290 APPLIED SCIENCE 



pulleys and the ratios between their diameters and speeds. 

 Pulleys are usually arranged in pairs, each with a different 

 diameter and on a separate shaft. The mechanical prin- 

 ciple involved in a pair of pulleys is that of the wheel and 

 axle, the larger pulley being the wheel and the smaller one 

 the axle. (See Chapter V.) Since the belt running over 

 the two pulleys always runs at the same speed as their 

 rims, it is plain that the rims of both pulleys run at the 

 same speed. The pulley running the smaller number of 

 revolutions must be the larger of the two. 



Take, for example, a 16 in. driving pulley making 180 R.. P. M. 

 running with a pulley making 320 R. P. M. The rim of the 16 in. 

 pulley will travel in one minute a distance equal to 180 times its 

 circumference, or 180 X 16 X 3.1416, and the rim of the other 

 pulley will travel, if we call D its diameter, 320 X D X 3.1416. 

 Since the rims of the two pulleys will always travel at the same speed 

 we can put these two expressions equal to each other, or 



180 X 16 X 3.1416 = 320 X D X 3.1416 

 and solving this equation to find D, we will have 



180 X 16 X 3.1416 



D = , or D = 9 in. 



320 X 3.1416 



Now, according to the rule, we will have 



16 X 180 = 9 X 320 

 or 2880 = 2880 



which proves that the rule is correct. 



333. Size of Pulley. To illustrate the method of find- 

 ing the size of a pulley, suppose a shaft is to make 360 

 R. P. M. and that it is driven from a line-shaft making 180 

 R. P. M. The larger pulley on the line-shaft is already in 



