Tilt EFFECTS OF MACHINES WHEN IN MOTION. 151 



Now by Problem 7, Cor. ^^s ^ ^'~^^ ^^'^^^ ex- 

 press the //of the whole beam reduced to B. Hence 

 P + —r-r-r,Xc-hd+~, will express the mass when 

 reduced to B, as to angular velocity. Then since | 

 is the weio'ht of the shorter end reduced to A , ^ is 

 the weight which applied at B, would balance the 

 shorter end. Therefore -^ +^ applied at B, would 

 sustain the shorter end, together with the weight .v, 

 in equilibrio. Kence P + —-—^—^ is the moving 



d a c ax 



power. And therefore nr/i is the ac- 



celerative force of P, or of x reduced to B, dnd 



ad a'-c d^x 

 4eP^ ; -. 



TT 7i — ^ is the accelerative force of x sus- 



pended at A : which, by substituting q for a P + 

 "--^, and <Jor iP +^XTT^ becomes t^:: 

 Hence '^^'^V^y is the motive force, whose fluxion be- 



tb-\-abK • 



ing equal to o, we have qbx-^la.vx'Kt b -{- cii)x ^ abxX, 

 qbx-a'x'—o, and.r=— \/flJ±L L. Now if a be 



' " a a ^ 



unity, Xhtnx'=iv^f-\-bqt-t, the same as in the last 

 Problem, when n- 1 will be equal b. 



Note. If in this accelerative force of P, q be sub- 



^3+^3 



stituted for P +-- \, and t for P -j — tzttp, • c + d 



then the accelerative force of x is ^rrrr-r- and its 

 momentum ^^Sr? from whence x ~ —\/i'' + tq- 

 — r, and in the preceding problem, if q be put for 

 p + "-^:Z ^_ and t for P+^'W, in the acce- 



' Zn %n.n — I ' ' C5 ' 



lerative force of P, and proceeding to find t he a c- 

 celerative force of ^r, &c. then.r=:;2-l.\/^^+^y-«-l. if. 



K 4 Prob. 



