M. E. Edluiid on the Nature of Electricity/, 181 



of —2 ds -pj ds' will be equal to aero. Now^ as this is true for 



any value of r, it must in like manner be true for the whole cir- 

 cuit. We can therefore^ in the place of formula (15), employ in 

 the integration the formula 



+ ^(a cos e+^kkco^w) cos 6' dsds'. . (16) 



Now this formula expresses the induction of the first instant 

 only, before the molecules both of the wire and of the surround- 

 ing medium have been able to quit their primitive positions of 

 equilibriuai. But the induction continues until the new posi- 

 tions of equilibrium are reached, when the inductive force be- 

 comes zero. The force of induction undergoes a continual 

 diminution from the commencement to the end of the duration 

 of the induction; and formula (15) only gives the maximum 

 value during the first instant. The result should be, that at the 

 commencement of their existence induction-currents appear very 

 strong and then diminish in intensity — a fact which has been 

 proved by experiment*. If, then, we wish to calculate the 

 amount of an induction-current in given circumstances, we must 

 take into account not only the maximum value of the induction 

 at the first instant A^, but also the sum of all the inductions 

 during the whole of the time of induction. If for the sake of 

 brevity we designate the maximum value of the induction 

 exerted by a current-element upon an element of the induced 

 circuit by At Ar when the distance between the elements is r, 

 we can express the induction which takes place during the im- 

 mediately folloAving instant by AtpAr, when p is less than unity. 

 In this way the sum of all the inductions will be 



At(l+p-^-p,+p,^ + . . . + 0)Ar, 



in which each consecutive term of the series is less than the 

 preceding. This can be expressed more briefly by A/FA?-, where 

 F denotes the sum of the series. For another element of the 

 induced current, of which the distance from the inducing element 

 is r^, we obtain in the same way At¥^Ar^. Now, if F were 

 always equal to Fj (that is, if the sum of the series were constant), 

 the sum of the inductions would be proportional to the maximum 

 value, whatever might be the variations in the force i of the cur- 

 rent and in the distance r between the elements, and we could 

 at once calculate from formula (16) the relative magnitude of the 

 induction-current. The fact that F is independent of i cannot 



* See Lemstiom, K. Vet.-Akademiens HaiidL ny foljd, vol. viii. (1869); 

 Blaserna, Giornale di Scienze Naturali ed Economiche, vol. vi. (Palermo, 

 1870). 



