Buch 
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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113

Cos. p log. tang.(45°4-^) = ~~ t from

which ? may be found by approximation ;and f being found, c, z, and x may be foundas in Case II.

Note. In this case we must observe that? may have two different values, the onebelow and the other above 56° 28, as willappear from what follows; and as <p mayhave two values, so c, z, and x must haveeach of them two corresponding values.

CASE XIII.

When z and x are given, to find the rest.c

Z

• X

t

Sec.?

y

2 x

2 s + X 1

2 x

2 * + X*

X

Z l - X*

“ lo g'

Z + X

• X

CASE XIV.

When si and y are given, to find the rest.Cot.?log.tang.(45°-f-|f) ~ fromwhich 9 may be found by approximation;

i