by Milton and Wohlers; 1919

Suppose a motor runs 1500 R.P.M. and is fitted with a 4" pulley. Suppose also, a main shaft should run 300 R.P.M.
Then, 1500 : 300 :: x : 4; Suppose again that a line shaft runs 300 R.P.M., and a counter shaft 600 R.P.M. The counter shaft has a pulley 4" in diameter. The pulley on the line shaft must then have a diameter of 8". |

300 : 600 :: 4 : x;

Or, 300x = 2400,

x = 8"

Suppose the cone pulley on the counter shaft runs 600 R.P.M.; a lathe spindle runs 2200 R.P.M., when connected with the small cone pulley which has a diameter of 3". The large cone pulley has then a diameter of 11".

600 : 2200 :: 3 : x

Or, 600x = 6600;

x = 11"

**RULES FOR FINDING THE SPEEDS AND SIZES OF PULLEYS**

1. To find the diameter of the driving pulley:

Multiply the diameter of the driven by the number of revolutions it should make and divide the product by the number of revolutions of the driver. (20 x 300 = 6000; 6000 ÷ 1500 = 4"--diameter of motor pulley.)

2. To find the diameter of the driven pulley:

Multiply the diameter of the driver by its number of revolutions and divide the product by the number of revolutions of the driven. (4 x 1500 = 6000; 6000 ÷ 300 = 20"--diameter of the driven pulley.)

3. To find the number of revolutions of the driven pulley:

Multiply the diameter of the driver by its number of revolutions and divide by the diameter of the driven. (4 x 1500 = 6000; 6000 ÷ 20 = 300--revolutions of driven pulley.)