l^S ON THE MAXIMUM QF MECHANIC POWERS, ANU 



It has already been demonftrated by mathema- 

 ticians that if s be the center of fufpenfion, or ro- 

 tation ; the center of percuffion, and j^ the center 

 of gyration j — and if/) be a particle and /its diftance 



- , all the W^ , all tht pd\ 



from J, then ^^^F^r^i^fTh^bSd^' a"^-^<r='^^lhrb5dy 

 which exprefHons are univerfal, let the form of the 

 body be what it will. Now as the lever and wheel 

 arc powers whofe operations a;^: materially influenced 

 by their own weight, I Hiall confider every cafe in 

 which they can poflibiy be efFe6^ed. And notwith- 

 ftanding that the part of mechanics relating to percuf- 

 flon and gyration, has been fo copioufly treated on by 

 others, yet as it becomes fo efTential a part in the pre- 

 fent theory, I fliall include fuch propofitions as imme- 

 fiiately apply, and put them in the moft convenient 

 forms. Some of them, I believe are new, and par- 

 ticularly fuited to the prefent fubject. 



Prob. 1. Let A B be a bar or beam perfe611y ^ 

 flreight and of uniform thicknefs, having its point 

 of fufpenfion S, at any variable diftance from the 

 extremity A : it is required to determine the dif- 

 tance ©[ the center of percuffion from S. 



Put AB=v, AS—x, and therefore SBm-y — x ; 

 and let the faid diftance of the center of percuf- 

 fion from s be y, then v being an indefinitely fmall 

 plane at right angles to the axis of the beam, 

 'j — x\^Xv will exprefs one pd"^ or the fluxion of 

 nil the pd"^ in A B j and by the fame reajToning, 



v—xxv is the fluxion of the force of A B. — 



licnce y— 7— ^^^==^- — :™ 7 : where .v and 



v may be taken in any ratio to each other. If .vzzo L 

 or the center of fufpenfion be at A, thenjyz::*-';:^ as 

 has been proved by others. If a^~4-'Z^, ihcn y:=z^v alfo, 

 in which cafe the center of percuflion will be at the 

 other extremity B, and when x=iv, then yzzo, and 

 the center of percuflion coinciding with the center of 



gravity. 



