148 On themaximumofmecUanic powers, atcd 



investigation unnecessary. Supposing then sc^=.Sa; 

 and call de::zLa, then sdzzr—a very nearly. Then 

 by Prob. Q, the p' of the braces at one end is 



^'-,'!" ^'''~''t'^ ^'"^~''l x'lo", or equal kzv\ by substitut- 

 ino-/cfor^:l±^3!ilE^^-. And therefore 2 A:a;' 



will be they/ of all the braces at the distance S3, 

 then by Cor. 2 of Prob. 7. As R\' r^ ; ; 2 W ; 



-—T-, they of all the braces reduced to the distance 



SB. Hence -^137, X -^4- — + -^7- expresses the J5 



of the beam, circular ends and braces together, very 

 nearly. 



Hence is obtained the value of/ in the most 

 useful cases that occur; and this p' being the pOwer, 

 which acting at the extremity of the different fi- 

 gures here enumerated, will give the same angular 

 velocity, as their respective masses acting at the 

 center of percussion or gyration : it is therefore the 

 masses themselves reduced to the distance from the 

 center of motion, at Avhich, if a weight be applied, 

 to act as a power for overcoming a resistance, this 

 p will be so much in addition to the mass to be 

 moved by that weight, and must therefore be con- 

 sidered in computing the effects of all machines 

 after they acquire a velocity. The ilse of these re- 

 suits Aviil appear in the following problems : 



Prob. 12. Let AB be a beam of equal thick- 

 ness, whose MTiglit call W, 

 and whose center of motion C 



C, is in the center of the beam. 

 Then if P be a given weight, 

 acting as a power to move 

 the weisrht .r ; the value of 

 vT is required wlien its mo- 

 mentum \s> the greatest pos- 

 sible. 



Since 



