39

Then by the formulae in the subsequentpart of this work, and by a table of sines,tangents, &c.

y Tang. <p _ 250 x. 1257 250 x ,1275.

% “» Log. Tang. (45° + m Log. Tang. 48°„35' 2.3025 x . 054464

= 250.655.

j _ y_250

_ m Cos.pLogTTang.(45° + J ?) = 2.3025 x .99218 x .054474 =2009-25.

= _y__ 250 i

m Log.Tang. (45° + £p) — 2.3025 x.054464 — 19 -56-

x _y V or.Sin. <p _ _ 250 x . 0078126 __

" m Cos.fLog.Tang.(45°+ 2.3025 x .99218 x .054464 15-69

„# = _ V J _1627

*t> -----

J —cos.plog.tan.(45+ £?>)—g 111.488 — 54.083 = 28.342

y

These values are more easily obtained■ from the table of the dimensions of a ca-tenary as follows :

As tab. y *. tab. z : • the given y the re-

. . tab. z

<i uired *=

By the table -at 7M0' = 1.00262a =

J y

1,00262 x 250 = 250.655.

* y is taken at 250 instead of 280;. for it is better toreduce the span 60 feet, and have the side of the piervertical, than to increase it 60 feet in order to have thepier batter 30 feet.

t See the formula when y and <p are given in thiswork.

D 4