proposed direction with respect to each other, when the wheels are in action. Parallel to A B, and at the distance of half the proportional diameter of the wheel, draw the line D E. In the same manner, draw FD at the distance of half the proportional diameter of the pinion from A C. From the point D, where these lines intersect, draw the line DG, perpendicular to A B, and also the line D H, perpendicular to CA. Make G I equal to ID, and K H equal to K D. Then D G is what we shall call the principal diameter, or the diameter at the pitch line of the wheel, and DH that of the pinion.

Join G A, D A, HA. Then G A D, is the outline of the proportional cone of the wheel, and DA H, that of the pinion.

Now proceed to draw the teeth of the wheel. With the distance, GA, from A, as a centre, sweep a small arc, such as G a; at the principal diameter to their extre

mity, set off the length of the teeth, from G. to b, and draw bc tending to A.

The line bc represents the breadth of the teeth, which, according to circumstances, may be more or less; only it is to be observed, that if continued to the point A, the teeth near that point would be so small as to be of little or no use.

Describe the arc ce, concentric to b a ;* and from G to f, set off part of the required length of the tooth, from the principal diameter to the root: then draw f g tending to A, the line f g becomes the root of the tooth. Parallel to fg, draw a e, then af ge, represents the section of the solid ring of the wheel. The particular direction of the line a e is no way essential; all that is necessary is, that the ring be of sufficient

* In practice, it is found easier, and sufficiently accurate, to use, instead of these curves, straight lines, as near as may be, in the same direction with the

curves.

H

strength for the purpose to which it is to be applied but patterns for cast iron wheels are usually made as represented in the plate.

Having thus drawn a section of a tooth at G, draw in the same manner one at D, then D, I, G, L, will be the section of the wheel, in which e, h, i, L, a, represent the space occupied by the arms. The dimensions of these, and their particular form, may however be varied according to cir

cumstances.

The mode of drawing the section of this pinion will now be obvious, by inspecting the figure, where it will be observed, that the teeth of the pinion are made a little broader than those of the wheel. This is a practice generally followed, as the teeth by this means wear more equally than otherwise they would.

[A. 43.] For the use of young mechanics, I will, in these additions, attempt to free the principles of constructing bevelled wheels of part of their intricacy, first briefly noticing the old principles.

The teeth of bevelled wheels, for moving

one another uniformly, may be formed according to different principles. Those which have been delivered, are, first, When the wheel drives the pinion, the acting faces of the teeth of the wheel, should be portions of a spherical epicycloid, generated by the revolution of a cone, (as described in Art. 43, Fig. 33.) of which the base is half the diameter of the pinion, and the teeth of the pinion plane surfaces directed to its centre. (Camus on the Teeth of Wheels, art. 569.

Ency. vol. xiii. p. 575.)

Brewster, Edin.

Second, If the teeth of the pinion be staves, or formed to act as staves, then, when the wheel drives the pinion, the acting faces of the teeth of the wheel should be portions of a curve parallel to a spherical epicycloid, generated by the revolution of a cone, of which the base is equal to the diameter of the pinion. (Camus, art. 560. Brewster, Edin. Ency. vol xiii. p. 575.) To these a third may be added, that is, When the pinion drives the wheel, the most advantageous form for the acting faces of the teeth of the pinion, will