100 



SYSTEM OF I 



<> weigh: : or falling, it will be 



that al the pullies move with angular 1110- 



. The degree of angular motion of each pully dep.-nds 

 Upon the m. tfl radius. Mr .lani.-s White took 



advantage of this, to choo- Hi of the pullies in such a 



manner as to give those in the same block the same a; 

 motion, and so to d by 



the friction of the pullies against each ntln-r. This bring the 

 case, the pullies in each block might be fastened together, or, 

 instead of this, cut out of one mass. 



,vill be seen without much dilHculty, that if the weight 

 IT be raised thr-uigh a space , each of the portions of Bl 

 between the two blocks will be shorten e I by the lengi 

 and therefore, that the portions of string which move 

 the pullies in the two blocks, taken alternately, will have, 

 their lengths equal to cr, 2a, 3a, 4rc... Suppose the 

 the string fastened to the lower block ; then if the radii of 

 the pullies of the upper block be proportional to the odd 



numbers 1, 3, 5, : dlics will move with the same 



angular velocity, and might be mad* 1 , all in one piece, as 



ioned above. And if the radii of the lower pulli< 

 proportional to the even integers 2, 4, G,... these also will 

 move with a common angular vel< 1 might 



be cut out of one piece. 



164. To find the ratio of the power to the weight when all 

 the strings are attached to the w> iyht. 



If we neglect the weights of the pullies, ^ I J* 



-nsion of the string b l a l = F; the ten- 

 sion of aj> t = 2P; and so on : if there 

 u puH'n-s. tln-n the sum of the .s, of 



the strings attached to the weight 



= P-r 2P + 2 2 P+ ... +2" -1 P= (2"- 1) P 



therefore = 2 W - 1 . 



If we suppose the weights of the pullies arc 

 a) l , (O , a) . : from the lowest, and 



w', o> , w"',... the portions of IT which t 

 respe >rt, since they evidently 



assist tlie portion of W sup- 



ported by !' then 



