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IX. On a Magnetic Potentiometer. By A. P. Chattock*. 



IN arranging some experiments on the magnetic resistances 

 (so-called) of certain air and iron fields with a view to 

 the more satisfactory designing of dynamos, I have been led, 

 by the familiar analogy between magnetic and electrical cir- 

 cuits, to adopt the following method of measurement ; which 

 I venture to describe, partly on account of its convenience, 

 partly because the measurement of magnetic resistances seems 

 likely to play an important part in the practical application of 

 electromagnetism. 



The resistance between two points on a magnetic circuit 

 may be expressed as the ratio of their potential difference to 

 the total induction passing from one to the other (provided 

 there is no reverse magnetomotive force between them). 



The measurement of the total induction is of course a simple 

 matter ; but, so far as I am aware, no method of directly 

 measuring differences of potential has yet been suggested. 



Let A and B be two points in a magnetic field connected 

 by any line of length I ; and let H represent magnetic force 

 resolved along I. 



Then, if V be the difference of potential between A and B, 



V=$K.dl 



If, instead of points, A and B represent two equal plane 

 surfaces of area a, and V be their average difference of 

 potential, 



aY=$Y.da=§TL. dv, 



v being the volume of a tube of constant cross section, a, con- 

 necting A and B by any path. 



Now let a wire helix be wound uniformly upon such a tube, 

 with n turns per unit length, and allow H to vary with time, t. 

 Provided there be no magnetic substance inside the helix, an 

 electromotive force, E, will be set up in the latter, such that 



dV 



E^^K.da.dn-tnfe.d^ 



™Tt 



The value of E is thus proportional to the rate of change of V; 

 and to this alone, if external inductive effects are guarded 

 against by winding the wire in an even number of layers (n 

 and a being constant). Hence, if the wire be connected with 

 a ballistic galvanometer, and Y be altered suddenly from V x 

 to V 2 , the needle of the galvanometer will be thrown through 



* Communicated by the Physical Society : read May 14, 1887. 



