1866.] 



Electricity given by Induction-Machines, 



173 



most probable is that the loss of magnetism is as the magnetism, which 

 gives ^=—fxdt, whence y=Me-'^^. 



Putting 5=—, and supposing (j) to vanish with f, 



The total current in the time t=^^=^ (l)dt=^——dy—^^d({), and hence 

 putting F for — — (M—y) and c for we obtain 



^ I 1 _L _ 



^=Tti\'+^rf^,\ ■ ■ ■ « 



The expression for the current due to the electric induction will be 

 similar to this, so far as having the factor F and the exponential. If, as 

 is not unlikely, the relation of dE to dt be the same as for the magnetism, 

 they would only differ in the values of /x and c. 



The quantity F is the current which would be produced were it not for 

 the inductive reaction of the current on itself. It is as P directly and r 

 inversely. The first of these, P, is as n the number of spires in the helix * 

 multiplied by a rather complex function of its length and diameter, which 

 is constant when they are given. The second, r, may be assumed propor- 

 tional to the length and section of the wire of the helix, for in general the 

 other resistances of the circuit are comparatively small. Hence it follows that 



If two equipotential helices equally excited be placed in series, the ten- 

 sion will be doubled ; but the current will be intermediate between that of 

 2P 



each, for Y=~—^ and if r—r' it will not be changed. If they be used 



collaterally (their homonymous terminals connected), P remains unchanged, 

 and therefore the currents of the helices are simply added. If there be an 

 external resistance, allowance must be made for it. This may be extended 

 to any number of helices ; for calling the external resistance p, we find 



— 7r~i nr\ 



i+p(-+-, — + -) 



The constant c must be a small fraction, for in any ordinary work of the 

 inductorium the residual magnetism of the core is very feeble. As 

 itz=ze-i^*y fit must be large ; and as'^ for wire cores does not exceed a few 

 hundredths of a second f, fJ- must be very large. 



^ Not as the mere length of wire, as is sometimes loosely stated. 



t I have been informed that with the inductorium which Mr. Whitehouse constructed 

 for the first Atlantic telegraph, the cores of which were massive iron cylinders, the 

 discharge lasted some seconds. If it be still in existence, it would be interesting to 

 examine the spectra which it would give. 



