Now, suppose that the pitch of the lead screw was 6 instead of 8 threads per inch, and the table will be as follows:—

6 12 18 24
18 36 54 72
6 12 18 24
17 34 51 68
6 12 18 24
16 32 48 64
6 12 18 24
15 30 45 60
6 12 18 24
14 28 42 56
6 12 18 24
13 26 39 52

Here, again, we find that in the first vertical column the denominators decrease by two for each thread less per inch, in the second column they decrease by three, and in the third by four; this decrease equalling the number the first fraction was multiplied by.

But suppose the lead screw pitch is an odd one, as, say, 3 threads per inch, and we construct the table as before, thus—

Pitch of lead screw3 6 9 12 15
Pitch to be cut18 32 54 72 90

Now it is useless to multiply by 2 or by 3, because they give a less number of teeth than the smallest wheel should have, hence the first multiplier should be 4, giving the following table:—

3 12 15 18
18 72 90 108
3 12 15 18
17 68 85 102
3 12 15 18
16 64 80 96
3 12 15 18
15 60 75 90

By continuing the table for other pitches we shall find that in the first vertical column the denominators diminish by 4, the second column by 5, and the third by 6; and it is seen that by diminishing the pitch of the lead screw, we have rendered necessary one of two things, which is, that either larger wheels containing more teeth must be used, or the change gears must be compounded.

Assuming that the pitch of the lead screw was 5 per inch, the table would be as follows:—

5 × 3 = 15 20 25
1854 72 90
5„15 20 25
1751 68 85
5„15 20 25
1648 64 80