We now come to a point at which, if we are to keep our pendulum vibrating, we must apply power to it, evenly, accurately and in small doses. In order to do this conveniently we must store up energy by raising a weight or winding a spring and allow the weight to fall or the spring to unwind very slowly, say in thirty hours or in eight days. This brings about the necessity of changing rotary motion to reciprocating motion, and the several devices for doing this are called “escapements” in horology, each being further designated by the names of their inventors, or by some peculiarity of the devices themselves; thus, the Graham is also called the dead beat escapement; Le Paute’s is the pin wheel; Dennison’s in its various forms is called the gravity; Hooke’s is known as the recoil; Brocot’s as the visible escapement, etc.

The Mechanical Elements.—We shall understand this subject more clearly, perhaps, if we first separate these mechanical devices into their component parts and consider them, not as parts of clocks, but as various forms of levers, which they really are. This is perhaps the best place to consider the levers we are using to transmit the energy to the pendulum, as at this point we shall find a greater variety of forms of the lever than in any other place in the clock, and we shall have less difficulty in understanding the methods of calculating for time and power by a thorough preliminary understanding of leverage and the peculiarities of angular or circular motion.

If we take a bar, A, Fig. 21, and place under it a fulcrum, B, then by applying at C a given force, we shall be able to lift at D a weight whose amount will be governed by the relative distances of C and D from the fulcrum B. If the distance CB is four times that of BD, then a force of 10 pounds at C will lift 40 pounds at D, for one-fourth of the distance through which C moves, minus the power lost by friction. The reverse of this is also true; that is, it will take 40 pounds at D to exert a force of 10 pounds at C and the 10 pounds would be lifted four times as far as the 40 pound weight was depressed.

If instead of a weight we substitute other levers, Fig. 22, the result would be the same, except that we should move the other levers until the ends which were in contact slipped apart.

If we divide our lever and attach the long end to one portion of an axle, as at A, Fig. 23, and the short end to another part of it at B, the result will be the same as long as the proportions of the lever are not changed. It will still transmit power or impart motion according to the relative lengths of the two parts of the lever. The capacity of our levers, Fig. 22, will be limited by that point at which the ends of the levers will separate, because they are held at the points of the fulcrums and constrained to move in circles by the fulcrums. If we put more levers on the same axles, so spaced that another set will come into action as the first pair are disengaged, we can continue our transmission of power, Fig. 24; and if we follow this with still others until we can add no more for want of room we shall have wheels and pinions, the collection of short levers forming the pinion and the group of long levers forming the wheel, Fig. 25. Thus every wheel and pinion mounted together on an arbor are simply a collection of levers, each wheel tooth and its corresponding pinion leaf forming one lever. This explains why the force decreases and the motion increases in proportion to the relative lengths of the radii of the wheels and pinions, so that eight or ten turns of the barrel of a clock will run the escape wheel all day.

We now come to the verge or anchor, and here we have the same sort of lever in a different form; the verge wire, which presses on the pendulum rod and keeps it going is the long arm of our lever, but instead of many there is only one. The short arm of our lever is the pallet, and there are two of these. Therefore we have a form of lever in which there is one long arm and two short ones; but as the two are never acting at the same time they do not interfere with each other.

These systems of levers have another advantage, which is that one arm need not be on the opposite side of the fulcrum from the other. It may be on the same side as in the verge or at any other convenient point. This enables us to save space in arranging our trains, as such a collection of wheels and pinions is called, by placing them in any position which, on account of other facts, may seem desirable.

Peculiarities of Angular Motion.—Now our collections of levers must move in certain directions in order to be serviceable and in order to describe these things properly, we must have names for these movements so that we can convey our thoughts to each other. Let us see how they move. They will not move vertically (up or down) or horizontally (sidewise), because we have taken great pains to prevent them from doing so by confining the central bars of our levers in a fixed position by making pivots on their ends and fitting them carefully into pivot holes in the plates, so that they can move only in one plane, and that movement must be in a circular direction in that predetermined plane. Consequently we must designate any movement in terms of the portions of a circle, because that is the only way they can move.

These portions of a circle are called angles, which is a general term meaning always a portion of a circle, measured from its center; this will perhaps be plainer if we consider that whenever we want to be specific in mentioning any particular size of angle we must speak of it in degrees, minutes and seconds, which are the names of the standard parts into which a circle is divided. Now in every circle, large or small, there are 360 degrees, because a degree is ¹/360th part of a circle, and this measurement is always from its center. Consequently a degree, or any angle composed of a number of degrees, is always the same, because, being measured from its center, such measurements of any two circles will coincide as far as they go. If we draw two circles having their centers over each other at A, Fig. 26, and take a tenth part of each, we shall have 360°÷10=36°, which we shall mark out by drawing radial lines to the circumference of each circle, and we shall find this to be true; the radii of the smaller circle AB and AC will coincide with the radii AD and AE as far as they go. This is because each is the tenth part of its circle, measured from its center. Now that portion of the circumference of the circle BC will be smaller than the same portion DE of the larger circle, but each will be a tenth part of its own circle, although they are not the same size when measured by a rule on the circumference. This is a point which has bothered so many people when taking up the study of angular measurement that we have tried to make it absurdly clear. An angle never means so many feet, inches or millimeters; it always means a portion of a circle, measured from the center.

There is one feature about these angular (or circular) measurements that is of great convenience, which is that as no definite size is mentioned, but only proportionate sizes, the description of the machine described need not be changed for any size desired, as it will fit all sizes. It thus becomes a flexible term, like the fraction “one-half,” changing its size to suit the occasion. Thus, one-half of 300,000 bushels of wheat is 150,000 bushels; one-half of 10 bushels is 5 bushels; one-half of one bushel is two pecks; yet each is one-half. It is so with our angles.

There are some other terms which we shall do well to investigate before we leave the subject of angular measurements, which are the relations between the straight and curved lines we shall need to study in our drawings of the various escapements. A radius (plural radii) is a straight line drawn from the center of a circle to its circumference. A tangent is a straight line drawn outside the circumference, touching (but not cutting) it at right angles (90 degrees) to a radius drawn to the point of tangency (point where it touches the circumference). A general misunderstanding of this term (tangent) has done much to hinder a proper comprehension of the writers who have attempted to make clear the mysteries of the escapements. Its importance will be seen when we recollect that about the first thing we do in laying out an escapement is to draw tangents to the pitch circle of the escape wheel and plant our pallet center where these tangents intersect on the line of centers. They should always be drawn at right angles to the radii which mark the angles we choose for the working portion of our escape wheel. If properly drawn we shall find that the pallet arbor will then locate itself at the correct distance from the escape wheel center for any desired angle of escapement. We shall also discover that it will take a different center distance for every different angle and yet each different position will be the correct one for its angle, Fig. 27.

Because an angle is always the same, no matter how far from the center the radii defining it are carried, we are able to work conveniently with large drawing instruments on small drawings. Thus we can use an eight or ten inch protractor in laying off our angles, so as to get the degrees large enough to measure accurately, mark the degrees with dots on our paper and then draw our lines with a straight edge from the center towards the dots, as far as we wish to go. Thus we can lay off the angles on a one-inch escape wheel with a ten inch protractor more easily and correctly than if we were using a smaller instrument.

Another thing which will help us in understanding these drawings is that the effective length of a lever is its distance from the center to the working point, measured in a straight line. Thus in a pallet of a clock the distance of the pallets from the center of the pallet arbor is the effective length of that arm of the lever, no matter how it may be curved for ornament or for other reasons.

The lines and circles drawn to enable us to take the necessary measurements of angles and center distances are called “construction lines” and are generally dotted on the paper to enable us to distinguish them as lines for measurement only, while the lines which are intended to define the actual shapes of the pieces thus drawn are solid lines. By observing this distinction we are enabled to show the actual shapes of the objects and all their angular measurements clearly on the one drawing.

With these explanations the student should be able to read clearly and correctly the many drawings which follow, and we will now turn our attention to the escapements. In doing this we shall meet with a constant use of certain terms which have a peculiar and special meaning when applied to escapements.

The Lift is the amount of angular motion imparted to the verge or anchor by the teeth of the escape wheel pressing against the pallets and pushing first one and then the other out of the way, so that the escape wheel teeth may pass. According as the angular motion is more or less the “lift” is said to be greater or less; as this motion is circular, it must be expressed in degrees. The lifting planes are those surfaces which produce this motion; in clocks with pendulums the lifting planes are generally on the pallets, being those hard and smoothly polished surfaces over which the points of the escape wheel teeth slide in escaping. In lever escapements the lifting planes are frequently on the escape wheel, the pallets being merely round pins. Such an escape wheel is said to have club teeth, as distinguished from the pointed teeth used when the lifting planes are on the pallets. In the cylinder escapement the lifting planes are on the escape wheel; they are curved instead of being straight; and there is but one pallet, which is on the lip of the cylinder. In the forms of lever escapement used in watches and some clocks the lift is divided, part of the lifting planes being also on the pallets; in this case both sets of planes are shorter than if they were entirely on one or the other, but they must be long enough so that combined they will produce the requisite amount of angular motion of the pallets, so as to give the requisite impulse to the pendulum or balance.

The Drop is the amount of circular motion, measured in degrees, which the escape wheel has from the instant the tooth escapes from one pallet to that point at which it is stopped by the other pallet catching another tooth. During this period the train is running down without imparting any power to the pendulum or balance, hence the drop is entirely lost motion. We must have it, however, as it requires some time for the other pallet to move far enough within the pitch circle of the escape wheel to safely catch and stop the next tooth under all circumstances. It is the freedom and safety of the working plan of our escapement, but it is advisable to keep the drop as small as is possible with safe locking.

The Lock is also angular motion and is measured in degrees from the center of the pallet arbor. It is the distance which the pallet has moved inside of the pitch circle of the escape wheel before being struck by the escape wheel tooth. It is measured from the edge of the lifting plane to the point of the tooth where it rests on the locking face of the pallet. A safe lock is necessary in order to prevent the points of the escape wheel teeth butting against the lifting planes, stopping the clock and injuring the teeth. We want to point out that from the instant of escaping to the instant of locking we have the two parts of our escapement propelled by different and entirely separate forces and moving at different speeds. The pallets, after having given impulse to the pendulum, are controlled by the pendulum and moved by it; in the case of a heavy pendulum ball at the end of a 40-inch lever, this control is very steady, powerful and quite slow. The escape wheel, the lightest and fastest in the train, is driven by the weight or spring and moves independently of the pallets during the drop, so that safe locking is important. It should never be too deep, as it would increase the swing of the pendulum too much; this is especially true with short and light pendulums and strong mainsprings.

The Run.—After locking the pallet continues to move inward towards the escape wheel center as the pendulum continues its course, and the amount of this motion, measured in degrees from the center of the pallet arbor, is called the run.

When the escapement is properly adjusted the lifting planes are of the same length on both pallets, when they are measured in degrees of motion given to the pallet arbor. They may or may not be equal in length when measured by a rule on the faces of the pallets. There should also be an equal and safe lock on each pallet, as measured in degrees of movement of the pallet arbor. The run should also be equal.

The reason why one lifting plane may be longer than the other and still give the same amount of lift is that some escapements are constructed with unequal lockings, so that one radius is longer than the other, and this, as we explained at length in treating of angles, Fig. 26, would make a difference in the length of arc traversed by the longer arm for the same angle of motion.