112 Statics. 



at right angles to their length, the ratio of the power to the 

 weight would always be found to be the same as above stated, 

 by substituting for radius of the wheel the words length of the arm; 

 this length being reckoned from the axis of the cylinder. But 

 Fig. 99. if the power acted in a direction not perpendicular to the arm IE, 

 instead of the length of the arm we should take that of the per- 

 pendicular IR let fall upon the direction of the power ; so that 

 in this case the power will be to the weight as the radius of the 

 cylinder to the perpendicular IR. 



Fig.101. 19a g ince ^ . p .. gf . ^ we Jj ave ^ x __ p x JT. 



that is, the moment of the power is equal to the moment of the 

 weight, these moments being taken with respect to the axis FF. 

 If, therefore, several powers are employed at the same time, ap- 

 plied to different arms, the sum of the moments of these powers 

 must be equal to the moment of the weight. 



191. If the cord which supports the weight or which transmits 

 the action of the power to the weight, were wound round a conical 

 surface, or a surface of a variable diameter, instead of that of a 

 cylinder, the ratio of the power to the weight, would also vary 

 continually ; and reciprocally, if the power, whose action is to be 

 communicated through the medium of such a machine as that 

 under consideration, varies continually, and is intended, notwith- 

 standing, to produce the same effect, we arrive at the end pro- 

 posed, by causing the action to be applied successively to radii 

 that increase in length according as the power diminishes. We 

 have an example of this adaptation of the machine to a varying 

 power in watches and chronometers, in which the moving or 

 maintaining power is a spring fixed at one of its extremities to 

 Fig.103. the axis or arbor of a barrel Z, and which, after several revolu- 

 tions or coils, is attached to the interior of this barrel. A chain 

 with one of its extremities fixed to the convex surface of the bar- 

 rel is wound round the conical axis or fusee F, to which the other 

 extremity of the chain is attached. As the spring uncoils, the 

 barrel turns, and drawing the chain, causes the fusee to turn ; 

 but since the force of the spring diminishes as it uncoils, a com- 

 pensation is made for this reduction of the power, by giving a 

 greater diameter to those parts of the fusee on which the last 

 coils of the spring are exerted. By this contrivance, the ma- 

 chinery receives nearly equal impulses in equal times. 



