Subsequently to the reading of the above paper, I had occasion to execute many wheels on this principle; and their appearance, and use, excited on the one hand much interest, and on the other much opposition. I had even to complain of real injury in that contest: against which I defended myself with a warmth that I thought proportionate to the attack.—But all this was local and temporary: and writing now for a more enlarged sphere, and perhaps for a more extended period, I feel inclined to lay aside every consideration, but those immediately connected with the influence of this work on the public prosperity. I shall therefore avoid all reference to the names either of my friends or my opponents. My friends will live in a grateful heart, as long as memory itself shall last; my enemies, if I have any, will be forgiven—or, at worst, forgotten; and my System is henceforward left to wind its way into public notice and usefulness, by its own intrinsic merits.
Certain Observations which I was induced to make on occasion of a re-print of the above Memoir, may assist in introducing what remains to be said on the subject. They commence thus:
The foregoing little work, which first brought this subject into public notice in this town, was not the only method employed to develope its principles, and urge its adoption. A second paper was read, at the next meeting of the society, and some time after, a third, at the Exchange Dining Room; on both which occasions new modes of reasoning were pursued, and new kinds of proof adduced. On the first, a model was exhibited of two screw-formed teeth (connected with proper centres) exactly like those represented in [fig. 6]; by the action of which on each other, it became manifest that teeth of this angular shape do work together without inconvenience, and therefore, that all sensible friction is, in this case, done away.
On the latter occasion (the lecture at the Exchange) two other methods were brought forward, to corroborate the principles before stated: (see [Plate 14], [fig. 1].) The first was a kind of transparency, in which a line of light represented the place of contact of two wheels working together; by the partial and variable obscuration of which, the successive action of every portion of the teeth was clearly shewn. The second method consisted of two pair of wheels, made from loaf sugar, the teeth of which were cut one pair in the usual form, and the other on the new principle. Here, the difference in the effects of the two methods was so great, that the common teeth were almost immediately worn or broken down, by the very same kind of impulse that the new wheels sustained without injury: and with a loss of matter almost imperceptible, since many thousand revolutions of the wheels took place without detaching so many grains of sugar!
These Observations include likewise the following remarks:
In adverting to a few of the difficulties we have encountered, it will appear curious that one of them should spring from a most useful property of the system: but the paradox is thus explained. As there is no method more effectual for giving the teeth a perfect form, than working the wheels together, (covering them with an abrasive substance) we have most frequently chosen to depend on that important property; and have therefore set the wheels at work as they came from the foundry, instead of chipping the teeth, as is usual when common wheels are expected to act well in the first instance. But our wheels being then full of asperities, their action would be of course imperfect and noisy, till time had smoothed and equalized the touching surfaces: a state of things that might well stagger the opinion of a candid observer unacquainted with the system. Happily however we can now appeal to the fact of many wheels having become silent, that were once referred to with triumph, as proofs of a radical defect in the principle. It may not be improper to add here, that if highly finished wheels were particularly desired, we would engage to cut them in metal on this principle, with all the perfection of surface given to common wheels by the first masters.
In the use of bevel wheels of this description (with singly inclined teeth) there is doubtless a tendency to approach toward or recede from each other; the extent of which (for cylindrical wheels) has been already determined. This tendency goes, so far, to give a bend to the shaft; and, if this be very weak, to create a degree of friction on the teeth as the wheels revolve. It is therefore desirable that the shafts should be rather too strong than too weak; since the principle can only exist entire, when the wheels in working, are kept in the same planes which they occupy when at rest. This is too evident to be further insisted on.