F

Rule to determine the length of the teeth of

Wheels.

Perpendicular to the line of centres CD, draw the line A B, a tangent to the

pitch lines. Take half the pitch, that is, half the distance between the centres of two adjoining teeth, within a pair of compasses, setting their points upon the pitch lines, E and F, parallel with the line of centres CD, draw the line ab, and where that is cut by the line AB, at c, gives the points of the teeth of wheel and pinion.

OBSERVATIONS.

On this rule, I beg leave to remark, that it does not seem to me to be founded on any satisfactory principle; were the pinion, at all times, the conductor, I should not perhaps differ from Mr. Murray, because the action of the teeth would be, in that case, generally after their arrival at the line of centres.

But in case the wheel were the conductor, the action of the teeth would generally be almost entirely in approaching the line of centres.

K

The evils arising from this mode of action, I have already, I hope, clearly proved, (see p. 50) it is therefore unnecessary here to repeat them.

When the wheel and pinion are nearly of the same diameters, as in p. 72, the effects are not so obvious as when the pinion is much smaller than the wheel, as in p. 75.

OF THE INTERNAL PINION.

14. When a pinion is to act internally, as in the figure, p.76, it is evident, that the teeth may be formed on the principles already laid down, with this difference only, that the epicycloid.generated by the proportional circle of the pinion upon that of the wheel, should be an interior epicycloid.

The internal pinion may be adopted in many cases with advantage, as it has less friction than the external one.

E

To illustrate this, (See Fig. p. 77) let A be the pitch line of a wheel, B that of an internal pinion, and c that of an external pinion.

Suppose the circle A, to be moved till the point a arrives at b, and that the points c, d, in the circles B, C, have both moved over a space equal to a, b. Now it is evident, that the distance from c to b, is