34 



MECHANICS. 



Fig, 59. 



Hence, in this case, 

 the weight is four 

 times the power. 



In general, in sys- 

 tems of pullies having 

 only one rope, and 

 one moveable block, 

 the weight is as many 

 times the power, as 

 there are different 

 parts of the rope en- 

 gaged in supporting 

 the moveable block. 

 This must be very 

 evident, when it is 

 considered that each 

 part of the rope which 

 passes between the 

 two blocks is equally 

 engaged in sustaining 

 the weight. 



In the system re- 

 presented in Jig. 59, 

 if the rope, instead 

 of being finally at- 

 tached to the fixed 

 block, were passed 

 over a third wheel in 

 that block, and finally 

 attached to the lower 

 block, the weight 

 would be five times 

 t ne power. 



(78.) In these systems the wheels 

 Fig. 61. 



Fig. 62, 



move on separate axles. They are 

 sometimes placed side by side on the 

 same axle, as represented in Jig. 60. 

 But the proportion of the power to the 

 weight is the same in all. 



In this arrangement of the sheaves 

 it is difficult to keep the strings parallel, 

 and to prevent the effect of the power 

 and weight deranging the position of 

 the blocks in the manner represented in 

 fig. 61. 



To remedy this incon- 

 venience the ingenious 

 and powerful arrange- 

 ment represented in Jig. 

 62, has been suggested. 

 To prevent confusion in 

 the figure, the rope has 

 been omitted, but its 

 course may be easily 

 traced. Suppose one ex- 

 tremity attached to the 

 hook at the bottom of 

 the upper block: the 

 rope from this point is 

 brought under the wheel 

 a, over b, under c, over 

 d, under e, over /, and 

 so on according to the 

 order of the letters, until 

 it finally passes over the 

 wheel u, and is then 

 attached to the power. 

 In this case there can be 

 no derangement in the 

 position of the blocks, 

 as in fig. 61, since the 

 power acts immediately 

 over the weight. The 

 weight is here sustained 

 by the ropes, which pass over ten 

 wheels, and therefore is distributed be- 

 tween twenty parts of the rope, so that 

 the weight is twenty times the power. 



(79.) All systems of pullies of this 

 kind, however, have still great defects. 

 The great number of wheels requisite 

 when much power is required increases 

 the quantity of friction prodigiously; 

 for each wheel has not only the friction 

 on its axle, but also the friction against 

 the side of the block in which it revolves. 

 Besides this, they are liable to great 

 inequality of wear, owing to the circum- 

 stance of revolving on their axles with 

 different velocities. Suppose that, by 

 the action of the power, the lower block 

 in fig. 62 is moved one foot towards the 

 upper block ; it is evident that the se- 

 veral parts of the rope between the 

 blocks will be each shortened by one 

 foot, Hence it appears that one foot of 



