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§ 1. FOr the exact and easie moving of the Wheels and Pinions to∣gether, it is necessary that they should fit each other, by having their teeth and leaves of the same wideness, or near of the same wideness. For many do make
the Leaves of the Pinion narrower than the Teeth of its Wheel, by reason of their running deep in each other; which is as if the Diameters of the Wheel and Pinion were less. But this I leave to those, whose practice and observations are great∣er than mine in these matters.
§ 2. To make the Teeth of a Wheel and Pinion alike, the way Arithmetically is thus, First you must find the Circumfe∣rence of your Wheel and Pinion; which you may best do by the Rule of Three (so often made use of before) the Rule is thus, as 7 is to 22:: so is the Diameter to the Circumference. Or more exactly thus, as 1, is to 3, 1416:: So Diam. to Circum.
Suppose you have a Wheel of 2 inches diameter, and 60 Teeth, and would fit to it a Pinion of 6 Leaves. First 7 22:: 2. 6, 3. The circumference of the Wheel, is then 6 inches, and 3 tenths of an inch. Then say, as the Teeth of the Wheel, to the cir∣cumference * 1.1of it:: So are the Leaves of the Pinion, to the circumference thereof. In numbers thus 60▪ 6, 3:: 6▪, 63. The Pinion then is 63 hundredth parts of an inch round.
Now to find the Diameter, 'tis but the reverse of the former Rule, viz. As 22. to 7:: So the Circumference to the Diame∣ter. In numbers thus, for the foregoing Pinion, 22. 7::, 63▪ 2, The Diameter then of the Pinion must be two tenths of an inch, to fit the aforesaid Wheel of 2 inches diameter.
sect 3. But because this way may be diffi∣cult to persons unacquainted with Deci∣mal Arithmetick, which is very necessary here; therefore I shall set down a way to do it mechanically. Having drawn a Circle, divide it into as many parts, as you in∣tend leaves in the Pinion you would size. From two of these points in the Circle, draw two lines to the Center: to which apply two of the Teeth of your Wheel, guiding them up and down until they touch at the same width on these Radii. Mark where this agreement is, and a small circle drawn there, will represent the circumference of the Pinion sought af∣ter.
Sir J. Moor Mat. Com. R. 5.