606 Mr. J. Viriamu Jones [May 24, 



where Ej is the electromotive-force between the centre and circum- 

 ference. 



But we may, instead of using the earth's field, obtain a magnetic 

 field by means of an electric current. The disc may be made to spin 

 in the magnetic field due to a current in a coil of wire placed so as to 

 be co-axial with it, and so that its middle plane coincides with the 

 plane of the disc. In this case the magnetic field is symmetrical with 

 regard to the common axis, and we have once more 



E x = I n, 



where E x is the electromotive-force between the centre and circum- 

 ference consequent on the rotation of the disc at the rate of n turns 

 per second in the induction flux due to the current in the coil, I 

 being the total amount of that flux which passes through the disc 

 circumference. 



Now the current strength in a given circuit is by definition pro- 

 portional to the intensity of the magnetic field produced by it at any 

 point, and hence the magnetic induction through the disc due to the 

 current in the coil is proportional to the strength of that current. 



It follows that the magnetic induction through the disc is made 

 up of two factors, viz. the current in the coil and the magnetic induc- 

 tion that would pass through the disc if unit current passed through 

 the coil. The latter factor is called the coefficient of mutual induc- 

 tion of the coil and disc circumference, and its value depends only on 

 their dimensions and relative positions, and the magnetic permeability 

 of the medium in which they are placed. If the latter quantity is 

 taken to be unity, the coefficient of mutual induction is expressible as 

 a length, and it may be calculated from observations involving nothing 

 else than measurement of the radius and breadth of the coil and 

 the radius of the disc. Let this coefficient of mutual induction be de- 

 noted by M, and the current in the coil by y x ; then 



and finally, 



' Ej = nl =»M yi ; 

 or 



5- 1 = nM. 



7i 



We have therefore two ways of expressing the ratio of an electro- 

 motive-force to a current. 



By definition (Ohm's law) this ratio is given to us as electrical 

 resistance, or 



7 

 By the experiment of the disc and coil it is given to us as the 

 product of their coefficient of mutual induction and the rate of rota- 

 tion of the disc (number of turns per second). 



