^{page 279 note *} The opposite extremities of the pivot-holes are faced with small portions of fine watch-spring, as at ef, Fig. 1. which mark the centres of the two front wheels. Thus all friction which might possibly arise from the occasional contact of the shoulder of the pivot is prevented.

^{page 279 note †} The loop is formed by a doubled piece of fine silk, inserted in a small hole drilled vertically into the centre of the upper part of the cylinder x, and secured there by a small peg of wood passed down into the hole between its two extremities.

^{page 280 note *} It is requisite to have several of these cylinders of different diameters, namely, from 0.2 of an inch, to an inch, each increasing in diameter about 0.1 of an inch. They should be very accurately turned, and, before being used, should be freely wetted throughout their whole length, which is best effected by allowing them to remain for a short time immersed in water as high as the upper stem. They are suspended in their situation by means of a loop of silk, inserted in the bottom of the hemispherical cup into a small hole drilled through its centre into the stem, and secured there with a small peg of wood in the way already described in note on p. 279.

^{page 281 note *} These weights being placed under the same circumstances as the weights in the celebrated machine of Mr Atwood.—See Atwood on Rectilinear Motion.

^{page 283 note *} The spaces are sufficiently large to receive one or more magnetic bars of a convenient size, the interval, when only one is employed, being filled up by a piece of wood placed behind the scale, to keep it steady. The scale extends about three inches above the magnet, and through its whole extent below: it can therefore be raised between the magnet and wood to any further altitude required.

^{page 285 note *} There should be several small cylinders prepared of very soft iron, for general use, being about two inches in length, and one quarter of an inch in diameter. The iron-wire of commerce is convenient for the purpose. They should be accurately turned, and great care should be observed in freeing them from any permanent polarity, which is readily done by making them red-hot in a clay tube, or in fine sand in a small crucible, so as to keep them out of contact with the air. They may be considered sufficiently free from polarity, if, when immersed in fine filings of soft iron, there is no tendency to adhesion, or polar arrangement of the filings about their extremities.

^{page 288 note *} The distance cd between the iron and magnet is readily varied, either by elevating the magnet m, or depressing the iron bc, the brass bands allowing them to slide beneath with sufficient ease, but yet, at the same time, exerting a sufficient degree of pressure to retain the iron and magnet in the required position.

^{page 289 note *} The point r consists of a very short piece of soft iron, about two-tenths of an inch in diameter. It is screwed firmly into the centre of the iron ab, so as to have a perfect contact, and projects vertically for about the one-tenth of an inch from its lower extremity; thus the steel ring r becomes always attached in the same place.

^{page 290 note *} The weight of the steel ring and brass pan S, with the silk lines, was just 100 grains. It was consequently taken into the account at each trial; and the weights finally added before the contact was broken, did not exceed 10 grains at a time, these being placed carefully in the pan.

^{page 293 note *} I employ this term to distinguish more particularly the magnets inducing the temporary development of magnetic properties in the unmagnetised iron.

^{page 294 note *} It may be from this circumstance that some profound investigators of magnetic phenomena have found, that a hollow sphere of iron exerted as much effect on a compass needle as a solid mass of the same dimensions; which might be reasonably supposed to be the case, as the iron could only become magnetic by induction, in which case the force of the proximate poles would be always the same. The force which such ball or shell, however, could exert on some third mass, not previously magnetic, would probably be found to be very different.

^{page 302 note *} Although this result, as disconnected with the previous investigations concerning induced magnetism, it may be readily imagined, must happen, admitting the general law of magnetic attraction about to be demonstrated, namely, that of the inverse square of the distance; yet, on examination, and as will be further shewn, it will be found to depend exclusively on the operation of induction, and that where this operation does not proceed, the law above named no longer obtains.

^{page 306 note *} Although by opposing two magnets at their dissimilar poles, we in great measure destroy their permanent magnetism, yet the inductive influence by which this is effected must still be considered as a new force induced in the magnets, since it has been capable of producing a certain effect.

^{page 314 note *} Although the polarity of the small magnet in these experiments seemed to be reversed, inasmuch as the repulsion was superseded by attraction even before contact, yet the new polarity by induction did not appear to be permanent, since the repulsion again obtained when the distance was increased. Thus, both the phenomena of attraction and repulsion ensued, merely by varying the distance in a small degree between the magnets. The forces indicated at near approximations with the repelling poles, are only given in illustration of the curious fact, that the pole of the weaker magnet becomes reversed before contact. We cannot consider them as quite accurate for any purpose of calculation, as the suspended magnet, in consequence of the great repulsive force, is thrown out of its perpendicular direction.

^{page 321 note *} It may not be improper to state, that, in the preceding inquiries, the attracting or repelling forces have been supposed to act in parallel lines. This appears to be an essential condition of this species of force; since the reciprocal influence of any two points directly opposed to each other, as ab, Fig. 21, 22, 24, must be such as to neutralize each other's action in relation to any other point more distant; the action, therefore, between the points immediately opposed to each other is exclusive, being the nearest, and consequently the forces are parallel.

It is, therefore, only when the attracting surfaces are of unequal extent, that it becomes necessary to take into the account any other force, as cd and ef, Fig. 22, which, in a great variety of instances, are of no assignable value; but to obviate any error which can arise from this cause, it is requisite, when very powerful magnets are employed, to give the attracting extremity of the bar an armature of soft iron, as represented in Fig. 23. A, which, in diminishing from its base, terminates in a cylindrical surface exactly equal to that of the suspended body x; by which means the angular forces, as cd, ef, Fig. 22, are so intercepted and reduced, as to be of no assignable value.

When the attracting surfaces are spherical and equal, it is requisite to determine a fixed point in each opposed hemisphere, as x and y, Fig. 24, from which the sum of all the attractions would produce the same effect as if those attractions were exerted from every point of the hemispheres; so that, in varying the distances, the intervals may be estimated from these points, and not from the immediate point of contact. These points I have found by numerous experiments fall within the opposed hemispheres, at a distance equal to one-fifth of the radius of the spheres, supposing them equal.