and then subtracting as before we get the required diameters

12 in. 10.30 in. 8.17 in. 6.13 in. 4 in.

Example 4. Let the conditions be as in the preceding example, the cone pulley having, however, three steps instead of five, the largest diameter will then equal 8 in.; and by dropping the end differences and subtracting

  8.00  =  2nd  step.
Difference of  2nd  and  3rd  =  1.96  
  6.04  =  3rd „
„ 3rd „ 4th  =  2.04  
  4.00  =  4th „

we get the diameters 8 in., 6.04, and 4 in., which correspond respectively to 2nd, 3rd, and 4th steps of the table, and to the 1st, 2nd, and 3rd steps of the three-step cone.

Example 5. Let the distance apart of the centres be 60 in., the average difference between the adjacent steps be 21⁄8 in., the smallest step 7 in. and the number of steps = 5. The largest step will then be 7 in. + (4 × 21⁄8) = 151⁄2 inches.

Now an inspection of Table II. will show that it contains no horizontal lines corresponding to the average difference 21⁄8 inches, we cannot, therefore, as heretofore, obtain the required differences directly, but must interpolate as follows: since 21⁄8 inches is quarter way between 2 inches and 21⁄2 inches, the numbers corresponding to 21⁄8 inches (for any given distance apart of the centres), will be quarter way between the numbers of the table corresponding to 2 inches and 21⁄2 inches. Thus, in Table II., we have under 60 inches,

and opposite  2 1⁄2  in.:   2.40   2.47   2.53   2.60
„ 2     1.93   1.98   2.02   2.07
    .47   .49   .51   .53

Dividing these differences by 4, we get:

.12 .12 .13 .13

to which we add,

1.93 1.98 2.02 2.07

and get for the differences corresponding to 21⁄8 inches

2.05 2.10 2.15 2.20

and subtracting as before,

  15.5   1st  step.
difference of  1st  and  2nd  =  2.0 5  
  13.4 5  =  2nd „
„ 2nd „ 3rd  =  2.1 0  
  11.3 5  =  3rd „
„ 3rd „ 4th  =  2.1 5  
  9.2 0  =  4th „
„ 4th „ 5th  =  2.2 0  
  7.0 0  =  5th „

III.—TABLE FOR FINDING THE EFFECTIVE DIAMETERS OF THE STEPS OF CONE PULLEYS, WHEN THE PULLEYS ARE CONNECTED BY AN OPEN BELT AND ARE UNLIKE.

Each vertical cone of the table corresponds to a given length of belt, and the numbers in these columns are the required effective diameters of the steps when the centres of the pulleys are a Unit’s distance apart.
Length of Belt When the Centres of the Cone Pulleys Are A Unit’s Distance Apart. Assumed
diameter
of steps,
divided by
distance
between
the centres
of Cone
Pulleys
2.09 42 2.18 85 2.28 27 2.37 70 2.47 12 2.56 55 2.65 97 2.75 40 2.84 82 2.94 25 3.03 67 3.13 10 3.22 52 3.31 95 3.41 37 3.50 80 3.60 22 3.69 65 3.79 07 3.88 50 3.97 92 4.07 35 4.16 77 4.26 20 4.35 62 4.45 04 4.54 47 4.63 89 4.73 32 4.82 74 4.92 17 5.01 59 5.11 02
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
.05 94 .11 77 .17 50 .23 13 .28 67 .34 13 .39 50 .44 79 .50 00 .55 14 .60 20 .65 18 .70 10 .74 95 .79 74 .84 47 .89 13 .93 73 .98 28 1.02 77 1.07 21 1.11 59 1.15 93 1.20 21 1.24 44 1.28 61 1.32 74 1.36 82 1.40 85 1.44 84 1.48 77 1.52 66 1.56 50 0.00
.03   .08 94 .14 77 .20 50 .26 13 .31 67 .37 13 .42 50 .47 79 .53 00 .58 14 .63 20 .68 18 .73 10 .77 95 .82 74 .87 47 .92 13 .96 73 1.01 28 1.05 77 1.10 21 1.14 59 1.18 93 1.23 21 1.27 44 1.31 61 1.35 74 1.39 82 1.43 85 1.47 84 1.51 77 1.55 66 0.03
  .06   .11 94 .17 77 .23 50 .29 13 .34 67 .40 13 .45 50 .50 79 .56 00 .61 14 .66 20 .71 18 .76 10 .80 95 .85 74 .90 47 .95 13 .99 73 1.04 28 1.08 77 1.13 21 1.17 59 1.21 93 1.26 21 1.30 44 1.34 61 1.38 74 1.42 82 1.46 85 1.50 84 1.54 77 0.06
  .02 94 .09   .14 94 .20 77 .26 50 .32 13 .37 67 .43 13 .48 50 .53 79 .59 00 .64 14 .69 20 .74 18 .79 10 .83 95 .88 74 .93 47 .98 13 1.02 73 1.07 28 1.11 77 1.16 21 1.20 59 1.24 93 1.29 21 1.33 44 1.37 61 1.41 74 1.45 82 1.49 85 1.53 84 0.09
    .05 94 .12   .17 94 .23 77 .29 50 .35 13 .40 67 .46 13 .51 50 .56 79 .62 00 .67 14 .72 20 .77 18 .82 10 .86 95 .91 74 .96 47 1.01 13 1.05 73 1.10 28 1.14 77 1.19 21 1.23 59 1.27 93 1.32 21 1.36 44 1.40 61 1.44 74 1.48 82 1.52 85 0.12
    .02 75 .08 94 .15   .20 94 .26 77 .32 50 .38 13 .43 67 .49 13 .54 50 .59 79 .65 00 .70 14 .75 20 .80 18 .85 10 .89 95 .94 74 .99 47 1.04 13 1.08 73 1.13 28 1.17 77 1.22 21 1.26 59 1.30 93 1.35 21 1.39 44 1.43 61 1.47 74 1.51 82 0.15
      .05 75 .11 94 .18   .23 94 .29 77 .35 50 .41 13 .46 67 .52 13 .57 50 .62 79 .68 00 .73 14 .78 20 .83 18 .88 10 .92 95 .97 74 1.02 47 1.07 13 1.11 73 1.16 28 1.20 77 1.25 21 1.29 59 1.33 93 1.38 21 1.42 44 1.46 61 1.50 74 0.18
      .02 44 .08 75 .14 94 .21   .26 94 .32 77 .38 50 .44 13 .49 67 .55 13 .60 50 .65 79 .71 00 .76 14 .81 20 .86 18 .91 10 .95 95 1.00 74 1.05 47 1.10 13 1.14 73 1.19 28 1.23 77 1.28 21 1.32 59 1.36 93 1.41 21 1.45 44 1.49 61 0.21
        .05 44 .11 75 .17 94 .24   .29 94 .35 77 .41 50 .47 13 .52 67 .58 13 .63 50 .68 79 .74 00 .79 14 .84 20 .89 18 .94 10 .98 95 1.03 74 1.08 47 1.13 13 1.17 73 1.22 28 1.26 77 1.31 21 1.35 59 1.39 93 1.44 21 1.48 44 0.24
        .02 00 .08 44 .14 75 .20 94 .27   .32 94 .38 77 .44 50 .50 13 .55 67 .61 13 .66 50 .71 79 .77 00 .82 14 .87 20 .92 18 .97 10 1.01 95 1.06 74 1.11 47 1.16 13 1.20 73 1.25 28 1.29 77 1.34 21 1.38 59 1.42 93 1.47 21 0.27
          .05 00 .11 44 .17 75 .23 94 .30   .35 94 .41 77 .47 50 .53 13 .58 67 .64 13 .69 50 .74 79 .80 00 .85 14 .90 20 .95 18 1.00 10 1.04 95 1.09 74 1.14 47 1.19 13 1.23 73 1.28 28 1.32 77 1.37 21 1.41 59 1.45 93 0.30
          .01 40 .08 00 .14 44 .20 75 .26 94 .33   .38 94 .44 77 .50 50 .56 13 .61 67 .67 13 .72 50 .77 79 .83 00 .88 14 .93 20 .98 18 1.03 10 1.07 95 1.12 74 1.17 47 1.22 13 1.26 73 1.31 28 1.35 77 1.40 21 1.44 59 0.33
            .04 40 .11 00 .17 44 .23 75 .29 94 .36   .41 94 .47 77 .53 50 .59 13 .64 67 .70 13 .75 50 .80 79 .86 00 .91 14 .96 20 1.01 18 1.06 10 1.10 95 1.15 74 1.20 47 1.25 13 1.29 73 1.34 28 1.38 77 1.43 21 0.36
            .00 64 .07 40 .14 00 .20 44 .26 75 .32 94 .39   .44 94 .50 77 .56 50 .62 13 .67 67 .73 13 .78 50 .83 79 .89 00 .94 14 .99 20 1.04 18 1.09 10 1.13 95 1.18 74 1.23 47 1.28 13 1.32 73 1.37 28 1.41 77 0.39
              .03 64 .10 40 .17 00 .23 44 .29 75 .35 94 .42   .47 94 .53 77 .59 50 .65 13 .70 67 .76 13 .81 50 .86 79 .92 00 .97 14 1.02 20 1.07 18 1.12 10 1.16 95 1.21 74 1.26 47 1.31 13 1.35 73 1.40 28 0.42
                .06 64 .13 40 .20 00 .26 44 .32 75 .38 94 .45   .50 94 .56 77 .62 50 .68 13 .73 67 .79 13 .84 50 .89 79 .95 00 1.00 14 1.05 20 1.10 18 1.15 10 1.19 95 1.24 74 1.29 47 1.34 13 1.38 73 0.45
                .02 71 .09 64 .16 40 .23 00 .29 44 .35 75 .41 94 .48   .53 94 .59 77 .65 50 .71 13 .76 67 .82 13 .87 50 .92 79 .98 00 1.03 14 1.08 20 1.13 18 1.18 10 1.22 95 1.27 74 1.32 47 1.37 13 0.48
                  .05 71 .12 64 .19 40 .26 00 .32 44 .38 75 .44 94 .51   .56 94 .62 77 .68 50 .74 13 .79 67 .85 13 .90 50 .95 79 1.01 00 1.06 14 1.11 20 1.16 18 1.21 10 1.25 95 1.30 74 1.35 47 0.51
                  .01 60 .08 71 .15 64 .22 40 .29 00 .35 44 .41 75 .47 94 .54   .59 94 .65 77 .71 50 .77 13 .82 67 .88 13 .93 50 .98 79 1.04 00 1.09 14 1.14 20 1.19 18 1.24 10 1.28 95 1.33 74 0.54
                    .04 60 .11 71 .18 64 .25 40 .32 00 .38 44 .44 75 .50 94 .57   .62 94 .68 77 .74 50 .80 13 .85 67 .91 13 .96 50 1.01 79 1.07 00 1.12 14 1.17 20 1.22 18 1.27 10 1.31 95 0.57
                    .00 29 .07 60 .14 71 .21 64 .28 40 .35 00 .41 44 .47 75 .53 94 .60   .65 94 .71 77 .77 50 .83 13 .88 67 .94 13 .99 50 1.04 79 1.10 00 1.15 14 1.20 20 1.25 18 1.30 10 0.60
                      .03 29 .10 60 .17 71 .24 64 .31 40 .38 00 .44 44 .50 75 .56 94 .63   .68 94 .74 77 .80 50 .86 13 .91 67 .97 13 1.02 50 1.07 79 1.13 00 1.18 14 1.23 20 1.28 18 0.63
                        .06 29 .13 60 .20 71 .27 64 .34 40 .41 00 .47 44 .53 75 .59 94 .66   .71 94 .77 77 .83 50 .89 13 .94 67 1.00 13 1.05 50 1.10 79 1.16 00 1.21 14 1.26 20 0.66
                        .01 74 .09 29 .16 60 .23 71 .30 64 .37 40 .44 00 .50 44 .56 75 .62 94 .69   .74 94 .80 77 .86 50 .92 13 .97 67 1.03 13 1.08 50 1.13 79 1.19 00 1.24 14 0.69
                          .04 74 .12 29 .19 60 .26 71 .33 64 .40 40 .47 00 .53 44 .59 75 .65 94 .72   .77 94 .83 77 .89 50 .95 13 1.00 67 1.06 13 1.11 50 1.16 79 1.22 00 0.72
                            .07 74 .15 29 .22 60 .29 71 .36 64 .43 40 .50 00 .56 44 .62 75 .68 94 .75   .80 94 .86 77 .92 50 .98 13 1.03 67 1.09 13 1.14 50 1.19 79 0.75
                            .02 92 .10 74 .18 29 .25 60 .32 71 .39 64 .46 40 .53 00 .59 44 .65 75 .71 94 .78   .83 94 .89 77 .95 50 1.01 13 1.06 67 1.12 13 1.17 50 0.78
                              .05 92 .13 74 .21 29 .28 60 .35 71 .42 64 .49 40 .56 00 .62 44 .68 75 .74 94 .81   .86 94 .92 77 .98 50 1.04 13 1.09 67 1.15 13 0.81
                              .00 81 .08 92 .16 74 .24 29 .31 60 .38 71 .45 64 .52 40 .59 00 .65 44 .71 75 .77 94 .84   .89 94 .95 77 1.01 50 1.07 13 1.12 67 0.84
                                .03 81 .11 92 .19 74 .27 29 .34 60 .41 71 .48 64 .55 40 .62 00 .68 44 .74 75 .80 94 .87   .92 94 .98 77 1.04 50 1.10 13 0.87
                                  .06 81 .14 92 .22 74 .30 29 .37 60 .44 71 .51 64 .58 40 .65 00 .71 44 .77 75 .83 94 .90   .95 94 1.01 77 1.07 50 0.90
                                  .01 38 .09 81 .17 92 .25 74 .33 29 .40 60 .47 71 .54 64 .61 40 .68 00 .74 44 .80 75 .86 94 .93   .98 94 1.04 77 0.93
                                    .04 38 .12 81 .20 92 .28 74 .36 29 .43 60 .50 71 .57 64 .64 40 .71 00 .77 44 .83 75 .89 94 .96   1.01 94 0.96
                                      .07 38 .15 81 .23 92 .31 74 .39 29 .46 60 .53 71 .60 64 .67 40 .74 00 .80 44 .86 75 .92 94 .99   0.99
                                      .01 57 .10 38 .18 81 .26 92 .34 74 .42 29 .49 60 .56 71 .63 64 .70 40 .77 00 .83 44 .89 75 .95 94 1.02
                                        .04 57 .13 38 .21 81 .29 92 .37 74 .45 29 .52 60 .59 71 .66 64 .73 40 .80 00 .86 44 .92 75 1.05
                                          .07 57 .16 38 .24 81 .32 92 .40 74 .48 29 .55 60 .62 71 .69 64 .76 40 .83 00 .89 44 1.08
                                          .01 31 .10 57 .19 38 .27 81 .35 92 .43 74 .51 29 .58 60 .65 71 .72 64 .79 40 .86 00 1.11
                                            .04 31 .13 57 .22 38 .30 81 .38 92 .46 74 .54 29 .61 60 .68 71 .75 64 .82 40 1.14
                                              .07 31 .16 57 .25 38 .33 81 .41 92 .49 74 .57 29 .64 60 .71 71 .78 64 1.17
                                              .00 50 .10 31 .19 57 .28 38 .36 81 .44 92 .52 74 .60 29 .67 60 .74 71 1.20
                                                .03 50 .13 31 .22 57 .31 38 .39 81 .47 92 .55 74 .63 29 .70 60 1.23
                                                  .06 50 .16 31 .25 57 .34 38 .42 81 .50 92 .58 74 .66 29 1.26
                                                    .09 50 .19 31 .28 57 .37 38 .45 81 .53 92 .61 74 1.29
                                                    .02 00 .12 50 .22 31 .31 57 .40 38 .48 81 .56 92 1.32
                                                      .05 00 .15 50 .25 31 .34 57 .43 38 .51 81 1.35
                                                        .08 00 .18 50 .28 31 .37 57 .46 38 1.38
                                                          .11 00 .21 50 .31 31 .40 57 1.41
                                                          .02 55 .14 00 .24 50 .34 31 1.44
                                                            .05 55 .17 00 .27 50 1.47
                                                              .08 55 .20 00 1.50