S8 LECTURE I?C. 



equal weights, connected with the former three, by threads passing over pul- 

 lies. The length of one of the planes is twice its height, that of anothei 

 considerably more, and that of a third less: if the M'eights begin to rise at 

 the same time, the first A\ill arrive at the top, before cither of the others. 

 (Plate V. Fig. 76.) 



If a given weight, or any equivalent force, be employed to raise another 

 equal weight, by means of levers, wheels, puUies, or any similar powers, the 

 greatest eftect will be produced, if the acting weight be capable of sustaining, 

 in equilibrium, a weight about twice and a half as great as itself. This pro- 

 position may be very satisfactorily illustrated by an experiment. Three double; 

 puUies being placed, independently of each other, on an axis, round which 

 they move freely, the diameters of the two cylindrical portions, which com- 

 pose the iirst, being in the ratio of 3 to 2, those of the second as 5 to 2, and 

 those of the third as 4 to 1, six equal weig-hts arc attaclicd to them in pairs, 

 so that three may be raised by the descent of the other three, on the principle 

 ' of the wheel and axis. If then Ave hold the lower weights, by means of 

 threads, or otherwise, and let them go, so that they may begin to rise at the 

 same instant, it will appear evidently that the middle pulley raises its weight 

 the fastest ; and consequently, tliat in this case, the ratio of 5 to 2 is more 

 advantageous, than either a much less, or a much greater ratio. If the weight 

 to be raised were very great in proportion to the descending weight, the ar- 

 rangement ought to be such, that this weight might retain, in equilibrium, a 

 weight about twice as great as that which is actually to be raised. If the 

 descending weight were a hundred times as great as the ascending weight, 

 the greatest velocity would be ohtaijied in this case, by making tlie descend- 

 ing weight capable of holding in equilibrium a M'cight one ninth as great as 

 itself. (Plate Vf. Fig. 77.) ^ 



The proportion required for the greatest effect is somewhat different, when 

 the heights, through which Ijoth the weights are to move, arc limited, as they 

 usually must be in practical cases. Here, if we suppose the operation to be 

 continually repeated, the cfi'ect will be greatest in a given time, when the 

 ascending weight is between two thirds arul one half, of the exact countci- 

 poise to the descending Aveiglit. If, however, the force were accunudated 

 daring the action of the machine, there would be no limit to the advantage of 



