276 



THE PULLEY. 



wheels in the upper block in the same time, are as the even numbers 2, 4, 6, 

 &c. If the wheels were all of equal size, as in fig. 8, they would revolve 

 with velocities proportional to the rate at which the rope passes over them : so 

 that, while the first wheel below revolves once, the first wheel above will re- 

 volve twice ; the second wheel below three times ; the second wheel above 

 four times, and so on. If, however, the wheels differed in size in proportion 

 to the quantity of rope which must pass over them, they would evidently re- 

 volve in the same time. Thus, if the first wheel above were twice the size 

 of the first wheel below, one revolution would throw off twice the quantity of 

 rope. Again, if the second wheel below were thrice the size of the first wheel 

 below, it would throw off in one revolution thrice the quantity of rope, and so 

 on. Wheels thus proportioned, revolving in exactly the same time, might be 

 all placed on one axle, and would partake of one common motion, or, what is 

 to the same effect, several grooves might be cut upon the face of one solid 

 wheel, with diameters in the proportion of the odd numbers 1, 3, 5, &c., for 

 the lower pulley, and corresponding grooves on the face of another solid wheel 

 represented by the even numbers 2, 4, 6, &c., for the upper pulley. The rope, 

 being passed successively over the grooves of such wheels, would be thrown 

 off exactly in the same manner as if every groove were upon a separate wheel, 

 and every wheel revolved independently of the others. Such is White's pul- 

 ley, represented in fig. 10. 



Fig. 10. 



The advantage of this machine, when accurately constructed, is very con- 

 siderable. The friction, even when great resistances are to be opposed, is 

 very trifling ; but, on the other hand, it has corresponding disadvantages which 

 greatly circumscribe its practical utility. In the workmanship of the grooves, 

 great difficulty is found in giving them the exact proportions ; in doing which, 

 the thickness of the rope must be accurately allowed for ; and consequently it 

 follows that the same pulley can never act, except with a rope of a particular 

 diameter. A very slight deviation from the true proportion of the grooves will 

 cause the rope to be unequally stretched, and will throw on some parts of it an 



