ADVERTISEMENT TO THE APPENDIX.

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 proposi tions 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, APRIL 5, 1808.

APPENDIX.

A PRACTICAL INQUIRY RESPECTING THE STRENGTH AND DURABILITY OF THE TEETH OF WHEELS

USED IN MILLWORK.

73. 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 approximation 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 perfect, is better in all cases, than to have no guide whatever.

And it is too evident to require proof, that it is essential to the beauty and utility of any machine, that the strength and bulk of its several parts, be duly proportioned to the stress or wear to which the parts may be subject.

Some general observations on the wheel work of mills, will serve greatly to simplify our inquiries on the subject.

General Observations on the Wheel Work of Mills.

74. Mistaken attempts at economy have. often prompted the use of wheels of too small diameter. This is an evil which ought carefully to be avoided. Knowing the pressure on the teeth, we cannot with propriety reduce the diameter of a wheel below a certain measure.

Suppose, for instance, a water wheel of 20 horses' power, moving at the pitch line with a velocity of 3 ft. per second. It is known, that a pinion of 4 feet diameter, might work into it, without impropriety; but we also know, that it would be exceedingly improper to substitute a pinion of only one foot diameter, although the pressure and velocity at the pitch lines in both cases would be, in a certain sense, the same. In the case of the small pinion, however, a much greater stress would be thrown on the journeys, (or journals) of the shaft. Not, indeed, on account of torsion or twist, but on account of transverse strain, arising, as well from greater direct pressure, as from the tendency which the oblique action of the teeth, particularly when somewhat worn, would have to produce great friction, and to force the pinion from the wheel, and make it bear harder on the journals. The small pinion is also evidently liable to wear much faster, on account of the more frequent recurrence of the friction of each particular tooth.

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