faces come into full contact ; and after passing the position of C D, the same 

 scraping and grinding effect is produced in the opposite direction, until, by the 



Fig. 25. 



revolution of the wheels, the teeth become disengaged. These effects are 

 avoided by giving to the teeth the curved forms represented in fig. 26 By 



Fig. 26. 



such means the surfaces of the teeth roll upon each other with very inconsid- 

 erable friction, and the direction in which the pressure is excited is always 

 that of a line, M N, touching the two wheels, and at right angles to the radii. 

 Thus the pressure, being always the same, and acting with the same leverage, 

 produces a uniform effect. 



When wheels work together, their teeth must necessarily be of the same 

 size, and therefore the proportion of their circumferences may always be esti- 

 mated by the number of teeth which they carry. Hence it follows that, in 

 computing the power of compound wheelwork, the number of teeth may al- 

 ways be used to express the circumferences respectively, or the diameters 

 which are proportional to these circumferences. When teeth are raised upon 

 an axle, it is generally called a pinion, and in that case the teeth are called 

 leaves. The rule for computing the train of wheelwork, given in fig. 9, will be 

 expressed as follows : When the wheel and axle carry teeth, multiply together 

 the number of teeth in each of the wheels, and next the number of leaves in 

 each of the pinions ; the proportion of the two products will express the power 

 of the machine. If some of the wheels and axles carry teeth, and others not, 

 this computation may be made by using for those circumferences which do not 

 bear teeth the number of teeth which would fill them. Fig. 27 represents a 

 train of three wheels and pinions. The wheel F, which bears the power, and 

 the axle which bears the weight, have no teeth ; but it is easy to find the num- 

 ber of teeth which they would carry. 



It is evident that each pinion revolves much more frequently in a given time 

 than the wheel which it drives. Thus, if the pinion C be furnished with ten 

 teeth, and the wheel E, which it drives, have sixty teeth, the pinion C must 

 turn six times, in order to turn the wheel E once round. 'The velocities of 

 revolution of every wheel and pinion which work in one another will, there- 

 fere, have the same proportion as their number of teeth taken in a reverse or- 



