tion of some of the foreign ones on above 40 small bells, which were added for that purpose to the eight of the peal; but they are not successful, and it is stated in Sir E. Beckett's book on clocks and bells, that he warned them that the large and small bells would not harmonize, though either might be used separately. Other persons have attempted chimes on hemispherical bells, like those of house clocks; but they also are a failure for external bells to be heard at a distance. This however belongs rather to the subject of bells; and we must refer to that book for all practical information about them.
Teeth of Wheels.
Before explaining the construction of the largest clock in the world it is necessary to consider the shape of wheel teeth suitable for different purposes, and also of the cams requisite to raise heavy hammers, which had been too much neglected by clockmakers previously. At the same time we are not going to write a treatise on all the branches of the important subject of wheel-cutting; but, assuming a knowledge of the general principles of it, to apply them to the points chiefly involved in clock-making. The most comprehensive mathematical view of it is perhaps to be found in a paper by the astronomer royal in the Cambridge Transactions many years ago, which is further expanded in Professor Willis's Principles of Mechanism. Respecting the latter book, however, we should advise the reader to be content with the mathematical rules there given, which are very simple, without attending much to those of the odontograph, which seem to give not less but more trouble than the mathematical, and are only approximate after all, and also do not explain themselves, or convey any knowledge of the principle to those who use them.
For all wheels that are to work together, the first thing to do is to fix the geometrical, or primitive, or pitch circles of the two wheels, i.e., the two circles which, if they rolled perfectly together, would give the velocity-ratio you want. Draw a straight line joining the two centres; then the action which takes place between any two teeth as they are approaching that line is said to be before the line of centres; and the action while they are separating is said to be after the line of centres. Now, with a view to reduce the friction, it is essential to have as little action before the line of centres as you can; for if you make any rude sketch, on a large scale, of a pair of wheels acting together, and serrate the edges of the teeth (which is an exaggeration of the roughness which produces friction), you will see that the further the contact begins before the line of centres, the more the serration will interfere with the motion, and that at a certain distance no force whatever could drive the wheels, but would only jam the teeth faster; and you will see also that this can not happen after the line of centres. But with pinions of the numbers generally used in clocks you cannot always get rid of action before the line of centres; for it may be proved (but the proof is too long to give here), that if a pinion has less than 11 leaves, no wheel of any number of teeth can drive it without some action before the line of centres. And generally it may be stated that the greater the number of teeth the less friction there will be, as indeed is evident enough from considering that if the teeth were infinite in number, and infinitesimal in size, there would be no friction at all, but simple rolling of one pitch circle on the other. And since in clock-work the wheels always drive the pinions, except the hour pinion in the dial work, and the winding pinions in large clocks, it has long been recognized as important to have high numbered pinions, except where there is a train remontoire, or a gravity escapement, to obviate that necessity.
And with regard to this matter, the art of clock-making has in one sense retrograded; for the pinions which are now almost universally used in English and French clocks are of a worse form than those of several centuries ago, to which we have several times alluded under the name of lantern pinions, so called from their resembling a lantern with upright ribs. A sketch of one, with a cross section on a large scale, is given at fig. 24. Now it is a property of these pinions, that when they are driven, the action begins just when the centre of the pin is on the line of centres, however few the pins may be; and thus the action of a lantern pinion of 6 is about equal to that of a leaved pinion of 10; and indeed, for some reason or other, it appears in practice to be even better, possibly from the teeth of the wheel not requiring to be cut so accurately, and from the pinion never getting clogged with dirt. Certainly the running of the American clocks, which all have these pinions, is remarkably smooth, and they require a much smaller going weight than English clocks; and the same may be said of the common "Dutch," i.e., German clocks. It should be understood, however, that as the action upon these pinions is all after the line of centres when they are driven, it will be all before the line of centres if they drive, and therefore they are not suitable for that purpose. In some of the French clocks in the 1851 Exhibition they were wrongly used, not only for the train, but for winding pinions; and some of them also had the pins not fixed in the lantern, but rolling,—a very useless refinement, and considerably diminishing the strength of the pinion. For it is one of the advantages of lantern pinions with fixed pins, that they are very strong, and there is no risk of their being broken in hardening, as there is with common pinions.
The fundamental rule for the tracing of teeth, though very simple, is not so well known as it ought to be, and therefore we will give it, premising that so much of a tooth as lies within the pitch circle of the wheel is called its root or flank, and the part beyond the pitch circle is called the point, or the curve, or the addendum; and moreover, that before the line of centres the action is always between the flanks of the driver and the points of the driven wheel or runner (as it may be called, more appropriately than the usual term follower); and after the line of centres, the action is always between the points of the driver and the flanks of the runner. Consequently, if there is no action before the line of centres, no points are required for the teeth of the runner.
Fig. 23.
In fig. 23, let AQX be the pitch circle of the runner, and ARY that of the driver; and let GAP be any curve whatever of smaller curvature than AQX (of course a circle is always the kind of curve used); and QP the curve which is traced out by any point P in the gene rating circle GAP, as it rolls in the pitch circle AQX; and again let HP be the curve traced by the point P, as the generating circle GAP is rolled on the pitch circle ARY; then RP will be the form of the point of a tooth on the driver ARY, which will drive with uniform and proper motion the flank QP of the runner; though hot without some friction, because that can only be done with involute teeth, which are traced in a different way, and are subject to other conditions, rendering them practically useless for machinery, as may be seen in Professor Willis's book. If the motion is reversed, so that the runner becomes the driver, then the flank QP is of the proper form to drive the point RP, if any action has to take place before the line of centres.
And again, any generating curve, not even necessarily the same as before, may be used to trace the flanks of the driver and the points of the runner, by being rolled within the circle ARY, and on the circle AQX.
Now then, to apply this rule to particular cases. Suppose the generating circle is the same as the pitch circle of the driven pinion itself, it evidently can not roll at all; and the tooth of the pinion is represented by the mere point P on the circumference of the pitch circle; and the tooth to drive it will be simply an epicycloid traced by rolling the pitch circle of the pinion on that of the wheel. And we know that in that case there is no action before the line of centres, and no necessity for any flanks on the teeth of the driver. But in asmuch as the pins of a lantern pinion must have some thickness, and cannot be mere lines, a further process is necessary to get the exact form of the teeth; thus if RP, fig. 24, is the tooth that would drive a pinion with pins of no sensible thickness, the tooth to drive a pin of the thickness 2Pp must have the width Pp or Rr gauged off it all round. This, in fact, brings it very nearly to a smaller tooth traced with the same generating circle; and therefore in practice this mode of construction is not much adhered to, and the teeth are made of the same shape, only thinner, as if the pins of the pinion had no thickness. Of course they should be thin enough to allow a little shake, or "back-lash," but in clock-work the backs of the teeth never come in contact at all.
Fig. 24.—Lantern Pinion.
Next suppose the generating circle to be half the size of the pitch circle of the pinion. The curve, or hypocycloid, traced by rolling this within the pinion, is no other than the diameter of the pinion; and consequently the flanks of the pinion teeth will be merely radii of it, and such teeth or leaves are called radial teeth; and they are far the most common; indeed, no others are ever made (except lanterns) for clock-work. The corresponding epicyeloidal points of
