As to the point of the pier down the stream, its fi gure must, for the sake of uniformity, be assimilated to the other. It were well if we could in this case ap ply the contrary flexure above mentioned. The same difficulties are not to he dreaded ; and although it may not be easy or agreeable to form it in the horizontal sec tion, yet, by prolonging the tail down the stream fur ther than usual, we will virtually obtain the same thing. The tail of the pier is of less consequence to the stabili ty of a bridge, though it may certainly be contrived So as to facilitate the transmission of the water. Bridges seldom fail on that side ; and as they are usually con structed, there is an eddy below the pier, which, although it obstructs the current, and injures the bottom, yet casts up a shoal below each pier that serves to protect the foundations of the building.
Bridges built in the way we have now mentioned, will appear greatly stronger than those of the usual construc tion; and they will really be so. Independent of their power ot preventing the action on the foundation at the shoulder of the pier, which we have shewn in an early part of this section to be the principal cause of the de cay of bridges, these sterlings will appear stout, curved buttresses, or as it were knees, to support the lofty side wails ; and by expanding the lower courses of the arch, advantage may be taken of the increased base, to cast the vault into a kind of groin, and thus give a greater degree of transverse strength to the whole structure.
This idea of extending the lower courses of the pier, and breaking, as it were, by degrees, the force of the current, is not new, and we do not give it as such. It may be seen with various degrees of perfection in many ancient and modern structures, particularly in the cele brated Pont St Esprit over the Rhone, which probably owes in a great measure its endurance to that expedient. But we wish merely to bring back to the builder a prin ciple, which, in modern times, seems too often to have been lost sight al, and which was, no doubt, originally the result of a successful experience.
When necessity obliges us to form a bridge at a con siderable obliquity to the current of a river, a danger is thereby incurred of producing a gyration on the lee-bow of the piers, which will be attended with all the evil consequences we have already explained. The obstruc tion to the current may be presumed to vary with the cosine of the angle of obliquity, and consequently the additional head must be as the versed sine of that angle.
But if the sides of the river be parallel straight lines, the water-way under the bridge will just increase as the secant of the angle of obliquity, or inversely as the co sine. This will just counterbalance the obstruction caused by deflecting the current, leaving only the reac tion of the bank, and the weather-side of each pier against the stream, to produce the deflection. There will be an accumulation on the one side of each arch therefore, and a depression on the other ; while a strong gyration will take place on one of the shoulders of each pier, and which is likely to be attended with much danger. The water-way of the arch too is likely to be much con tracted by this cause. All these appearances frequently occur, although the bridge appears to pass directly across the stream ; because in such a case the bridge has been designed for the low waters, whereas the stream, when in flood, may have a very different direction. The course of the river therefore, above the bridge, should be carefully attended to, especially when the waters are high, and either corrected, or the position of the bridge adapted to it.
The effect of the gyration at the shoulder of the piers is curious ; and, as it is one of the chief causes of their destruction, it is well deserving of attention. The beds of all rivers are porous, and will therefore be glutted with water ; which again is every where pressed by the whole depth in the river : but at the shoulder of the pier there in a void, so that the bottom at that spot will not have the same vertical pressure that there is every where round it. Water will therefore rise out of the bottom at that place, like a spring or fountain, and so much the more forcibly as the void is deeper. Or, if prevented from issuing, it will exert a strong pressure upwards, upon whatever forms the bottom of the void. Now, this void being sometimes even four or five feet deep, we need not be in the least surprised, that not only gravel and shiver, but even large stones, arc lifted in it, and shoved away by the vertical motion.
For these, and other reasons, it is difficult to ascer tain the exact amount of the obstruction caused by ob liquity. Like every other department of our inquiry connected with hydraulic principles, experiments arc yet wanting to assist us in making this a subject of calculation.