10 



MECHANICS. 



be placed a cylindrical piece of lead X. 

 Let the apparatus be so adjusted that. 

 when the lead is put into the hole be- 

 tween the bars, the centre of gravity will 

 be between them, and that the centre of 

 gravity will be below or above them 

 when the lead is put into the hole which 

 is below or above the bars. Let strings 

 be attached to the extremities of the 

 bars, and passing them over wheels as 

 represented in the figure, let the whole 

 apparatus be supported in the horizon- 

 tal position by equal weights, P and P', 

 the lead being placed in the hole between 

 the bars. Now, it will be found that 

 the same equal weights will support 

 the apparatus when it is inclined to the 

 horizon, provided the strings by which 

 the weights P P' act continue parallel. 

 Let, then, the lead be removed to the 

 upper hole ; the same weights will sup- 

 port the apparatus in the horizontal 

 position ; but if it be inclined, it will be- 

 come necessary to increase the weight 

 which supports the lower end, and di- 

 minish that which supports the upper 

 end. On the other hand, if the lead be 

 placed in the lower hole, when the ap- 

 paratus is inclined, it will be necessary 

 to increase the weight which supports 

 the upper end, and to diminish that 

 which supports the lower end. 



TA 



Throughout these experiments- the 

 strings which support the weights should 

 be kept parallel. 



Mechanical writers have sometimes 

 investigated this problem erroneously. 



CHAPTER IV. Compound Levers 

 Rectangular Lever Weighing Ma- 

 chine All simple and complex 

 Machines reducible to equivalent 

 Levers. 



(26.) THE power may act upon the 

 weight through the intervention of a 

 series of levers, in which case the ap- 

 paratus is called a composition of levers, 

 or a compound lever. There is one 

 general condition which applies to every 

 combination of levers, viz. that "When 

 the system is in equilibrium, the power 

 multiplied by the continued product of 

 the alternate arms commencing from, 

 the power, is equal to the weight mul- 

 tiplied by the continued product of the 

 alternate arms beginning from the 

 weight." This will be more easily un- 

 derstood by observing its application to 

 the following examples. 



The system of levers represented in 

 fig. 16 consists of three levers of the 

 first kind. The power acting at B 

 exerts a certain pressure at B'. Let 



Fig. 16 



this pressure be called x. Again, the 

 pressure x by means of the lever B' C' 

 produces a pressure, which we call y, at 

 C', and the pressure y at C' supports 

 the weight W at C". 



Let the alternate arms B G, B' G', 

 B" G", commencing from the power, be 

 called p, p and p" ; and let the alternate 

 arms C" G", C' G', C G, commencing 

 from the weight,: be w", w\ and w. Now, 

 since the power P equilibrates with the 

 pressure x, we have 



P p = x . w. 



Also, since the pressure x equilibrates 

 with the pressure y, we have 



( xp'=y w' ; 



ahd since me pressure y equilibrates 

 with the weight W, we have 

 yp" = \V t w " f 



Since P p, x p', and y p" are respec- 

 tively equal to x w, y w', and W iv", it 

 follows that, if the former be multiplied 

 together, they will be equal to the latter 

 multiplied together. Hence we have 

 P p x p' y p" x w y w' W w". 

 In these equal products, by omitting the 

 common multipliers x and y, we obtain 



P . p p' p" =Www' w" ;* 

 that is, the power multiplied by the 

 continued product of the alternate arms 

 commencing from the power, is equal 

 to the weight multiplied by the continued 

 product of the alternate arms commenc- 

 ing from the weight. 



Those students who are not sufficiently 

 masters of the signification of the alge- 



* See PARLEY'S Algebra, p. 61. 



