 7-1 to 8G, could be but Iil'-Ic uHcctcd by a motion in tlic hoiiiontal 

 pluiie. 



