1460NTHE MAXniUnr ©r MEGHANiCI'O^XRS, AND 



Prob, 9. Let it be required to determine the p' 

 of the whole beam AB m rrob. 3, acting at A, while 

 the beam revolves horizontally on the center S. 



in this case, when a vanishes, then p' becomes 



iz '^^-rrrh X W : when d vanishes, and D coincide5 



with S, in which case v becomes equal A S, and A D 

 and DB become two beams revolving on one end 

 each ; then the />' of both the beams together is 

 equal ^ W, where W is the weight of both the 

 beams; and therefore the p' of each, acting at the 

 extremity A or B, is -| its own weight, the same as 

 in Prob. 6, Cor. 1. 



Prob. 9. Let the annulns in Prob. 5 be pro- 

 posed, to determine the p' of the whole, acting at 

 the distance S A, any where in the circumference. 



Then since tt'"' is equal ; ^_ ^^ , where Rzi S A, and 

 r — sa we shall have // = (~ X the body) ^^iii^ X 



' — r-^T the weitrht of the annulus : 

 and when ?" = o, so that the interior circle may va- 

 nish, and ABC become an entire circle or solid 

 wheel, thenyn^ the mass, the same as iu Prob. 8. 



CoR. If A represent the area of a sector of a 

 circle whose diameter is unity, similar to the sectors 

 AS or a s in Cor. of Prob. 8 ; then the/ of both 

 the parts A a and B C together, will be equal ^i_^^ 



X2 AJT — 2Ar^~ -;^o;r^i the mass of the two parts 

 together. 



Prob. 10. Let Aa, ^B, cC, be a solid ring, hav- 

 ing a solid beam whose center is the center of the 

 annulus, as in the nex:t fig^we ; it is required to de- 

 termine they of the wlwle acting at B. 



Let 



