movable needle of any other points than that which was in the same horizontal plane with it; he no longer had occasion to take account of the directive force of the earth, since the needle remained in the magnetic meridian. The angles of torsion necessary for maintaining them exactly represented, therefore, in each case, the magnetic force of the point acting upon the fixed needle. In the second method, Coulomb caused the proof-needle to oscillate before the different parts of a long magnetised bar, which he made to glide along vertically, so that all its points were to be found successively in the horizontal plane of the needle, and at the same distance. Calling m', m", and m", the total action exercised upon the needle, when it is successively before each of the points of the bar, m being still that of the terrestrial magnetism, and n', n", n'" the number of oscillations made by the proof-needle before each of these points, n being the number of oscillations when terrestrial magnetism alone m, m" = n2 n n Now m' — m, m'"'—m, represent the magnetic forces emanating respectively from each point of the magnet; because these quantities are the total action diminished by that of the terrestrial magnetism, and we may compare these together when once we have by experiment determined n, n', n", n"", &c. The following is a table of the results obtained by Coulomb with a steel wire 283 in. long, and 176 in. in diameter. The proof-needle, before the steel wire was presented to it, made one oscillation in a minute, or 60". Before the extremity of the wire it made 64 oscil. in 60" ⚫53 in. 58 "9 1.06 44 Thus, setting out from the point situated from 4 in. to 4 in. below its extremity, the steel needle presented no sensible magnetic force. By continuing to lower the needle, it was found that the almost complete absence of action continued to about a distance of 4 in. to 4 in. from the other extremity. But, setting out from this distance, the same were again produced in an inverse order; and the proof-needle made a complete rotation to present its other pole to the action of the steel wire, the second pole of which, in like manner, commenced acting upon it. By the employment of this method, we may easily prove the presence of consecutive points or intermediate poles, in the portion of a magnetised wire or steel bar comprised between its extreme points: we can also determine the intensity of the magnetic forces with which they are endowed. With regard to the intensity of the forces that emanate from the very extremities of the magnetised wire, it is necessary, in order to obtain the true expression, to double the result obtained; for the effect would evidently be, for these extreme points, the double of what it is really if the magnet were prolonged beyond and presented points on the outside as efficacious as those that are within; which takes place for the other parts of the bar. Coulomb also succeeded in representing geometrically all the results that he obtained, by erecting upon each of the points of a horizontal line, representing a magnetised wire, perpendiculars of lengths proportional to the intensities obtained by experiment. The extremities of these perpendiculars, in the experiment that we have related above, form a curve, which is confounded with the axis of the wire, which was 283 in. long, for a length of about 19 in., and goes on receding rapidly from this axis from the 4 in. and the 24th in. to the extremities, where it attains its maximum (Fig. 77.). It is very remarkable that this curve, or, which comes to the same thing, the distribution of the magnetism of which it is the representation, is exactly the same for wires or plates of different lengths, provided that the length exceeds eight inches; there is no other difference, except that the space left in the middle, where the magnetism is sensibly null, varies in length. It follows also from this, that all magnets of the same force, and of greater length than eight inches, have their poles at the same distance from their extremities: this distance is about 1 in., according to Coulomb's calculations. The same philosopher found that, when magnets are too short, their poles are very nearly one-third of their half-length from their extremities: thus, for a needle of 3 inches, the poles will be at a distance of in. at least from its extremities. All these results are only true for magnets whose length is very great in respect to their transverse dimensions, whose form is perfectly regular, such as the cylindrical or rectangular, and which are magnetised in a normal manner. With needles in the form of a lozenge the poles are much more distant from the extremities: in this case, as in others, the proof-needle must be employed, in order to determine their position; calculation cannot lead to it à priori. M. Becquerel endeavoured, by means of the torsion balance, to determine the distribution of magnetism in excessively fine steel wires: he obtained these wires by drawing through the draw-plate a steel cylinder, of small diameter, which he had placed in the axis of a cylinder of silver ten times larger. Then, after having obtained a very fine silver wire, having for its axis an almost capillary steel wire, he dissolved the silver in mercury, which did not attack the steel, and obtained an almost microscopic steel wire. These wires are not susceptible of acquiring strong magnetism: however, they become sufficiently magnetised to enable us to prove that the distribution of their magnetism follows very nearly the law deduced from Coulomb's observations. M. Becquerel found that, in a wire 00052 in. in diameter, and 5 in. in length, the poles were 334 in. from its extremities. One might have thought that they would have been at the extremities themselves, which would probably have happened, had the wire been composed of only one range of consecutive particles; an ideal case, which it is not possible to realise. M. Kupffer has remarked, by means of very delicate experiments, made by the method of oscillations, that there exists in a magnetised bar a point, which exercises absolutely no action upon the needle, and which he has termed point of indifference. The position of this point is influenced in a very pronounced manner by terrestrial magnetism, when the bar is not strongly magnetised. If this bar is arranged in a vertical position, its north pole being below, the point of indifference is found to be nearer to the north than to the other pole. If the bar is inverted, the point of indifference approaches the middle. In the former case, the north pole of the bar was stronger than the south pole. In the latter case, the two poles approached gradually towards having the same power. It would follow from this, that the point of indifference would be always nearer to the stronger pole; and that the kind of influence of terrestrial magnetism that has just been pointed out, would consist simply in determining a greater intensity in one of the poles than in the other. The same effect may be remarked upon a horizontal magnet; its north pole is stronger than its south, when it is in its natural direction. Elevation of temperature, as we have seen, diminishes the magnetic intensity of a bar. M. Kupffer has shown that it also modifies the distribution of magnetism in the same bar. The displacement of the point of indifference is especially sensible, when only one of the poles is heated. The point of indifference recedes from the heated pole, which also becomes more feeble. It would seem to result from these observations of M. Kupffer, that the relative intensity of the two poles is the only cause exercising an influence over the distribution of the magnetism; and it is only because they modify this intensity, that different circumstances, such as terrestrial magnetism and variation of temperature, cause this point of indifference to undergo a change of place. Finally, we should be led to believe that, if the point of indifference does not remain in the middle of a bar, but is carried from the stronger side when the two extremities have not the same magnetic power, it is because the sum of all the opposed forces being necessarily always equal to each other, this condition can be fulfilled only so long as the points from which the more feeble emanate are more numerous than the points from which the more intense emanate; and, consequently, that the portion of the needle whose extremity has the greatest amount of magnetism is shorter than the portion whose extremity has the least. Theory of Magnetic Fluids and of the Coercitive Force. The sort of considerations that we have been discussing lead us to entering upon the theory of magnetism, a subject which the labours of Coulomb, followed by the mathematical researches of Poisson, would seem to have exhausted, when the discoveries of which we shall speak in the following Chapter, if they did not totally overthrow, at least modified considerably, the theoretical ideas of these two philosophers. However, their theory is too important, and at this time too widely extended, to permit of our passing over it in silence. The importance and the utility of being acquainted with it, in order to comprehend that which has been substituted for |