the teeth cf the driver arc more curved, or a less pointed arc, than those required for a lantern pinion of the same size and number. The teeth in fig. 25 are made of a different form on the opposite sides of the line of centres CA, in order to show the difference between driving and driven or running teeth, where the number of the pinion happens to be as much as 12, so that no points are required to its teeth when driven, since with that number all the action may be after the line of centres. The great Westminster clock affords a very good illustration of this. In F - - both the striking parts the great wheel of the train and the great winding-wheel on the other end of the barrel are about the same size ; but in the train the wheel drives, and in winding the pinion drives. And there fore in the train the pinion-teeth have their points cut off, and wheel-teeth have their points on, as on the right side of fig. 25, and in the winding-wheels the converse ; and thus in both cases the action is made to take place in the way in which there is the least friction. Willis gives the following table, " derived organi cally" (i.e., by actual trial with large models), of the least numbers which will work together without any action before the line of centres, provided there are no points to the teeth of the runner, assuming them to be radial teeth, as usual:—
Fig. 25.
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Driver 54302420171514131211109 876 Runner 11 12 13 14 15 16 17 18 19 21 23 27 35 32 176
In practice it is hardly safe to leave the driven teeth without points, unless the numbers slightly exceed these ; because, if there is any irregularity in them, the square edges of those teeth would not work smoothly with the teeth of the driver. Sometimes it happens that the same wheel has to drive two pinions of different numbers. It is evident that, if both are lanterns, or both pinions with radial teeth, they cannot properly be driven by the same wheel, because they would require teeth of a different shape. It is true that on account of the greater indifference of lantern pinions to the accuracy of the teeth which are to drive them, the same wheel will drive two pinions of that kind, differing in the numbers in the ratio of even 2 to 1, with hardly any sensible shake ; but that would not be so with radial pinions, and of course it is not correct. Accordingly, in clocks with the spring remontoire, as in fig. 21, where the scape-wheel or remontoire pinion is double the size of the fly pinion, the larger one is made with radial teeth and the smaller a lantern, which makes the same wheel teeth exactly right for both. In clocks of the same construction as fig. 22, and in the West minster clock, there is a case of a different kind, which cannot be so accommodated ; for there the great wheel has to drive both the second wheel s pinion of 10 or 12, and the hour-wheel of 40 or 48; the teeth of the great wheel were therefore made to suit the lantern pinion, and those of the hour- wheel (i.e., their flanks) then depend on those of the great wheel, and they were accordingly traced by rolling a generating circle of the size of the lantern pinion on the inside of the pitch circle of the hour-wheel ; the result is a tooth thicker at the bottom than usual. These are by no means unnecessary refinements ; for if the teeth of a set of wheels are not properly shaped so as to work smoothly and regularly into each other, it increases their tendency to wear out in proportion to their inaccuracy, besides increasing the inequalities of force in the train. Sometimes turret clocks are worn out in a few years from the defects in their teeth, especially Avhen they are made of brass or soft gun-metal.
In the construction of clocks which have to raise heavy hammers it is important to obtain the best form for the cams, as pins are quite unfit for the purpose. The conditions which are most impor tant are that the action should begin at the greatest advantage, and therefore at the end of the lever, that when it ceases the face of the lever should be a tangent to the cam at both their points, and that in no part of the motion should the end of the lever scrape on the cam. In the common construction of clocks the first con dition is deviated from as far as possible, by the striking pins beginning to act at some distance from the end of the lever; and con sequently, at the time when the most force is required to lift the ham mer there is the least given, and a great deal is wasted afterwards.
The construction of curve for the cams, which is the most perfect mathematically, is that which is described in mathematical books under the name of the tractrix. But there are such practical difficulties in describing it that it is of no use. It should be observed that, in a well-known book with an appropriate name ( Camus on the Teeth of Wheels), a rule for drawing cams has been inserted by some translator, which is quite wrong. It may be proved that epicycloidal cams described as follows are so nearly of the proper mathematical form that they may be used without any sensible error. Let r be the radius of the circle or barrel on which the cams are to be set theoretically, i.e., allowing nothing tor the clearance which must be cut out afterwards, for fear the fever should scrape the back of the cams in falling ; in other words r is the radius of the pitch circle of the cams Call the length of the lever I. Then the epicycloidal cams may be traced by rolling on the pitch circle a smaller one whose diameter is Vr a + P - r Thus, if I is 4 inches and r 8 inches (which is about the proper size tor an 18-inch striking wheel with 20 cams), the radius of the tracing circle from the cams will be 0-9 inch. The advantage of cams of this kind is that they waste as little force as possible in the lift, and keep the lever acting upon them as a tangent at its point the whole way ; and the cams themselves may be of any length according 1 to the angle through which you want the lever to move ,
Most people however prefer dealing with circles, when they can instead of epicycloids ; and drawing by compasses is safer than calculating in most hands. We therefore give another rule, suggested by Mr E. J. Lawrence, a member of the horological jury in the 1851 ^Exhibition, which is easier to work, and satisfies the principal conditions stated just now, though it wastes rather more in lift than the epicycloidal curve ; and the cams must not have their points cut off, as epicycloidal ones may, to make the lever drop off sooner ; because a short cam has to be drawn with a different radius from a long one, to work a lever of any given length. But, on the other hand, the same curve for the cams will suit a lever of any length, whereas with epicycloidal cams you must take care to put the centre or axis of the lever at the exact distance from the centre of the wheel for which the curve was calculated an easy enough thing to do, of cours e, but for the usual disposition of workmen to deviate from your plans, apparently for the mere pleasure of doing wrong. It is astonishing how, by continually making one machine after another, with a little deviation each time, the thing gradually assumes a form in which you can hardly recognise your original design at all. The prevention of this kind of blundering is one of the many advantages of making machines by machinery, for which no machine offers more facilities than clocks, and yet there is none to which it is less applied.
Fig. 26.
In fig. 26 let CA be a radius of the wheel, L in the same straight line the centre of the, lever, and AB the space of one cam on the pitch circle of the cams, A being a little below the line of centres; AP is the arc of the lever. Draw a tangent to the two circles at A, and a tangent to the cam circle at B ; then T, their point of in tersection, will be the centre of the circle which is the face of the cam BP ; and TB also ?TA, which is a convenient test of the tangents being rightly drawn. The action begins at the point of the lever, and advances a little way up, but recedes again to the point, and ends with the lever as a tangent to the cam at P. The backs of the cams must be cut out rather deeper than the circle AP, but retaining the point P, to allow enough for clearance of the lever, which should fall against some fixed stop or banking on the clock-frame, before the next cam reaches it. The point of the lever must not be left quite sharp, for if it is, it will in time cut off the points of the cast-iron cams.
Oil for Clocks.
We will add a few words on the subject of oil for clocks. Olive- oil is most commonly used, sometimes purified in various ways, and sometimes not purified at all. We believe, however, that purified animal oil is better than any of the vegetable oils, as some of them are too thin, while others soon get thick and viscid. For turret clocks and common house clocks, good sperm oil is fine enough, and is probably the best. For finer work the oil requires some purifi cation. Even common neat s foot oil may be made fine and clear by the following method. Mix it with about the same quantity of water, and shake it in a large bottle, not full, until it becomes like a white soup ; then let it stand till fine oil appears at the top, which maybe skimmed ofT; it will take several months before it has all separated into water at the bottom, dirt in the middle, and fine oil at the top. And it should be done in cold weather, because heat makes some oil come out as fine, which in cold would remain among the dirty oil in the middle, and in cold weather that fine oil of hot weather will become muddy. There are various vegetable oils sold at tool-shops as oil for watches, including some for which a prize medal was awarded in the Exhibition, but not by any of the mechanical juries ; we have no information as to the test which was
