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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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120

Suppose f = 50°, then

cosec. $ cosec. 50° 1.305407

log.tang.(4‘5°+-2-<p) log.tang.70° .438934

= 2.97407.

And suppose <p = 60°, then

cosec. <f> _ cosec. 60* 1.1547

log.tang.(45°+!<$) log.tang.75“ .571947

= 2.01889.

But the true value of

cosec. <p

— m

log.tang.(45°+^4>)

= 2.302585.

Whence 2.97407 — 2.01889 : 60° — 50°: : 2.97407 — 2.302585, or .95518 : 10°:: .671485 : 7° nearly.

Consequently <p = 50 o -f~7 o = 57° nearly.Again, suppose <p = 57° then

cosec. 57 _ ° _ _ 1.192 3 6 3 _ 2,256516

log.tang.73°.30' .528395

And suppose <p = 56°, then

cosec. 56° __ 1.206218 2 343714

log.tang.73° — .514661

Then 2.343714—2.256576 : 57°-2.343T14 —2.302585, or .087138.041129° .041129X60'

56°: 1 °

.041129

2.46774'

.087138

.087138 .087138

28'. Wherefore 9 = 56°4-28'

 
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