| 2 | .0944 | = | arc pitch. |
| 2 | .0934 | = | chord pitch. |
| .0010 | = | difference. |
For the 144 teeth we have
| 2 | .0944 | = | arc pitch. |
| 2 | .0937 | = | chord pitch. |
| .0007 | = | difference. |
We find, then, that the variation decreases as the size of the wheels increases, and is so small as to be of no practical consequence.
If our examples were to be put into practice, and it were actually required to make one cutter serve for wheels having, say, from 12 to 18 teeth, a greater degree of correctness would be obtained if the cutter were made to some other wheel than the smallest. But it should be made for a wheel having less than the mean diameter (within the range of 12 and 18), that is, having less than 15 teeth; because the difference between the arc and chord pitch increases as the diameter of the pitch circle increases, as already shown.
A rule for calculating the number of wheels to be cut by each cutter when the number of cutters in the set and the number of teeth in the smallest and largest wheel in the train are given is as follows:—
Rule.—Multiply the number of teeth in the smallest wheel of the train by the number of cutters it is proposed to have in the set, and divide the amount so obtained by a sum obtained as follows:—
From the number of cutters in the set subtract the number of the cutter, and to the remainder add the sum obtained by multiplying the number of the teeth in the smallest wheel of the set or train by the number of the cutter and dividing the product by the number of teeth in the largest wheel of the set or train.
Example.—I require to find how many wheels each cutter should cut, there being 8 cutters and the smallest wheel having 12 teeth, while the largest has 300.
| Number of teeth in smallest wheel. | Number of cutters in the set. | |||
| 12 | × | 8 | = | 96 |