of Unipolar Induction . 419 



consequently changes its sign at d, and it retains this change 

 of sign until it comes to/. It follows from this that the ele- 

 mentary magnets upon the arc dpf produce an, induction of 

 opposite sense to those upon the arc fmgd. If these con- 

 trary inductions become of equal value, no induction will be 

 produced in the element of circuit at rest As. It is moreover 

 clear that if the element As were situated at a vertical dis- 

 tance H above or below the horizontal plane in question, the 

 induction would change its sign when the elementary magnet 

 passed the points d and/. If, on the contrary, the element 

 of the circuit is situated at the centre o of the circle, the in- 

 ductions of all the elementary magnets would act in the same 

 direction, and the result would consequently be equal to their 

 arithmetical sum. 



6. In the preceding explanation we have taken into consi- 

 deration only the induction of the elementary magnets upon 

 the periphery of the magnet. But it is evident that the same 

 deductions are equally applicable to each ring of elementary 

 magnets of which the radius is less than the radius of the 

 magnet. The difference is this : that, in consequence of the 

 rotation of the magnet on its own axis, the induction produced 

 by these rings or layers in an element of the circuit situated 

 at a distance is less than the effect of the ring or layer of ele- 

 mentary magnets at the periphery of the magnet. In the 

 same way no account has been taken of the one pole of the 

 magnet ; but it is evident that the same proof applies equally 

 to the second. It follows, therefore, that the preceding de- 

 monstration applies to the whole magnet. 



§7. 



1. The experimental result given under No. 3 of § 2 is, 

 as already mentioned, explained on the old theory by the 

 supposition that an electromotive force is produced in the 

 jacket of the same magnitude as if the magnet were at rest 

 but the jacket in rotation in the opposite direction with the 

 same angular velocity, and that an electromotive force of 

 equal magnitude was produced in the metallic wire. Where 

 these two forces of equal magnitude neutralized each other, 

 the intensity of the current is equal to zero. According to 

 the requirements of the mechanical theory of heat, this ex- 

 planation is erroneous. It is true that the rotation of the 

 magnet causes the production of an electromotive force in the 

 jacket at rest ; but, as we have seen, this force is very small. 

 It produces in the same way a feeble electromotive force in 

 the metallic wire. These two forces are opposed, but they 



