of Unipolar Induction. 407 



ment forms with the line drawn from the element to the pole, 

 by the cosine of the angle between the direction of rotation 

 of the element and the normal to the plane passing through 

 the element and the pole, and, lastly, by the velocity and the 

 length of the element. It should be observed in this respect 

 that h does not denote the angular velocity of the element of 

 the circuit, but the length of path described by the element in 

 unit time. Without consumption of mechanical work no in- 

 duced current, with its resulting development of heat, could 

 be produced. 



When the element of the circuit moves in a uniform and 

 homogeneous magnetic field, as, for example, that due to the 

 horizontal component of the earth's magnetism, Helmholtz 

 and Sir W. Thomson* have obtained the same expression for 

 the induced current as that contained in the preceding equa- 

 tion (5) . It is thus evident that these formulae ought to be 

 equal in the two cases ; since the action of a magnetic pole 

 upon an element of the circuit which moves at a uniform dis- 

 tance from the pole ought to be continually of the same mag- 

 nitude, and consequently would be under the same conditions 

 as if the element moved in a homogeneous magnetic field. 



§4. 



The law given above in formula (5) for the inductive action 

 of a magnetic pole upon an element of a circuit in motion 

 does not indicate in any manner how the current is produced, 

 nor the relation of this phenomenon to other electrical phe- 

 nomena. I now propose a new formula showing this relation- 

 ship, which is also of a more convenient form, and I shall 

 show mathematically that this new formula may be deduced 

 from formula (5). 



I imagine to myself that the induction is produced in the 

 following manner : — If the electric current consists really in 

 the transport of a fluid, as soon as the element of the circuit 

 begins to move the fluid would be carried with it in the direc- 

 tion of motion, and would thus produce a current upon which 

 a magnetic pole could act, according to the known law of 

 Biot-Savart. If /3 be the angle formed by the direction of 

 motion with the line drawn from the element of the circuit to 

 the pole, and yfr the angle made by the element with the 

 normal to the plane passing through the direction of motion 

 and the line joining the pole and the element; if then A. be 

 the velocity of the element of the circuit, and As its length, 

 we shall have, in accordance with the law mentioned above, 



* Blavier, JDes grandeurs electriques, p. 358 (Paris, 1881). 



