72 Of Wheel [Book I. 



wheel turns round once ; and fo on the other hand, if 

 this makes one revolution, the nut D and the vertical 

 wheel H will make four in the fame time. For in- 

 fiance, fuppofe that to each of the great wheels II and 

 E, a handle G or F is fixed, and turned by a man 

 once in a fecond, the velocity will be four times as 

 great when he turns by the handle F as if he turned 

 by the handle G. But it is true, that in this cafe he 

 inuft ufe four times the force; becaufe whatever is 

 gained in fcrce is loft in time ; and on the contrary, 

 what is gained in time is loft in force j yet ic is often 

 advantageous to have the liberty of choice. 



As to wheels of the fecond kind, which have two 

 fores of motion, as thofe of carriages, the center of 

 which advances in a right line while the other parts 

 turn round it, they may be regarded as a lever of the 

 fecond order, the action of which is repeated as often 

 as there is fuppofed to be points in the circumference. 

 For each of thefe points is the extremity of a radius 

 C M (fig. 4.) fupported at one end by the ground M ; 

 and the other end C charged with the axle which fup- 

 ports the carriage is at the fame time drawn by the 

 power P which moves it along. So that if the plane 

 was perfectly level, and the circumference of the wheels 

 witho-ut any inequalities j if there was no friction be- 

 tween the axle and the nave, and if the direction of 

 the power conftr^ntly remained parallel to the plane, 

 then a fmall force would draw a very heavy carriage; 

 for the re/iftance which proceeds from the weight, 

 refts entirely upon the ground by the radius or fppke 

 C M, or by another fpoke which immediately fuc- 

 cecds. But thefe circumftances are never or very fel- 

 dom to be found in practice. The wheels of carriages 

 are frequently rounded in a coarle manner, and large 

 nails driven into them; the roads are uneven, or made 



fo 



