3rd. The deduction which shows that the depth of the magnetising coils of an electro-magnet should be equal to the diameter of the cores which they cover, may easily be verified. In order to demonstrate this experimentally, I took three electro-magnets with bobbins of the same length but very different diameters.

One of these magnets had a diameter of 2 centimetres, another of 1 centimetre, and the third of ⚫65 centimetre. I applied one pole only to the balance, and each bobbin, covered with No. 16 wire, had 23 layers of 111 turns in each, or 2553 turns in all. Nothing of the thickness of paper even was introduced between the layers, and all the turns were pressed closely one against another, which gave these coils a uniform depth of 1 centimetre. The result was that the electro-magnet of which the core was 1 centimetre in diameter was the only one which answered to the maximum conditions previously given. This magnet had a resistance of 3200 metres, the large one of 5200 metres, and the small one of 2800 metres. The following (p. 54) are the results I obtained in passing through these different electromagnets the current from a Leclanché battery containing from 1 to 3 cells, each having an internal resistance of about 400 metres, estimating the attractive force at a distance of 1 millimetre.

We see by this table that, for a like resistance of exterior circuit, and with a sufficient electric intensity, it is the electro-magnet of which the depth of the coil equals the diameter of the core, which has

the advantage; this advantage is found to be invariable when we compare the forces produced on exterior circuits of different resistance, adapted to the resistances of the magnets, the only case which has been discussed in the formulas. It is only when the electric force is so weak that the increase of the magnetic action with the diameter is not very palpable, that the maximum of the electro-magnet of 1 centimetre loses ground a little; and this is as it should be, for Muller's law, which supposes the attractive forces to be proportional to the diameter of the magnetic cores, is only true when these cores are magnetised to a pitch approaching that of their magnetic saturation; and by this word saturation must be here understood that magnetic state which

the electro-magnet would preserve, if, instead of being iron, it were tempered steel magnetised. When the magnetic force developed is much below this point, it is on the electric intensity that the attractive force produced chiefly depends, and this is naturally greatest with the least resisting circuit. The figures in parentheses in the preceding table point out, in each of the three series of experiments made with different electric intensities, the forces corresponding to the maximum conditions with reference to the circuit, and these conditions were naturally established, supposing the resistance of the exterior circuit to be equal to that of the coil; for I started in the construction of my electro-magnets from a given depth of bobbin. But if I based my calculations on the maximum conditions relative to a given electro-magnet without considering its dimensions, the preceding law is still further verified, for the maximum resistances of the exterior circuit then become 1400 metres for the small magnet, 2600 metres for the large one, and 1600 metres for the other. Thus the attractive forces of these three electro-magnets are as follows:

CHAPTER VII.

EFFECTS OF A MORE OR LESS COMPLETE
MAGNETIC SATURATION.

As I have said, the laws of electro-magnets are not as definite as might be desired, by reason of the various effects resulting from the state of saturation of their magnetic core; but this cause of perturbation is far from being as great as certain scientists would have it thought, and it interferes in a less proportion with the definite results deduced, than do the effects of polarisation with the calculated results of the laws of electric currents. At the time of my last investigations concerning electro-magnets, I wished to assure myself of the importance of this disturbing cause, and I undertook a great number of experiments which seem to me interesting to report here, for in consequence of the development that takes place every day in the application of electro-magnetism, it is, above all, important to be well grounded in the conditions for the good construction of magnets on which depends the success of these applications.

In the first part of this work I gave several general deductions which I had drawn from experi

ence, but I did not insist on my experiments themselves, for they led to no law besides those given by Dub and Muller; but it is important that I should explain myself more explicitly in this respect; I will, therefore, begin by demonstrating that if we take 11 as the value of the coefficient m, by which the diameter of the magnetic core must be multiplied to find its length, so as to satisfy the different conditions of maximum relating to it, its attractive force always increases in proportion to its length. In fact, if we start with a given length of wire representing the resistance of the exterior circuit, and wind it on electro-magnets of different diameters so as to get a depth of coil equal to their diameters, their lengths must be different and calculated to satisfy the equations

and then these lengths will be inversely proportional to the squares of their diameters. In this case the factor m is no longer constant and becomes proportional to the cube of the diameters; but then the law which supposes the E. M. F. proportional to the squares of the number of turns multiplied by the

cube of the diameter, is no longer applicable, and we must then, to compare the forces, have recourse to the law which takes the latter to be proportional to the number of turns multiplied by the diameters of the cores, and the square roots of the lengths.