351 



Tiie values of /i thus obtained are not adequately re- 

 presented by the formula which has been already deduced 

 for the case of small magnets, the differences between the 

 calculated values and the means of the two observed results 

 being, in general, greater than the differences of the latter 

 inter se. It was accordingly natural to inquire whether the 

 agreement might not be rendered more complete by pushing 

 farther the approximation in the value of the function which 

 represents the law of magnetic distribution. This was found 

 to be the case on trial. But it was also found that the observed 

 results were represented, with nearly equal exactness, by the 

 empirical formula, 



h = 2{l-cf-S{l'-cf; 

 a formula which agrees with the hypothesis, that the whole 

 force of each magnet is concentred in two points, or poles, at 

 given equal distances from the ends. If we expand the pre- 

 ceding formula, and add together the resulting equations, we 

 have for the determination of c, 



Qe' + 2S(2/-30c + '2.h-'2.{2P -SP) - 0; 

 or, substituting the numerical values of the coefficients de- 

 duced from the preceding Table, 



