then the fraction .0020⁄.00506 = 0.04 nearly will represent the position of the required intermediate column; namely, that its distance from column 16 is about 4⁄100 of the distance between the adjacent columns, 15 and 16.
To find other numbers in this intermediate column we have only to multiply the difference between the adjacent numbers of columns 16 and 15 by 0.04, and subtract the product from the number in column 16. But it is not necessary to find as many numbers of the intermediate columns as are contained in either of the adjacent columns; it is only necessary to find as many numbers as there are steps in each of the cone pulleys. We will now illustrate what has preceded, by finding the partner to the 12 in. step of cone a. Find, as before, the horizontal line corresponding to 12⁄40 = 0.30, then take the difference between the numbers 0.6413 and 0.5867 of columns 16 and 15, and multiply this difference, 0.0546, by 0.04; this product = 0.0022 subtracted from 0.6413, will give 0.6391, a number of the intermediate columns corresponding to the length of belt of the present problem. Multiplying by the distance between the axes = 40 in. we get 0.6391 × 40 = 25.56, for the diameter of the step of cone b which is partner to the 12 in. step of cone a.
To find the companion to the 18 in. step, we proceed in the same manner, looking for the horizontal line 18⁄40 = 0.45, and interpolating as follows:
0.5094 - (0.5094 - 0.4500) × 0.04 = 0.5070.
Consequently, 0.5070 × 40 in. = 20.28 in. will be the required partner of the 18 in. step.
In like manner, for the 24 in. step, we have
0.3500 - (0.3500 - 0.2840) × 0.04 = 0.3474, and 0.3474 × 40 = 13.90.
The effective diameters are therefore
| 6 | in. | 12 | in. | 18 | in. | 24 | in. | on cone | A. | |||
| 30 | 25 | .56 | 20 | .28 | 13 | .9 | „ | B. |
The actual diameters, when thickness of belt = 0.20 in., are: