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“ and in the same proportion of parts,“ neither art nor even nature herself can“ go beyond.”

If the weight of the roadway and incum-brances be omitted in the calculation, andtheangles, at the points of suspension, be takenat 7° 10' as the maximum angle or hill for aroad-way, and 224000 ounces the practicalstrength per inch square of iron, being one-fourth of the breaking strength, and 54.083ounces the weight of a foot linear of ironinch-square, then the ordinate becomes515.36* feet; and if the ordinate be given,viz. 250, then the smallest angle becomes2° 44', affording an ascent so small as to beunobjectionable in any roadway; so thatnature has limited, under these circum-stances, the span of a bridge by suspen-sion to 1080.72 feet f, at a maximum

* See formulae y cos. $ log. tang. (45° + -| <f>)

g

and cos. <f> log. tang. (45° + \ <p — j~

f The distance between the points of suspension ofthe proposed bridge at Runcorn is 1000 feet, the angleof the catenary, with a horizontal line, 11° # 15', con-sequently the deflection would be 100 feet, which, added

C