The teeth of wheels for watches and clocks need particular care in shaping, and it may be of interest if I describe briefly the principles upon which these wheels are made. What is required is that the motion shall not be communicated by jerks as the teeth successively engage one another, but that the motion shall be perfectly smooth. The problem therefore becomes this: How are we to arrange the teeth of the wheels so that as one of them turns and drives the other round the leverage or turning power exercised by the driving wheel on the driven wheel shall always be uniform? Now if the teeth were simple spikes one can easily see that this would not be the case. For instance, as the arm a c turned round, driving before it the arm b d, the point c would scrape along, and the leverage between the two teeth would constantly alter. Evidently some other construction must be adopted. Before we can determine what it is to be, we must inquire what the leverage would be between two rods, a c and d b, mounted on pivots at a and d. The answer to this question is, that when a lever such as a c presses with its end against another, d b, the power is exercised in a direction c e at right angles to d b. Hence the leverage between the two arms is in the ratio of a e to d c. The system is just as if we had a lever a e united to a lever d c by a rigid rod e c at right angles to both of them.
Whence then the ratio of the power is as a e is to d c.
But since the triangles a e f, d c f, are similar, a e is to d c as a f to f d. Whence then we get this general proposition: If one body mounted on an axis is pressing upon another body mounted on an axis, the pressure exerted between them is always exercised in a direction, shown by the dotted line, at right angles to the two surfaces in contact; and the ratio of the leverage is found by drawing a line from one axis to the other, so as to cut the line of direction of pressure in f. The leverage of one on the other is then as a f to f d. Our problem has now become the following: Given a rod b d, suppose that it is pressed upon by a curved surface mounted on an axis at a. Then the direction of the pressure that the curved surface (called in engineering language a cam) will exercise on the rod b d is shown by the dotted line; and the ratio of the driving power to the driven power is as d f to a f. Now how can we shape the cam so that as it moves round, and different parts of its surface come successively into contact with b c, the ratio of the leverage is always the same; that is to say, the ratio of a f to f d shall always be constant; that is to say, the line drawn through the point of contact perpendicular to the curve at that point, shall always pass through the point f?
Evidently, if this is to be so, the point d must be on a semicircle, whose diameter is f b, for in that case the angle f d b will always be a right angle.
The surface must then be so arranged that, whatever be the position of the cam and of the rod b d, the point of contact between them must always be on the semicircle f c d; that is to say, as the cam moves round the axis a its shape must be such that a line drawn from f to the point where it cuts the circle f d b is always perpendicular to the curve.
Now suppose that we move a circle whose centre is at a, and radius a f, so as to roll the circle f d b by simple surface friction round its centre o, then any point d on it would mark out a curve on a piece of paper attached to the moving circle whose centre is at a, and the direction of motion of the curve would always be such that the point d on it would at any instant be describing a circle round f, and the direction of the curve would thus at any point always be at right angles to the line d f for the time being.
This curve, caused by the rolling of one circle on another, is called an epicycloid. Hence, then, for a clock, if we make the pinion wheel with straight spokes and the driving wheel with its teeth cut in the form of epicycloids, caused by rolling a circle with a diameter equal to the radius of the pinion upon the driving wheel, we shall get a uniform ratio of leverage one upon the other.
The circles with radii a f, b f, are called the “pitch circles,” and these radii are in the ratio of the movement that is required for the wheels, usually six to one or eight to one, as the case may be. The sides of the teeth of the pinion wheels are straight lines radiating from the centre, and rounded off at the ends so as to avoid accidental jambing. The teeth of the cogwheel have epicycloidal sides. The tips are cut off so as to be out of the way, and spaces are left between them for the width of the leaves of the pinion wheel.
Both pinion wheels and cogwheels are cut by cutters rotating at a high speed, about 3,500 times in a minute, the cutters being carefully shaped for the pinion wheels with straight edges, for the cogwheel in epicycloids. It is a pretty thing to see a wheel-cutting engine at work, the cutter flying round with a hum, cutting the rim of a brass wheel into teeth, the brass coming off in flakes thinner than fine hairs and falling in fine dust. When a tooth is cut, the wheel is moved round one division of an apparatus called a “dividing plate,” so as to present a new part of the wheel to the cutter. Of course, the cutter and wheels must all be properly proportioned. Cutters are sold in sets duly shaped for the work they have to do. Wheel-cutting is a special branch of the clockmaking industry. The reason the speed of cutting is so high is because it is desired to take off small portions of metal at a time, and thus not strain the wheel and the cutting machinery. If bigger cuts were made, then the machine would have to go slower, for it is a principle in the construction of cutting machinery that the speed of the cut must always be proportioned to the depth of it. If you want to take deep cuts you must move the cutting edge slowly, and vice versâ. The most modern method of making cogwheels of brass, and the best, is to stamp them out of solid sheet metal at a single punch of a punching machine, and cheap watches are always made in this way. In fact, the whole method of watch and clock-making is undergoing a transformation.
Before the time of the great engineering development which took place towards the end of the eighteenth century, the making of machines was a sort of fine art. Cogwheels were cut by hand. The circumference was marked out by means of compasses. Then holes were drilled round the rim, and teeth cut out leading into them, and shaped by means of special files constructed for the purpose (Fig. 82). Big machinery was all shaped out at the forge and by the file. The engineers complained that you could not get big work made true even to the eighth of an inch. But watches and clocks were beautifully made, though only at the cost of hours of patient measuring and filing. The taste for ornament still existed. The wheels and backs of watches were chased over with the most beautiful patterns; the frames of the clocks were wrought into beautiful figures and forms. Even astronomical instruments were embellished.
Then came the era of severe accuracy. Men of science took the government of machine-making whose feelings were repugnant to art in any form. They hated to see any effort expended in ornament. With severely utilitarian aims, they banished all appearance of beauty from instruments and tools of all sorts, so that our modern machines, from a steam engine down to a watch, are now models of precise but perfectly unornamented workmanship. They are the fitting implements of a nation that wears trousers and tall hats. One has only to compare an old vessel of war, with its sculptured prow and streamers, with a modern ironclad to take note of the difference. The art of ornamentation is now little more than a spasmodic imitation of the past, with a historical interest only. As a living entity it has almost ceased to exist.
But in precision of manufacture the present age is without a rival in the history of the world. People believe no longer in the old methods of scraping and filing, and hand-work directly exercised on metal is rapidly falling into desuetude. It is possible, of course, with a file and scraper and days of labour to get two flat surfaces of metal so perfect that when put together one will lift the other like a sucker on a stone, but it is waste labour. A small machine will do it as well in a few minutes. No longer is a watch built up as one would build a house, fitting part to part. By expensive machines thousands of watch parts are stamped and cut out to pattern, and then a watch is made by taking one of each indiscriminately and just putting them into their places. Comparatively unskilled workmen can do this. Where the skill is wanted is to design and make the machinery and watch the cutters, measuring them with microscopic gauges from time to time, and at once remedying them if an edge is found to be a ten-thousandth part of an inch out of place. So that the labour of man is becoming more and more a labour of design and of supervision. Machines are the slaves that do the work, for in a good machine we have an eye and an arm that never tires, and only needs to be kept in working order. But machines are not artistic, and thus art is lost while precision is gained. At present a desperate attempt is being made to supply by means of machinery the craving of the human mind for art. But it is destined to failure. Art of this kind is generally produced by the same brain that designs machines, and therefore presents an appearance of rigid accuracy and uniformity, which, while essential to an engine, is out of place in an artistic product.
The great manufacturers of our Midlands do not seem to understand that there is no object in making a towel-horse as geometrically accurate as a turning lathe. It will apparently be years before they learn to put art and precision each in the place where it is wanted—precision in the works of the watch, art in the face and the case of it; machine work in the inside of a watch, hand work on the outside. When the public taste is educated so as to see the odious character of the jumble of Gothic, Egyptian, and meaningless ornament on such an article as the case of an American organ, one step will have been made towards the revival of artistic taste.
But to propose as a means of reviving art that we should discontinue the use of machinery or abandon our modern cutters of precision to go back to a hack-saw and file is ridiculous, and could only be suggested by men quite destitute of scientific ideas. Art and precision each has its place: there is room for both; let neither intrude on the domain of the other.