Chap. 7.] Wbeek. 69 



wheel and a fmall one, called a pinion, and fbmetimes 

 a nut, the teeth of which coincide with the teeth of 

 another large wheel. In large machines, trundles are 

 often fubftituted for pinions or nuts, and perform their 

 office ; thefe are cylinders or fpindles parallel to each 

 other, and placed circularly in two plain pieces of 

 wood at the top and bottom. The teeth of the wheel 

 then catch the fpindles of the trundle as they do the 

 cogs of the nut or pinion. The mechanifm is the 

 fame in both cafes : fo that it fuffices to examine the 

 manner of hooking or catching of wheels and pi- 

 nions. 



Wheels of the firft kind, thofe whofe motion is con- 

 fined to the fame place, may be confidered as levers of 

 the firft order; the arms of which are the radii of the 

 wheels and nuts, and which have their prop at the axle. 

 Let A B C (Plate III. fig. i .) be three wheels, and a b c 

 their correfponding pinions or nuts. The nutj or what 

 is the fame thing, the cylinder a fuftains the weight P ; 

 the wheel A, which has the fame axle as the cylinder a, 

 catches the nut b ; the wheel B, which has the fame axle 

 as the n\Qb, catches the nut c\ the wheel C, which 

 has the fame axle as the nut c, is drawn at its circum- 

 ference by the power Qj and the whole fyftem is 

 in equilibrium. Here the weight P a<5bs by the radii 

 of the nuts ; but the power Q^acts by the radii of the 

 wheels. Suppofe the radii of the wheels to be four 

 times thofe of the nuts; and that the firft are eight 

 inches, and the other two inches. To preferve an 

 equilibrium, it is neceffary that the power fhould be 

 to the refiftance, as the product of the arms of the 

 lever of refiftance is to the product of the arms of the 

 lever of power, that is, in an inverfe ratio of the length 

 of the arms of the lever ; thefe products are found by 

 multiplying the one by the other, that is, the radii of 

 F 3 the 



