TRANSMISSION OF POWER 291 



place and is 16 in. in diameter. What diameter should we 

 make the pulley on the shaft making 360 R. P. M? 



Since we know the ratio of the speeds and diameters, we have the 

 proportion: Speed of small pulley is to speed of large pulley as 

 diameter of large pulley is to diameter of small pulley, or using 

 the same figures as above, we have 



360 : 180 = 16 : diameter of small pulley 



The rule thus deduced is as follows : 



The diameter of the driving pulley multiplied by its speed 

 equals the diameter of the driven pulley multiplied by its speed. 



In practice it is found that a belt creeps or slips so that it 

 does not usually drive a pulley quite so fast as the calcula- 

 tions indicate. For this reason, the relative speeds of pul- 

 leys are only approximately exact and are always subject to 

 slight variation. 



334. Object of Gears. The liability of belts and ropes to 

 slip when transmitting heav}^ loads renders their use prac- 

 tically impossible when a constant ratio of velocity between 

 the driving and driven shafts must be maintained. In these 

 cases toothed wheels, called gearing, are usually employed. 



335. The Principle of Gearing. The principles under- 

 lying the design of gears may be best understood by con- 

 sidering the historical development of the gear. Origin- lly 

 transmission of power in machines was carried out by two 

 smooth cylinders placed close together, as in Fig. 146, the 

 revolution and friction of one causing the revolution of the 

 other. Smooth cylinders, however, tend to slip when under 

 a load, so projections or notches were placed on their sur- 

 faces, as in Fig. 147. Here the diameters D and d are the 



