41

HH be horizontal and EK vertical; AD = a, BD = b,

AH = —-- \- a= c, AE = x, and HE = c — x ;

tan a

EK = (c - x) , sin a ;

» O ^ ^2

and FE 2 = . ar 2 ; the circle FEG = —5- . .r',

a a

t r/i 2

and (65) the pressure on FEG oc.—— . ,v 3 . (c — x) . sin a,

oc x~ . (c — x) ;cor — a: 3 = max.and Qcxdx — 8 x~dx = 0;whence x c = :l r AH.

(19) If a globe, whose radius at the bottom of the sea = a,ascend to the top, the depth being = h ; what will be its dia-meter at the top, and what will be the locus of the extremity ofits radius, the line in which the centre ascends being the ab-scissa.

Let CBD be the surface of the water, EFthe radius of the globe at the bottom; FID,

GKC the curves described by the radii in as-cending. Let i 4 .B = the height of a column ofwater of the same weight as the atmosphere = h !, EF — a,EB = h, BI 1 = x, HI = y. The magnitude of the globebeing inversely as the pressure, h + h 1 : ft + x :: y : a' ;

• • y = 0 • v 77

+ h'

h + X

the equation to the curve ;

and at the surface, when x = 0 , y

= a ■ \/

h + />'h'

The line drawn through A parallel to CD is an asymptoteto the curve.

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