Mechanics.

233

Carriage. (3.) A Carriage upon fourJarge Wheels, of equal Size, is drawn

with

ing perpendicularly, D F will express that with whichit supports A G ; therefore D F multiplied by the Dis-tance from the Fulcrum A, or Lever A E, ought to beL Maximum.

15. Now from the similar Triangles A C B, A D F,

we have CB:BA::DF : F A — — x, also FE =

n

a a — xx, therefore A E — ^ a a — x x -j- — x,

n

which multiplied by D F — x, isAEXDF = x

></'aa — xx -j-— xx, whose Fluxion made equal ton

nothing wilj give x — >/ \aa ± am, as before. Ifthe Angle A D E be acute, the Point E will fall be-tween F and A, and we shall have AE - - x —

n

•J a a — xx and A E X D F - xx—x s/ a a — xx,

n

which fluxed will give the fame Value of x as beforefound.

i6t In each Caso, it is plain x V t ^ ^ ql ^ —•

Sine of 6o°, must be the Maximum, which if substituted

jn the Expression x s/ a a — x x -f- - xx, (where the

Angle A D E is oblique) will give ^. ! l± aam + 2aaK

2 n

— Force of D E which supports the Piece A G: But

jf a/ \ aa + am be put for X in the other Expression

m

n

xx—• s/ a a — xx, we shall have for the said Force

(when the Angle is acute)-— - -,

which is less than the other Forces; and therefore theJatter Position is less advantageous than the former.