1 66 The Rev. H. Lloyd on the mutual Action of permanent Magnets. 



be resolved each into two, in the magnetic meridian, and perpendicular to the 

 magnetic meridian. The former components are 



, 2-Bm . , Bm . 

 -j- — ;^sin7C0S7, -1 -3- sm 7 cos 7; 



and the latter 



, 2 5m . „ Bm „ 



+ —5- sm' 7» — — ,- cos''7. 



c 



Again, the forces exerted by c upon the element m of a, in the direction ac, 

 and in the direction perpendicular to ac, are 



. 2 Cm , ^, Cm . , ^. 



+ -^cosa-^), --^sm(f-^); 



and the resolved portions of these forces in the magnetic meridian are 



+ ?^cosa-i3)cos^, +^sin(f-^)sin^; 



while the components perpendicular to the magnetic meridian are 



+ ^^ cos (^ - p) sin p, - ^? sin (f - /3) cos /3. 



Accordingly, the conditions of the complete equilibrium of the forces exerted 

 by B and c on a, are 



-T5 1 2 cos ((3 — ^) cos /3 — sin (]3 — f ) sin j3 1 + 3 -^ sin 7 cos 7 = 0. 



-^3 12 cos (i3 - f ) sin i3 + sin (jS— f ) cos iSJ + — (2 sin^ 7 - cos' 7) = . 



In like manner, the forces exerted by the magnet a upon any element m of 

 the magnet b, in the direction ab, and in the direction perpendicular to ab, 

 respectively, are 



, 2 Am , Am . 



+ --r— C0S7, +--j-sm7. 



