DYNAMOS. 715 



the factor within the bracket only depends on the magnetic field 

 that is to say, on the inductors ; the ( two former depend on the 

 ring, and on the intensity of the current. 



The excitation of the inductors, if they are not permanent 

 magnets, requires an expenditure of energy, which should be made 

 as small as possible. Given the armatures of the inductors, the 

 magnetisation is defined by the currents which surround them. In 

 this case, with wires covered by an insulating layer proportional to 

 their thickness and occupying a given volume, the energy expended 

 in producing the same magnetic field is independent of the diameter 

 of the wire, as well as of the intensity of the current, and only depends 

 on the density of the current in the meridian section occupied by the 

 wire ; we ought then to seek for economy simply in the choice of the 

 wire, the shape of the cores, and the pole pieces, and the mode of 

 distribution of the currents. 



Other things being equal, the energy expended in heating the 

 inductors is proportional to the square of the intensity of the 

 current, while the magnetisation increases more slowly, and tends 

 towards a maximum. The ratio of the energy expended to the field 

 produced increases then rapidly, and there is a degree of mag- 

 netisation which it is not advantageous to exceed in practice. 



On the other hand, the field being determined, the motor couple 

 is proportional to the product PI that is to say, to the total current 

 for unit section of the whole of the wires which surround the ring, 

 or the density of the current. Then, again, if we neglect the effects 

 of self-induction which show themselves at the passage of the 

 brush, the thermal energy does not alter if this product remains 

 the same. 



With some allowance for the effects of mutual induction or of 

 self-induction of the various parts of the circuit, we may say then, 

 with M. Deprez, that the energy necessary to produce a given motor 

 couple (or a static effort) is independent of the resistance of the 

 wires which are coiled on the inductors and on the ring, provided 

 the volume occupied respectively by these two systems of wires does 

 not change. 



1270. The characteristic function may be experimentally de- 

 termined by various methods. 



i st. An auxiliary current I is passed in the inductor, the brushes 

 being left in the position which they are to occupy, and the ring 

 is rotated; the electromotive force '#<(!) will be measured by op- 

 position, either by an electrometer, or with a galvanometer of great 

 resistance. 



