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;
Or, 300x = 6000,
x = 20, or the diameter of the large pulley on the main shaft.
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"