impose a certain duty on the pendulum, which is, to unlock the train at the moments when it is necessary that the remontoir motor should be raised. This cannot be done without friction, although the friction is less than in the case of pallet escapements. It is also true that, in proportion as the friction required to unlock is reduced, these escapements become liable to the accident of failing to lock-or of tripping, as it is technically called -whereby error is introduced into the time shown upon the dial.

Of all these escapements, remontoir escapements and pallet escapements alike, it may finally be said that they require the pendulum to swing through a certain arc larger than would be necessary if the maintaining power could be applied to it from without, leaving it subject to no disturbances whatever, beyond those occasioned by the varying temperature and density of the air. The usual extent of the arc of vibration is 2° on each side of the vertical. About one quarter of this distance is required merely to unlock the train of the remontoir. If now, at a definite point of the swing, a light weight could be deposited upon an arm projecting from the pendulum rod, allowed to remain there during the descent, and then removed, and if this could be repeated on one side and on the other alternately, with perfect regularity and at precisely the same distance always from the centre of motion, and if this could be done without any friction or concussion, we should have a pendulum subject to no forces accelerating or retarding but such as may be accurately estimated in their amount, and in their effects upon the time of vibration.

I do not overlook the fact, that the manner of suspending the pendulum may have some influence on its performance. But as the suspension is almost invariably by means of a very flexible but also very elastic spring, the effect due to the resistance of this spring in the ascent may be considered as neutralized, so far as regularity of vibration is concerned, by its recoil in the descent; and for the variations of its elasticity with change of temperature, a special compensation may be made.

The problem which is here proposed, seems to present a condition difficult to be fulfilled. The impulse is to come at the proper moment, but the pendulum is to do no work in order to induce it. Yet it can be nothing but the pendulum itself which is to determine the moment of application; since if we possessed any independent mechanism sufficiently regular to do this, we should have no need of the pendulum. It is believed that the difficulty which this consideration presents has been overcome.

The clock which is herewith presented for the examination of the Association is one in which electricity is made to work a remontoir apparatus, by which very slight weights are made to impel the pendulum, alternately, on either side. There is nothing new in the idea of an electric clock; but there is something

sufficiently novel in a clock in which the pendulum does absolutely no work at all (not even in making battery connections), to deserve attention. There have probably been as many varieties of electric clocks as of escapement clocks-conceived, at least, if not constructed. All of these known to the writer, involve as much friction as the dead-beat escapement-most of them a great deal more-or else are otherwise objectionable. That which seems to be least so, is a contrivance described in the third volume of Becquerel's Electricity, and attributed to Mr. Vérité, in which two light balls are suspended by metallic threads to a horizontal lever oscillating on pivots placed just above the point of suspension of the pendulum. Two arms from the pendulum alternately touch these balls, closing a battery circuit by the contact. The corresponding end of the oscillating lever is thereupon depressed, relaxing the suspending thread, so that the ball presses upon the pendulum arm until the latter is carried by the swing out of its reach; when, the circuit being broken, the lever rights itself again. Ingenious as this arrangement is, the objections to it are too obvious to require enumeration. It furnishes a force which fails in the three essential requisites, perfect uniformity in quantity, uniformity in duration, and uniformity in the point of application. The suspending thread, however flexible, must interfere with the first of these conditions, and the agitation produced by the sudden tilting of the lever must affect the other two.

The construction of the clock herewith exhibited, may be explained by reference to the accompanying diagram, (see Plate,) which shows the upper portion of the pendulum rod with the contrivance employed to apply the impelling weight. Two levers are represented, marked A A' and B B'.

The first of these, from its office, is called the remontoir lever -the second, which is employed to control the first, is called the governor. The former is provided at each of its extremities with two hooks (as shown in perspective at the bottom of the diagram). These hooks are designed to carry a very light weight in the form of a small cylinder of metal. This cylinder is slightly indented in the latter at the points where it rests on the hooks, to prevent liability to displacement.

The pendulum-rod is furnished with two semicircular arms, to which, at their extremities, are attached two parallel plates of metal which pass between the hooks of the remontoir lever, and receive the weights, at the proper moments from the hooks, being also slightly notched or indented, to secure uniformity in regard to the point of application of the force.

Both the levers are pivoted in agates, their pivots being in the same horizontal line as the centre of motion of the pendulum. They are also provided with adjustable weights at their extremi

ties designed to make them tilt slowly in one direction or the other, as may be necessary in order to apply the impulse on either side of the pendulum at the proper moment.

The remontoir lever, when free from control by the other, tends to preponderate toward the right. The governor has a sufficient preponderance in the opposite direction to carry the remontoir with it, when in action, by means of a projection seen at D, which overlaps a corresponding projection on the other, as shown in perspective at the foot of the diagram. This lever in the position exhibited, is caught by a detent at D, and the remontoir lever is free to tilt toward the right, in doing which, it will carry the impulse weight of the extremity A along with it, while it will leave that at the extremity A' on the higher arm of the pendulum. In its swing toward the left, the pendulum will then be impelled by this small weight until it reaches a corresponding inclination on that side, when it will deposit the weight A' upon the hooks of the remontoir, and will take up the other upon the opposite arm.

This mechanism is so simple as to require no further explanation. It only remains to point out in what manner the levers are controlled by the electric battery.

The remontoir lever is insulated by the agates in which it turns. By a tangent spring at its axis it is put into the battery circuit. It has no other contact with the mechanism except where it is acted on by the governor; at which point insulation is also effected; and likewise through the springs shown at C and C', upon which the hooks remotest from the observer alternately rest. These springs are fixed in insulated pins to which are soldered the extremities of the enveloping wires of the magnets M and M. The pin C is connected with the magnet M', and the pin C' with the magnet M. The continuation of these wires beyond the magnets is not shown; but they are united into a single one, which, after enveloping a third magnet in the time-register (of which no drawing is given), returns to the battery.

From what has thus far been said, it would appear that the moment the hook of the remontoir lever touches either of the springs, C or C', the battery circuit would be complete. But this is not the case: for the hook in contact with the spring is insulated from the lever, and the circuit is only completed at the moment when the pendulum, in its swing, deposits the impulse weight upon the two hooks.

In the position shown, the weight A is supposed to have just been deposited. The magnet M has acted and has raised the extremity B of the governor to the detent, D. The remontoir lever will now slowly tilt, the gentle motion being necessary to prevent the impulse weight from being thrown off; and the balance weights being so adjusted as to secure the necessary

change of position within the second. A stop prevents the spring C from following the hook as it rises.

When the impulse weight A' is deposited on the hooks, it is the magnet M which acts; and the effects of this, through the bent lever pivoted at E, is to release the governor, which, by its preponderant weight will cause the remontoir to tilt again.

Whenever either magnet acts, the magnet of the time-register simultaneously acts, and advances the second-hand one division on the dial.

The remaining parts of the mechanism it is hardly necessary to describe. Adjusting screws are provided to secure the exact position of the pendulum arms, and to cause the impulse to be precisely equal in duration on opposite sides. In adjusting for this latter purpose, the graduated arc on the right, and the index attached to the remontoir lever, are employed. The manner of making the adjustment is obvious.

A pendulum impelled in this manner is subject to the action of no forces which cannot be definitely appreciated. The impelling power is constant and known. The mean resistance of the air may be computed, and even its fluctuations may, if necessary, be taken into account. The irregularities, therefore, which cannot be ascribed to these causes, must be due to imperfect compensation.

There is a possibility that a steel pendulum rod may, to some extent, be affected by the vicinity of the electro-magnets em. ployed in this contrivance. In order to guard against this danger, if it be one, the rod of the pendulum of the clock, here exhibited, is made of brass; and the compensation, which is mercurial, is adjusted accordingly.

The effect of the impelling and resisting forces acting upon a pendulum is to alter its rate of motion; but this circumstance is of no importance, so long as these forces are invariable, like gravity. If, however, any variation occurs, either in the impulse or in the resistance, the time of vibration will be altered. The kind of alteration which occurs, in consequence of a given change of arc, is not, nevertheless, the same, with pendulums impelled on different plans. The recoiling escapement, for instance, accelerates the rate for an increase of arc, while the dead beat retards it beyond the amount which would be due to circular motion, as compared with motion in the cycloid.

The remontoir escapement has the advantage that, though it accelerates the rate of going of the pendulum, it applies invariably the same amount of impelling force at every swing; so that if the pendulum had no work to do in the unlocking of the train, it would be subject to no disturbance of its regularity except such as may be consequent upon fluctuations of atmospheric

SECOND SERIES, VOL. XXVII, No. 80.-MARCH, 1859.

density, and upon changes in its own temperature. In studying experimentally the subject of compensation, it would not be difficult to eliminate the effects of the first of these causes, so as to exhibit truly the merit or defect of any given mode of compensation for the expansion and contraction of the materials of the pendulum.

The remontoir escapement does not perfectly fulfil these conditions; but it is believed that the electric clock herewith presented does so completely.

This pendulum has an additional advantage over an escapement remontoir; which arises from the fact that its arc of vibration may be reduced much lower than is at all practicable with a clock driven by a train. All the errors of the pendulum, except those arising from the varying temperature of the rod, increase with the arc. It is believed that this pendulum may be run with so small a motion as to make such errors quite insensible. The degree, moreover, to which external forces affect the rate without altering the are, is proportional to the forces themselves; and these, in the present case, must necessarily be less as the arc is less.

In order to show in what manner a pendulum of this description differs in its rate of going from one entirely free and vibrating in vacuo, we may take the ordinary differential equation of the angular motion of an oscillating body, and introduce into it terms expressing the forces which in this case are in action, besides gravity. This equation then becomes ( being the variable are, measured from the vertical, t the time of one vibration, g the force of gravity, 7 the length of the simple pendulum, m the maintaining and r the resisting forces, or rather their constant coefficients as compared with gravity).

The maintaining force, in the present case, is a weight applied at the extremity of an arm of the pendulum at the height of the centre of motion. Represent the weight by w, the length of the arm by a, and the total mass of the pendulum by M, and we have the value of m equal to

w a

Mi

The function of on which

its effect depends is obviously the cosine.

The resistance is, in this case, nothing but the atmospheric inertia, so long as the impulse lasts; after this, the maintaining weight becomes itself a resisting force, and its sign must be changed. The resistance of the atmosphere may be computed on the supposition that the velocity with which a falling body, of equal weight with the pendulum, and presenting an equal surface of resistance, ceases to be accelerated by gravity, is