584 MAGNETIC FIELD. 



second, making A = . With the preceding values of A, and />, 



o o 

 we should have 







/= 0-078125, /'= 0*005078; 



q= -o'o87898, q = -0*009825. 



The best arrangement, if we propose solely to diminish the 

 importance of the terms of corrections, is then to employ a small 

 magnet the length of which is half that of the principal magnet, 

 and to place it in the equator of the second. 



1156. The a priori calculation of the terms of correction can, 

 moreover, be of no use practically ; for the action of the two 

 magnets is not reducible to that of four poles. If the values of 

 p and A are not higher than those which hav served for the 

 previous calculations, when the deflected magnet is in a principal 

 position in respect of the first and almost perpendicular or parallel 

 to its direction, we may express the moment of the couple by one 

 of the formulae (12) or (13) in which only the second term of the 



series is taken in the form , the coefficient h being determined 



R" 



by comparison of the results obtained for two different distances 

 R and R'. It is not even necessary to assume that the term of 

 the fourth power is negligable ; for the mode of determination 

 includes in the value obtained for the first term, the greater part 

 of the correction for the next term. 



1157. LAW OF MAGNETIC ACTIONS. The investigation of the 

 field of a magnet may serve to determine the law of magnetic 

 actions. Let . us assume, in fact, that the action between two 

 magnetic masses is inversely as the wth power of their distance. 



The magnetic field of a mass ;//, at a distance r, is equal to 



m i /// 



, and its potential to - . 



r n n- i r n ~' 



If we consider two very near masses + m equal and of opposite 

 signs, and at a distance 2#, the potential at a point P, the distances 

 of which to the masses in question are respectively r and r', is 



But the product mdr is the projection of the magnetic moment 

 2am = M, of the two masses on the right line joining the middle of 



