MAGNETIC FIELD. 



3^7-9 , 4 _ 

 2.4.6.8 \ 5 2 R 2 



.5. ..13 6 /4__L^\ 



. 4 . ..12* \ 7 2RV + '"J ' 



Msinio |" T , 3-5 , 9 ,3-5-7-9,^ 



.4 2 .A.. .8 



~ _J 



If we replace z by its value, putting R as a factor everywhere, 

 and expand in series, we ultimately get only even powers of the 



Fig. 239. 



L 



ratio in the bracket; but the law of the formation of succes- 

 Jx 



sive terms is then very complicated. 



We may observe, in particular, that in the equator of the magnet, 

 where s = 0, the value of H is simply inversely as the cube of the 

 distance to the poles \/R 2 + L 2 . 



1153. RECIPROCAL COUPLE OF Two MAGNETS. Consider more 

 generally two symmetrical magnets, the magnetic moments of which 

 are M and m (Fig. 239), the lengths 2L and 2/, and the magnetic 

 axes of which, situated in the same plane, make the angles o> and 8 

 with the right line OO' = R which joins their centres. If the two 

 magnets were very small compared with their distance, the mo- 

 ment D of their reciprocal couple will be 



D = m (Z sin 8 - H cos 8) = - (2 cos o> sin 5 - sin w cos 8) . 



