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It is usual to make columns and walls di-minish in thickness as they increase inheight; but this case should be an exception;for it is important to reduce the ordinate ofthe catenary as much as possible, becausethe diminution of the ordinate, and, con-sequently, the length of the chain and ten-sion, (the angle being the same,) more thancounterbalances the excess of stone re-quired in a pier whose section is a paral-lelogram above one whose section is thefrustrum of a triangle. Therefore the piershould have perpendicular sides, B I. W K,instead of battering sides O E, as in theproposed bridge over the Strait of Menai.

In the bridge of Salamanca, the bearing

tables, being a similar curve to that of the catenary ofthe bridge, viz. at the angle 7° 10'

Then as tab. 2 y : tab. x :: 2 A I : V N

.2508 : .00787 :: 29 : .29^00787 = 1.4623980 log .

.2508 1.3993275 log.

.0630705 log.= 1.1563 = V N

making the pier at V a little more than one foot higherthan at B.