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Tracts on vaults and bridges : containing observations on the various forms of vaults; on the taking down and rebuilding London Bridge : and on the principles of arches: illustrated by extensive tables of bridges : also containing the principles of pendent bridges, with reference to the properties of the catenary, applied to the Menai Bridge : and a theoretical investigation of the catenary / Samuel Ware
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171

eg : tg i: y : z and eg : -J- F' tz : : y : x, or

c : t : : y : z, and c 1 : F l tz i : y : x

From the first of these proportions, we

i t k

nave, — = —

7 c y

t 3

or, — = —

C f

or, by taking 1 from each side,

t 1 —c* z 7 —jr*

but

z a ~y 2

f

t'-CP

or,

r

X*

7

x

and from the second,

F Hk _ x

c* j

But from the preceding equation,

X

y

F ‘tk

C

or F l tz — c^/f _ c %

Hence, by taking the fluxion of each side,

cti

tz

V>

Ct

Vt l

 
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