36 



MECHANICS. 



Fig. 64. 



remain, as well the 

 friction on their axles 

 or pivots, as the late- 

 ral friction of their 

 surfaces with the 

 blocks. To remove 

 this defect, Mr. White 

 conceived the notion 

 of reducing all the 

 wheels in the same 

 block to one; or ra- 

 ther, instead of using 

 separate wheels, to 

 cut several circular 

 grooves, with the dia- 

 meters we have al- 

 ready described upon 

 the same wheel. Thus, 

 all the friction was re- 

 duced to that of the 

 pivots, and the lateral 

 friction of one wheel. 

 This pulley is repre- 

 sented in figs. 63, 64, 

 and it will be easily 

 understood from the 

 preceding observa- 

 tions. In this, like 

 every other system in 

 which there is a single 

 rope, the weight is as many times the 

 power as there are ropes sustaining the 

 lower block. 



(81.) The condition of equilibrium 

 m all such systems may be mathemati- 

 cally expressed thus : 



W=nP; 



where n signifies the number of parts 

 of the rope which sustain the lower 

 block, and where W expresses the 

 weight sustained and the weight of the 

 lower block. 



(82.) We have now 

 ^mentioned the princi- 

 pal systems of pullies 

 in which there is but 

 one rope. Much pow- 

 er, however, may be 

 gained by increasing 

 the number of ropes. 

 In figs. 65, 66, are re- 

 presented systems with 

 two ropes and two 

 moveable pullies, call- 

 ed Spanish burtons. 



In the system repre- 

 sented in fig. 65, the 

 tension of the rope P 

 B is equal to the pow- 

 er, and this rope being 

 finally attached to 

 the pulley which sus- 



Fiff. 65. 



tains the weight, supports a part of the 

 weight equal to the power. The rope 

 from C to B balances the united tensions 

 of both parts of the rope extending from 

 B to the weight and power, and therefore 

 its tension is twice the power, and being 

 brought under the pulley which sustains 

 the weight, and finally attached to the 

 fixed point, it sustains a part of the 

 weight equal to four times the power. 

 Thus, the whole weight must be equal 

 to five times the power. The power 

 being taken as the unit, the number 

 placed at each rope expresses the part 

 of the weight which it sustains. 



The system repre- Fig. 66. 



sented in fig. 66 has<g 

 also two ropes, but 

 is not so powerful as 

 the former. The ten- 

 sion of the rope ex- 

 tending from the 

 power to the fixed 

 point is equal to the 

 power, and the ten- 

 sion of that extend- 

 ing from the pulley 

 B to the weight is 

 obviously equal to 

 twice the power. 

 Thus, the weight is 

 four times the power. 

 The tensions are 

 here, also, expressed 

 by the figures placed 

 at the ropes. 



In both these systems the weight of 

 the pulley B assists the power, and that 

 of A opposes it. In the system repre- 

 sented in Fig. 65, if the weight of the 

 pulley B be half that of A, the weights 

 of the two pullies will balance one ano- 

 ther ; but if the weight of B be more 

 than half of A, the power will be assist- 

 ed, and a less power than the fifth part 

 of the weight will sustain equilibrium. 

 If the weight of B be less than half of 

 A, a contrary effect will take place. 



In the system represented in Fig. 66, 

 if the weight of B be equal to that of 

 A, it will exactly balance it. If it be 

 greater or less, it will assist or oppose 

 the power. 



(83.) In fig. 67, a system of. pullies 

 is represented with four ropes, in which 

 the weight is sixteen times the power ; 

 for the tension of the rope D E is evi- 

 dently equal to the power, because it 

 sustains it. D, being a moveable pulley, 

 must sustain a weight equal to twice the 

 power ; but the weight which it sustains 

 is the tension of the second rope D C. 



W 



