Each of these differences is subtracted from the larger diameter of the two adjacent steps to which it corresponds, thus:
| 17.50 | = | 1st | step. | |||||
| Difference of | 1st | and | 2nd | = | 2.37 | |||
| 15.13 | = | 2nd | „ | |||||
| „ | 2nd | „ | 3rd | = | 2.43 | |||
| 12.70 | = | 3rd | „ | |||||
| „ | 3rd | „ | 4th | = | 2.50 | |||
| 10.20 | = | 4th | „ | |||||
| „ | 4th | „ | 5th | = | 2.57 | |||
| 7.63 | = | 5th | „ | |||||
| „ | 5th | „ | 6th | = | 2.63 | |||
| 5.00 | = | 6th | „ | |||||
Example 2. If we suppose the same conditions as in Example 1, with the exception that each cone is to have four steps instead of six, the largest diameter will, in this case, equal 121⁄2 in. and we may obtain the remaining diameters by omitting the end differences of the above example, and then subtracting the remaining differences as follows:
| 12.50 | = | 2nd | step. | |||||
| Difference of | 2nd | and | 3rd | = | 2.43 | |||
| 10.07 | = | 3rd | „ | |||||
| „ | 3rd | „ | 4th | = | 2.50 | |||
| 7.57 | = | 4th | „ | |||||
| „ | 4th | „ | 5th | = | 2.57 | |||
| 5.00 | = | 5th | „ | |||||
The 2nd, 3rd, 4th, and 5th steps of the table correspond respectively to the 1st, 2nd, 3rd, and 4th steps of the cone, having but four steps. If the smallest diameter had not been assumed equal to 5 in. we might have dropped a step at each end of the six-step cone of the preceding example, and employed the remaining four diameters, 15.13 in. 12.70 in. 10.20 in. and 7.63 in. for one four-step cone.
The present and the previous examples show that we can assume the size of the smallest step anything that we please, and, other things being equal, can make the required cones large or small.
II.—TABLE FOR FINDING CONE PULLEY DIAMETERS WHEN THE TWO PULLEYS ARE CONNECTED BY AN OPEN BELT, AND ARE EXACTLY ALIKE.
| The numbers given in table are the differences between the diameters of the adjacent stepson either cone pulley, and can be employed when there are either five or three steps on a cone. | |||||||||||||||
| Average difference between the adjacent steps. | Adjacent steps, whose difference is given in table. | Distance between the Centres of Cone Pulleys. | |||||||||||||
| 10 inches. | 20 inches. | 30 inches. | 40 inches. | 50 inches. | 60 inches. | 70 inches. | 80 inches. | 90 inches. | 100 inches. | 120 inches. | 240 inches. | ||||
| 1 inch | 1st | and | 2nd | 0.90 | 0.95 | 0.97 | 0.98 | 0.98 | 0.98 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 1.00 |
| 2nd | „ | 3rd | 0.97 | 0.98 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | |
| 3rd | „ | 4th | 1.03 | 1.02 | 1.01 | 1.01 | 1.01 | 1.01 | 1.01 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | |
| 4th | „ | 5th | 1.10 | 1.05 | 1.03 | 1.02 | 1.02 | 1.02 | 1.01 | 1.01 | 1.01 | 1.01 | 1.01 | 1.00 | |
| 11⁄2 inch | 1st | and | 2nd | 1.28 | 1.39 | 1.43 | 1.45 | 1.46 | 1.46 | 1.47 | 1.47 | 1.48 | 1.48 | 1.48 | 1.49 |
| 2nd | „ | 3rd | 1.43 | 1.46 | 1.48 | 1.48 | 1.48 | 1.49 | 1.49 | 1.49 | 1.49 | 1.49 | 1.49 | 1.49 | |
| 3rd | „ | 4th | 1.57 | 1.54 | 1.52 | 1.52 | 1.52 | 1.51 | 1.51 | 1.51 | 1.51 | 1.51 | 1.51 | 1.51 | |
| 4th | „ | 5th | 1.72 | 1.61 | 1.57 | 1.55 | 1.54 | 1.54 | 1.53 | 1.53 | 1.52 | 1.52 | 1.52 | 1.51 | |
| 2 inches | 1st | and | 2nd | 1.61 | 1.81 | 1.87 | 1.90 | 1.92 | 1.93 | 1.94 | 1.95 | 1.96 | 1.96 | 1.97 | 1.98 |
| 2nd | „ | 3rd | 1.87 | 1.94 | 1.96 | 1.97 | 1.97 | 1.98 | 1.98 | 1.98 | 1.99 | 1.99 | 1.99 | 1.99 | |
| 3rd | „ | 4th | 2.13 | 2.06 | 2.04 | 2.03 | 2.03 | 2.02 | 2.02 | 2.02 | 2.01 | 2.01 | 2.01 | 2.01 | |
| 4th | „ | 5th | 2.39 | 2.19 | 2.13 | 2.10 | 2.08 | 2.07 | 2.06 | 2.05 | 2.04 | 2.04 | 2.03 | 2.02 | |
| 21⁄2 inch | 1st | and | 2nd | 1.89 | 2.20 | 2.30 | 2.35 | 1.38 | 2.40 | 2.41 | 2.42 | 2.43 | 2.44 | 2.45 | 2.47 |
| 2nd | „ | 3rd | 2.30 | 2.40 | 2.43 | 2.45 | 2.46 | 2.47 | 2.47 | 2.47 | 2.48 | 2.48 | 2.48 | 2.49 | |
| 3rd | „ | 4th | 2.70 | 2.60 | 2.57 | 2.55 | 2.54 | 2.53 | 2.53 | 2.53 | 2.52 | 2.52 | 2.52 | 2.51 | |
| 4th | „ | 5th | 3.11 | 2.80 | 2.70 | 2.65 | 2.62 | 2.60 | 2.59 | 2.58 | 2.57 | 2.56 | 2.55 | 2.53 | |
| 3 inches | 1st | and | 2nd | 2.10 | 2.57 | 2.71 | 2.78 | 2.83 | 2.86 | 2.87 | 2.89 | 2.90 | 2.91 | 2.93 | 2.96 |
| 2nd | „ | 3rd | 2.71 | 2.86 | 2.90 | 2.93 | 2.94 | 2.95 | 2.96 | 2.96 | 2.97 | 2.97 | 2.98 | 2.99 | |
| 3rd | „ | 4th | 3.29 | 3.14 | 3.10 | 3.07 | 3.06 | 3.05 | 3.04 | 3.04 | 3.03 | 3.03 | 3.02 | 3.01 | |
| 4th | „ | 5th | 3.90 | 3.43 | 3.29 | 3.22 | 3.17 | 3.14 | 3.13 | 3.11 | 3.10 | 3.09 | 3.07 | 3.04 | |
| 4 inches | 1st | and | 2nd | 3.22 | 3.49 | 3.62 | 3.69 | 3.75 | 3.78 | 3.81 | 3.83 | 3.84 | 3.87 | 3.94 | |
| 2nd | „ | 3rd | 3.48 | 3.74 | 3.83 | 3.87 | 3.90 | 3.91 | 3.92 | 3.94 | 3.94 | 3.95 | 3.96 | 3.98 | |
| 3rd | „ | 4th | 4.52 | 4.26 | 4.17 | 4.13 | 4.10 | 4.09 | 4.08 | 4.06 | 4.06 | 4.05 | 4.04 | 4.02 | |
| 4th | „ | 5th | 4.78 | 4.51 | 4.38 | 4.31 | 4.25 | 4.22 | 4.19 | 4.17 | 4.16 | 4.13 | 4.06 | ||
| 5 inches | 1st | and | 2nd | 3.77 | 4.20 | 4.40 | 4.52 | 4.60 | 4.66 | 4.71 | 4.73 | 4.76 | 4.80 | 4.90 | |
| 2nd | „ | 3rd | 4.19 | 4.60 | 4.73 | 4.80 | 4.84 | 4.87 | 4.89 | 4.90 | 4.91 | 4.92 | 4.93 | 4.96 | |
| 3rd | „ | 4th | 5.81 | 5.40 | 5.27 | 5.20 | 5.16 | 5.13 | 5.11 | 5.10 | 5.09 | 5.08 | 5.07 | 5.04 | |
| 4th | „ | 5th | 6.23 | 5.80 | 5.60 | 5.48 | 5.40 | 5.34 | 5.29 | 5.27 | 5.24 | 5.20 | 5.10 | ||
| 6 inches | 1st | and | 2nd | 4.21 | 4.83 | 5.13 | 5.31 | 5.42 | 5.51 | 5.57 | 5.62 | 5.66 | 5.71 | 5.86 | |
| 2nd | „ | 3rd | 4.82 | 5.42 | 5.62 | 5.71 | 5.77 | 5.81 | 5.83 | 5.86 | 5.87 | 5.88 | 5.90 | 5.95 | |
| 3rd | „ | 4th | 7.18 | 6.58 | 6.38 | 6.29 | 6.23 | 6.19 | 6.17 | 6.14 | 6.13 | 6.12 | 6.10 | 6.05 | |
| 4th | „ | 5th | 7.79 | 7.17 | 6.87 | 6.69 | 6.58 | 6.49 | 6.43 | 6.38 | 6.34 | 6.29 | 6.14 | ||
Example 3. Let distance apart of the centres = 30 in. the average difference between adjacent steps = 2 in. the diameter of the smallest step = 4 in., and the number of steps on each of the cones = 5. The largest step will then equal 12 in., and from [Table II.], under 30 in. and opposite 2 in., we obtain the differences
| 1.87 | 1.96 | 2.04 | 2.13 |