87

SECT. 4. THE FORCE AND FALL OF THE WATER, &.C.

It must be noted, however, that in determining the bestform of the end of the pier to be a right-lined triangle, thewater is supposed to strike every part of it with the samevelocity: had the variably increased velocity been used, theform of the ends would come out a little curved ; but as theincrease of the velocity in the best bridges is very small, thedifference in them is quite imperceptible.

PROP. XVII.

To determine the Fall of the Water in the Arches.

Having, in the foregoing propositions, treated of the re-sistance made by the piers to the current of water, it will nowbe proper to contemplate the effects of that resistance, and ofthe contraction of the passage they produce in the water-way. These effects are, a fall, or sudden steep descent, andan increase of velocity in the stream of water, just under thearches, more or less in proportion to the quantity of the ob-struction ; being somewhat observable at the place of allbridges, even where the arches are very large and the pierssmall, but in a high and extraordinary degree at Londonbridge , and some others, where the piers, and the sterlings,are so very large, in proportion to the arches. Now, in anopen canal or river, an equal quantity of water passing inevery part, in tlic same time, if in any part the passage benarrower, there, the bottom continuing the same, the velo-city of the stream must be so much the greater, and a corre-spondent rise in the surface must also take place, to producethat increased celerity. Similar effects also occur in a riverwhen any obstacles, as the piers of a bridge, are placed inthe way of a stream. Tins is resisted and obstructed by thepiers; of course the water rises against them, and conse-quently, the .stream from thence descends the more rapidly.And this is the case, not only in such canals or rivers wherethe stream runs always the same way, but in tide rivers also,both upward and downward. During the time 6f flood, when