Publisher's Synopsis
Excerpt from A New General Theory of the Teeth of Wheels
The whole subject may be condensed into one proposition in this way. Having arbitrarily prescribed the form of one toothed wheel A, and communicated to it, by any imaginable contrivance, the requi site angular velocity let a blank disc B turn alongside of A also with its appropriate motion. Trace now upon the blank surface the successive instantaneous outlines of the wheel A, and draw a curve enveloping all these traces then this enveloping curve is the form for the wheel B. In this way, whatever may have been assumed for the form of the wheel A, the delineation of the second wheel B is always geometrically possible. Having now obtained the form of B, let the wheel A be removed, and its place supplied by a blank disc and, treating B as the primary wheel, draw its traces upon the new blank the curve enveloping all these traces must clearly be a copy of the original form A. Hence the two forms A and B are conjugate, neither of them having, as it were, any claim to be regarded as the original and thus we are led to consider A and B not as derived the one from the other, but as both deduced from some datum still more elementary in its nature.
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