completed five barometers of very different capacities and diameters, whose difference from the mean and from the standard, with all corrections made, was only .006 of an inch,

ART. II. On the Alterations of Rate produced in Chronometers by the influence of Magnetism. By George Harvey, Esq., F.R.S.E., &c.

THE power which a magnetic force possesses, of accelerating the rate of a time-keeper in some situations, and of retarding it in others, is a fact which has been verified by many interesting and important experiments. It is singular, however, that the same attractive power, which when applied in different directions to one chronometer, tends either to accelerate or retard its rate, should in another, when allowed to operate under the same conditions, as to intensity and position, produce results precisely the reverse. It will be the cbject of the following paper, to refer these apparent anomalies, to the varieties of imperfect isochronism, existing among different chronometers.

To illustrate this view of the subject, suppose the balance of a chronometer in its quiescent position, having its thermometerpieces in an active, but opposite state of polarity; and let the line joining those pieces, and which therefore passes through the centre of the balance, denote the direction in which the magnetic force acts. Now since the thermometer-pieces possess opposite polarities, let that portion of the attractive influence which is destined to operate on the time-keeper, and is of an opposite kind to the polarity of the thermometer-piece on which it first acts, be allowed to exert its energy, the moment the oscillations of the balance take place. The effect of such an application will be, a decrease in the arc of vibration, in consequence of the effort made by the thermometer-piece, on which the magnetic force acts, to approach the attracting pole. This alteration in the amplitude of the arc of vibration, will therefore occasion some variation of rate in the timekeeper. If instead of supposing the attractive power to pass im

mediately through the thermometer-pieces, it be allowed to produce its effects, on either side the point of quiescence, within certain limits, the arc of vibration will still be diminished, but in a less ratio than before; and changes of rate proportional to the variation of amplitude, will be the result.

Suppose in the next place, the direction of the magnetic force to pass through the centre of the balance, and the limit of the semiarc of vibration; it is manifest, when motion is communicated to the balance, its effect will be to increase the arc of vibration, both from its attracting one of the thermometer-pieces, and repelling the other; and that therefore an alteration of rate, entirely the reverse of the former, will be the necessary result. It is also evident, that if the same attracting pole be applied on either side of its lastmentioned position, within certain limits, the arc of vibration will still be increased, but in a less ratio than before; and alterations of rate of the same kind, but of a less remarkable degree, will be produced.

If the time-screws are supposed to be magnetic, and the thermometer-pieces free from the attractive influence, similar results will take place.

Conceive in the next place, that in addition to the magnetism of the thermometer-pieces, the entire arcs of compensation possess also a property of the same kind; one half of each having northern polarity, and the other half southern; then will the time-screw attached to the arc of compensation, whose thermometer-piece has northern polarity, become a south pole; and that attached to the arc, whose thermometer-piece has southern polarity, a north pole; the transverse arm connecting the two, if of steel, presenting all the properties of a perfect magnet.

In this point of view, the entire balance may be regarded as a species of compound magnet, having two pair of opposite poles; and different phenomena will be exhibited, according to the direction in which the magnetic force acts. If, for example, the magnetic power be allowed to develop its influence, in a direction equally remote from the opposite poles of each of the arcs of compensation; and that we moreover suppose each pole to possess the

same degree of intensity, the acceleration or retardation produced by the action of the exciting force on one of the poles, will be entirely neutralized, by the opposite effects of the other. But if the attracting power be allowed to operate in a position nearer to one pole than the other, an alteration of rate will result from the change in the arc of vibration, necessarily produced by the inequality of action. If on the other hand, the magnetic force be applied, in a direction between the thermometer-piece and time-screw belonging to the separate arcs of compensation, and having a polarity of a contrary kind to them, a constant effort will be made by the balance, to accommodate its arcs of vibration to the united effect produced by the maintaining power, and the intensity of the magnetic action; and a similar tendency will likewise be displayed by the balance, if the disturbing pole be placed in the vicinity of a thermometer-piece and time-screw, having the same kind of polarity with it.

From the same considerations we may also infer, why a chronometer, having a balance powerfully magnetic, should present variations of rate, from the influence of the earth alone, according as it is situated with respect to the magnetic meridian. If the thermometer-pieces alone are magnetic, and the line joining them be placed in any other direction than that of the magnetic meridian, a continual effort will be made by the balance to regain this position, thereby producing a change in the arc of vibration. If also, the entire balance be considered as magnetic, some line may be found passing through its centre, in which it would repose in the direction of the magnetic meridian, if detached from the other chronometrical parts, and freely suspended. Hence it follows, that the moment the timekeeper is so placed, as to remove the balance from the last-mentioned position, a tendency will be created in it, to return to that state; and which, by producing variations in the arc of vibration, must at the same time be accompanied by sensible alterations of

rate.

Having made these general observations, I shall finally consider the cause, why similar changes in the arc of vibration, should be frequently attended, in different chronometers, with opposite alterations of rate.

It may be questioned, if ever a chronometer existed, in which the vibrations of the balance were perfectly isochronous; or in other words, in which the adjustments of the spiral spring were such as to admit of its elastic force, varying precisely with the arcs of vibration. Mr. Atwood has shewn in the Philosophical Transactions for 1794, that although the relation between. the elastic force of the spring, and the magnitudes of the arcs of vibration, may appear to be in a perfect ratio of equality, there may nevertheless exist such exceedingly minute deviations from this state, as to render it impossible to be detected, by the most delicate experimenter; and yet these minute inequalities may be considerable enough to produce in the interval of twenty-four hours, a sensible alteration of rate. Hence it is, that the application of a magnetic force to a chronometer, having a balance in any degree magnetic, in almost every case, produces a visible alteration of rate. In an example furnished by the able mathematician before quoted he demonstrates, that a variation of a thousandth part from a perfect state of equality, in the relation between the elastic force of the spring, and the arcs of vibration, is capable of producing an acceleration of + 2′′.62 in the daily rate, when the semi-arc of vibration is diminished 8°; and he even states, that an increase of rate amounting to 20 or 30 seconds may exist, and yet the differences arising from the deviation of the elastic force of the spring, from the law of isochronism, be too minute to be reudered sensible by any statical counterpoise of the force of the spring.

Assuming therefore a perfect isochronism in the vibrations of a balance, as a condition scarcely to be obtained, the deviations from it, may be contemplated under two points of view; since the elastic force of the spring may vary either in a less ratio than the angular distances from the point of quiescence, or in a greater; and which suppositions will account for the apparent anomalies presented by different chronometers, when subject to the action of a magnetic force.

This will appear evident, by referring to the function, which according to Mr. Atwood, represents the daily abberration of a time

keeper, when the magnitude of the arc of vibration is changed, and which is

where a denotes the primitive arc of vibration, a' that produced by the action of a disturbing force; and which, according to the direction of its action, may be either greater or less than a; and n the exponent dependent on the peculiar ratio existing between the elastic force of the spring, and the angular distances from the point of quiescence.

If we suppose the primitive arc constant, and the other elements a' and n of the formula variable, the entire function, as Mr. Atwood observes, will be susceptible of different modifications. Suppose, for example, we attribute to n a less value than unity*, a condition which corresponds to that of the elastic force of the spring, varying in a less ratio than the angular distances from the point of quiescence; it is manifest, that different values will be communicated to the function, according to the value assumed for a. If the supposition alluded to in an early part of the paper, of the attracting force passing through the thermometer-pieces be referred to, and in which the arc of vibration would be shortened by its operation, the value of a' must necessarily become less than a; and a positive value being thus communicated to the function, the time-keeper will gain.

In the next place, if the attracting force be conceived, as in the second supposition, to pass through the centre of the balance and the limit of the semi-arc of vibration, and which application will necessarily occasion a' to become greater than a, the numerical value of the formula will be negative, and the chronometer will lose.

If again we supposen to be greater than unity, or the elastic force of the spring to vary in a greater ratio than that of the distances from the point of quiescence, the first of the preceding suppositions with respect to a', will give to the function a negative value, indicating a retardation of rate in the time-keeper.

* If we suppose n = 1, the whole function will vanish, in indicating a perfect isochronism; so that whether the arcs of vibration be increased or diminished by the action of a disturbing force, no alteration of rate will take place.