0.5592 will be the number on the 2⁄3rd line, which is greater than 0.5500, and 0.5049 will be the one which is less than 0.5500. The position of the intermediate column, corresponding to the length of belt of the present example, may now be found, as before, briefly. It is:
| 0.5592 | - | 0.5500 | = | 0.0092 | = | 0.17. |
| 0.5592 | - | 0.5049 | = | 0.0543 |
Consequently the required column lies nearest column 13, 17⁄100th way between columns 13 and 12. To find any other number in the required column, we have only to multiply the difference between two adjacent numbers of columns 13 and 12 by 17⁄100, and subtract the product from the number in column 13. For example, to find the diameter of the partner to the 18 in. step of cone a, we find the numbers 0.4750 and 0.4177 of columns 13 and 12, which lie on the horizontal line corresponding to 18⁄60 = 0.30; the difference, 0.0573, between the two numbers is multiplied by 0.17, and the product, 0.0573 × 0.17 = 0.0097, subtracted from 0.4750. This last difference will equal 0.4653, and will be the number sought. If we now multiply by 60, we will get 27.92 in. as the effective diameter of that step on cone b which is the partner to the 18 in. step of cone a.
To find the companion of the 24 in. step, we proceed after the same fashion; the horizontal line 24⁄60 = 0.40 lies 1⁄3rd way between 0.39 and 0.42; hence,
In column 13, 0.3900 - 1⁄3(0.3900 - 0.3594) = 0.3798;
In column 12, 0.3294 - 1⁄3(0.3294 - 0.2975) = 0.3188;
And 0.3798 - (0.3798 - 0.3188) × 0.17 = 0.3694.
The required effective diameter of the step, which is partner to the 24 in. step, will therefore be 0.3694 × 60 = 22.16 in.
In like manner we obtain partner for the 30 in. step, thus:
In column 13, 0.2944 - 2⁄3(0.2944 - 0.2600) = 0.2715.