the Electricity given by Induction-Machines, 65 



Patting # = — , and supposing 9 to vanish with t, 



*=;"*M(0-i} (J) 



The total current in the time ^=$=1 (hdt= \— —dy — 7- 1 ddt, and 



Jo r J r bj 



y. 



M 1 



hence putting F for — — (M — y) and c for ^-, we obtain 



* = i 1 1 + ;rM (c) 



1 — c [ fi — o n — b 



The expression for the current due to the electric induction will 

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

 If, as is not unlikely, the relation of c?E to dt he the same as for the 

 magnetism, they would only differ in the values of ji 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 proportional 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 

 tension will be doubled ; but the current will be intermediate between 



2P 



that of each, for F= — — \ and if r=i J 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 he 

 made for it. This may be extended to any number of helices ; for 

 calling the external resistance 0, we find 



P P' P 



— 4— -4- 



. . . . 00 



i+p(i+V...*i) 



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 it=e-^, /dt must be large; and as t for wire cores 

 does not exceed a few hundredths of a second f, \x must be very large. 

 The potential IT is as ri 2 multiplied by another function of the length 

 and diameters of the helix (see Maxwell's valuable paper "On the 



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



f I have bsen 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 he still in existence, 

 it would be interesting to examine the spectra which it would give. 



Phil. Mag. S. 4. Vol. 33. No. 220, Jan. 1867. F 



