the base is a circle, and which ends in a

point.

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66

14. Velocity is equivalent to speed.

15. Mr. Smeaton thus defines the term power: “The word power, as used in practical mechanics, I apprehend to signify the exertion of strength, gravitation, impulse, or pressure, compound"ed with motion, to be capable of producing an effect; and that no effect is

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properly mechanical, but what requires “ such a kind of power to produce it.”

16. A proposition is a sentence in which any thing is affirmed.

17. A corollary is an inference or deduction.

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POSTSCRIPT.

I HAD almost despaired of seeing the preceding Essay in print; when after being about eighteen months in the press, I was at last informed that it was nearly all printed off, and that I might have the opportunity of making any additions that might occur. I do not think, that I can here express myself better than in the words of Professor Leslie, which he uses on a similar occasion.

"My distance from the press, besides occasioning other inconveniences, had prevented me from bestowing the degree of correction which I was solicitous to attain. Some mistakes of a more important kind may have escaped notice, which I should probably have rectified, if the impression had been more immediately under my command."*

I, however, have much satisfaction in ac

*Leslie's Experiments on Heat, p. 9.

knowledging, that on this occasion, I have possessed one very great advantage. Dr. Young (of whose merits, as a mechanician and philosopher, it were superfluous for me to speak),, was so very obliging as to examine most of the sheets as they came from the press. Having long had it in contemplation, to make a collection of facts respecting wheels actually in use in millwork, and by arranging them, to endeavour to draw some useful practical inferences, I take the present opportunity of offering to the public the hints on that subject, which may be found in the following Appendix.

I could have wished, that time and other circumstances had allowed me to have entered more minutely into the subject. Yet hoping, that these hints, even in their present state, may lead to a fuller investigation, I trust, they will not be altogether without some advantage. As, I believe, nothing exactly of the same kind, has hitherto been published, it is hoped, that these observations will be received by the public with indulgence and due allowance for their unavoidable imperfections.

With respect to the elementary propositions which we have to guide us in this inquiry into the proportional strength of the teeth of wheels, I shall not enter into their demonstrations. To the artisan, unacquainted with mathematics, they would be unintelligible; and the mathematician can either demonstrate them himself, or have recourse to those elementary writings where the demonstrations may be found: of these last, as being more generally accessible, I have referred to "Emerson's Mechanics," quarto edition.

Glasgow,

5th April, 1808.

APPENDIX.

A PRACTICAL INQUIRY RESPECTING THE STRENGTH AND DURABILITY OF THE

TEETH OF WHEELS USED IN MILLWORK,

HAVING treated of the forms of the teeth of wheels, I come now to consider their proportional strength with relation to the resistance they have to overcome.

I am aware, that owing to a great variety of circumstances, this subject is involved in much difficulty, and that it is no easy task to form any general rule with regard to the pitches and breadths of the teeth of wheels. I do not pretend to more than a mere ap proximation towards general rules; yet, were this judiciously done, I am of opinion, that it might be useful to the millwright, who has not had leisure or opportunity for scientific inquiries. A rule, though not absolutely per