RECIPROCAL COUPLE OF TWO MAGNETS. 583 



In order that the second terms of correction, p' or q ', should 

 have the value null, the ratio A of the lengths of the magnets must 

 be given by the positive root less than unity of one of the equations 



X 4 = 0, or X = 

 8 2>I 5 



A 4 = X = 



The first condition is almost satisfied with the value A = 



i 2 



which annuls q; taking / = -, we have 



/ = - 3^7^5 ~ 0*000097 ; 

 q = , q = - - /a 4 - = - 0*000685 . 



O 2 



When the magnets are almost parallel, the angles a and ft 



differ little from 90. If c^ and /^ are the complementary angles 



-d, and --/?, the expressions for the couples A and B become 



(13) 



B = - sin 



The sines of the angles a and /3 being replaced by unity in 

 the terms of correction, we have then 



/= 2/r> (I +6X2) f / = 3/0 4 (l 



^_2 (l + IlA2)) / = /=>*(! + 34X2- 49 6X*). 



In this case we cannot any longer nullify the second term /' 

 for the first principal position, and the term would be null for the 



