59

or a parabolic, the difference will be verytrifling.

By the parabolic, B w = 159By the catenarian, B w = 163By the parabolic, uO = 120.69By the catenarian, v O = 120.86

Let I B W K be a bearing pier, and the Fig. ft.triangle BIA similar to the triangle BDL,

B D and B I homologous sides.

It is manifest that the smaller theangle (D B C = D B L) the catenarymakes with a horizontal line, the greaterwill be the lateral force represented by B I,and the smaller the bearing force repre-sented by I A. And as the pier B I ishigher or lower, these measures will in-crease or decrease.

Let the bridge, including its incumbentweight, weigh 1175 tons, as before; and leta foot cube of the stone of which the pieris to be built weigh J36 lbs. If the bridgebe 30 feet wide,

1175 X 2240 (lbs. in a ton) „

30 X 136 —

Then, if the pier be one foot wide it would