454 IiiJlutHcc of Masses oj Iron 



The same law probably obtains for other solids, but tiotlwng 

 that we have yet dcmorivStrated will enable us to draw so general a 

 conclusion : that it is true for spheres and spheroids, may be de- 

 monstrated as follows. Since we have seen (page 447-S) that the 

 development of the magnetic fluids which produces on any par- 

 ticle p of the sphere an attraction e(]ual and contrary to that of the 

 terrestrial magnetism, takes place at the surface ; it follows that 

 if we were to take away all that interior portion of the mass which 

 is bounded by a concentric sphere, having the radius p O, the 

 equilibrium of the fluids in p would still be maintained ; and the 

 distribution and consequent attraction of the magnetisin in the 

 shell thus produced, \\ould be the same as for the whole sphere. 



Since moreover the attraction of each of the equal spheres 

 A N B S, A N' B S', varies as either of their masses ; the differ- 

 ence of their attractions, which is proportional to the magnetic 

 attraction of the first sphere, must also vary as the same mass, 

 or as the cube of the diameter. 



The same demonstration will evidently extend to spheroids. 



Hence, to complete the investigation which we have proposed 

 to ourselves, it will now be necessary to examine the attractions 

 of irregular bodies ; which may be effected by the following 

 theorem, analogous in its nature and demonstration tothatgiven 

 in page 449. 



J/" a, a', a" he three rectangular co-axes ; and ^ , a , a be the 



attractions of any mass of iron according to each of these axes 

 respectively, when the dip is in the direction a; a', a', a/ the 

 same attractions when the dip is in the direction a ; and 

 a ", a ", a " when the dit is in the direction a": Then will 



' 1 ' 2 ' 



a cos a 4- a '. cos n + a" cos a" 



(1 



a cos a -\- a' cos a' + a" cos a'' 

 a cos a + a' cos a' -{- a " cos a'' 



be the attractions according to each of the axes a, a', a" respec' 

 lively, when the dip makes with them the respective angks 

 a, a' and a". 



This theorem may be readily demonstrated, as we have observed 

 al)Ove, from that in page 449. For since we there learn that the 

 thickness of the shell of magnetism arising from the new position 

 of the dip, is the aggregate of the thicknesses in its former direc- 

 tions, multiplied respectively by the cosines of the angles made 

 with those directions; we conclude that the part of the magnetic 

 force which acts in the direction o, will produce the several at- 

 tractions a , cos o, a cos a and a cos o, which act according 



to the axes a, a a' respectively; that the attractions in the same 



directions 



