24 M. L. Schwendler on an Arrangement for the 



Two bobbins of wire, r and b, are connected parallel to the two 

 poles of a battery, E, the circuit of which may be closed and 

 opened at will by a stopper, 1. Only one of the bobbins (r for 

 instance) contains iron, which becomes a magnet as soon as the 

 battery circuit is closed. When the circuit is opened the mag- 

 netism mr ceases, causing an extra current in (r-\-b) which acts 

 in the same direction as the original battery current, and conse- 

 quently causes the loss of magnetism in r to go on much slower 

 than it would without such a shunt b ; and therefore, if the mag- 

 netism in r were made use of for closing a contact, 2, this con- 

 tact would be somewhat prolonged by such a shunt. Conse- 

 quently the question to be solved is, what must be the resistance 

 of this shunt, supposing r and every thing else were given, in 

 order to make the remanent magnetism a maximum, i. c. the 

 prolonging effect of the shunt as regards contact 2 greatest. 



That for a given r a certain b does exist for which the extra 

 current, or its equivalent the remanent magnetism, is greatest 

 follows simply enough. Suppose, for instance, the resistance of 

 the shunt b were infinite, which is the same as having no shunt 

 at all, then no extra current would exist, though its cause {i. e. 

 the magnetism produced in r by closing the battery circuit) 

 would be greatest. On the other hand, if the resistance of the 

 shunt b were taken as infinitely small, then (though there would 

 be the best possible channel for an extra current) no such cur- 

 rent could be established, because no original current would pass 

 through r, and therefore no magnetism in r could have been de- 

 veloped. Knowing, therefore, that for Z> = co and for 6 = the 

 extra current is =0, it follows that there must be one or more 

 values of b between these limits for which the extra current is a 

 maximum. 



However, the function by which this extra current (or, better, 

 the remanent magnetism in r) is expressed is of such a nature 

 that it has only one maximum ; and this can easily be calculated, 

 since all the laws determining it are perfectly known. 



In fig. 2 we will designate by r the resistance of the bobbin 

 producing the magnetism (which in the discharging arrangement 

 represents the resistance of the coils of the discharging relay) ; 

 and. for brevity we may suppose that the whole resistance between 

 the points p and q through r is used for producing magnetism. 



Suppose also : — 



n the number of convolutions in r; 



x the resistance of the bobbin acting as a shunt to r, and ex- 

 tending between p and q ; 



E the electromotive force producing the original current; 



/ the resistance between the points p and q through the bat- 

 tery E, including the resistance of the battery; 



