Chap. 7.] of Patties. 



barrel e or E, furnifhed with a fpring like that of a 

 watch. If the force of the fpring is fuch, that any 

 given power (a weight, for example, acting at D E) 

 keeps it in equilibrium; when the fpring is rolled 

 three or four rounds more, the fame weight acting at 

 g F will keep it ftill in equilibrium, if the radius E F 

 is lengthened in proportion to the augmentation of 

 force in the fpring ; what has been obferved of the 

 point F may be faid of all the others. Hence it fol- 

 lows, that thefe two pov/ers, the fpring and the weight, 

 will always act againft each other in a certain ratio or 

 proportion, even though the force of either mould be 

 occafionally augmented : It is upon thefe principles 

 that clock and watch-makers are able to calculate the 

 force of their fprings, weights, and pendulums, and to 

 adapt them with the utmcft precifion to the other 

 movements. 



The axis c (fig. I.) of a fimple pulley can never be 

 charged with a greater force than that which is equal 

 to the fum of the two powers I and H, but it may be 

 fomewhat lefs. When the directions b I and i H of 

 two powers are parallel, that is, when the cord em- 

 braces half the circumference of the pulley, the axis is* 

 charged with a force equal to the fum of the two* 

 powers. But if the direction of the two powers is 

 oblique to each other, the axis is then charged witli a 

 lefs force than the fum of thofe of the two powers j 

 and in that cafe, the force with which the axis ii 

 charged is to the fum of the forces of the two powers, 

 as the chord of the arch embraced by the chord is to 

 the diameter d i ; the effort is then made upon the 

 axis c y in a direction which, paffing through f, tends 

 to the point of meeting according to the direction of 

 the two powers. 



In all thefe cafes the force H mult be equal to the. 



refiftance 



