422 CURRENTS AND MAGNETIC SHELLS. 



N' are the numbers of oscillations of the needle in a given time / in 

 the three experiments, then if K is a constant depending on the 

 magnetisation of the needle and on its moment of inertia, we have 



From which is deduced 



But experiment showed that by employing the method of alter- 

 nate distances to eliminate the effect of variations in the strength 

 of the current, the following ratio was always obtained : 



It follows from this that <$>a = <$>&', that is to say, that the action 

 of the current on a point is inversely as the distance. 



On the other hand, experiments made on the discharge of 

 batteries those of Colladon and of Faraday particularly and the 

 more accurate measurements made with the voltameter, have shown 

 that 'the magnetic action of a current is proportional to the quantity 

 of electricity which flows during unit time that is to say, to the 

 intensity / of the current. 



The action exerted by a rectilinear current on a magnetic mass 

 m at a distance #, may then be represented by the expression 



' \ 



to 



in which k is a coefficient to be determined. 



The action observed in this experiment, as well as in that of 

 CErsted, is always the action of a closed current ; but it is easy to see 

 that if the rectilinear portion is sufficiently great, and the rest of the 

 current sufficiently distant, the action of this latter part is inappre- 

 ciable, and the effect observed only depends on the nearest part. 

 The action of the rectilinear portion may then be considered as 



