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_? [Illustration: FIG. 77.] [Illustration: FIG. 78.] 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. [Illustration: FIG. 79.] 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. [Illustration: FIG. 80.] 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.