MECHANICS.

H7

by the lever FW, and KP by the lever FG, bothtending to keep the pier in its place, while the forceKQ acts by the lever KG or FY to overthrow it.Farther, though the pier is properly only FGAG',yet it is usual to have it loaded with masonry tothe height K, and even higher, so that its weightis proportional to the rectangle FK. This willgive an equation between the forces, when theiranalytical expressions have been obtained.

Angle UHI=0, and VHI = 20, the area MLOND,

— a 1 , EC — r, make IIU = — , then 1H =

r

2 r cos 0

= Kll.

lienee QK = ^

and

KP =

2 r cos ^

r cos 0 x sin 0 r sin 2 0

Let GK = A, and FG = x,

then the rectangle FK =r k x, and the line that re-

• h X

presents the weight of the pier will be ——-.

Therefore,

A xr

- +2

2 r cos 0*

x x =

r sin 2 0

X h,

and hence, r =- - — + asj —? +- °

2 A cos 0 l sin 20 4 A 1 cos 0 4

This determination of the thickness of the pier,proceeds on a hypothesis usually employed for de-k 2 termining