TO THE THEORY OF MAGNETISM. 113 



. 



proximate value of -777 - , V2 , 2 . , shall be a minimum for 



J-W{(-aO +<*} 

 the whole length of the wire. In this way I find when X is so 



great that quantities of the order -^- may be neglected, 



pA, 



A = .231863 - 2 log a/3 + 2aj3 ; 



where .231863 &c. = 2 log 2 - 2 (A) ; (A) being the quantity 

 represented by A in LACUOIX' Traite da Cal. Diff. Tome 3, p. 521. 

 Substituting the value of A just found in the equation 



before given, we obtain 



(*) t (1 "tf2 = -231863 - 2 log a/3 + 2a. 

 6g . a p 



We hence see that when the nature of the substance of which 

 the wires are formed remains unchanged, the quantity a/3 is 

 constant, and therefore /3 varies in the inverse ratio of a. This 

 agrees with what M. BIOT has found by experiment in the 

 chapter before cited, as will be evident by recollecting that 



From an experiment made with extreme care by COULOMB, 

 on a magnetized wire whose radius was inch, M. BIOT has 



found the value of p' to be .5 1 7948 ( TraitS de Phy. Tome 3, p. 78). 

 Hence we have in this case 



a/3 = log fju = .0548235, 



which, according to a remark just made, ought to serve for all 

 steel wires. Substituting this value in the equation (a) of the 

 present article, we obtain 



g = .986636. 



With this value of g we may calculate the forces with which 

 different lengths of a steel wire whose radius is inch, tend to 



