1512
THEORY AND PRACTICE OF ENGINEERING. Book IE
but use has sometimes been made of them to bind together the abutments with the walls ofthe shoulder. It is doubtless the most dangerous of all: setting off from the starling, thewater rose considerably as far as the angle of the shoulder, where it formed a fall strongerthan in all the other experiments, and the bottom of which was lower than the general levelof the current: the lateral current, obliged to turn itself, was accompanied on each sideby two others; the one joining the pier was weak, the other, but little elevated at first, soonacquired more volume, because it was raised by the principal current, and was not loweredbut at a considerable distance down the river.
The eighth experiment, fig. 2759. The starling of the pier had the same form as fig.2758.,but we have supposed here the springing of the arches surmounted by the current; theeddy was also very considerable, and the currents which resulted from it diverged almost asmuch as in the first experiment; thefall was very strong and very wide,and of the three separate currentswhich were formed on each side,those which joined the pier werethe least elevated ; they were all con-founded together at some conside-rable distance.
We see by these experiments thatwhenever the faces of the starlingare united to those of the pier by acurve which is tangent to them, andthat the water does not surmount thespringing of the arches, the fall is notformed at the shoulder, but two othercurrents are produced by the side ofthose which envelope the pier, whichare not very rapid. The under-mining then is not much to be fearedin this case, the less so as the mostrapid currents are those which aremost removed from the pier : we mayalso remark that the elliptical formhas great advantages over all theothers, and occasions contractionmuch less considerable, because the lateral currents diverge at much less distances.
With regard to starlings the plan of which is triangular, the equilateral triangle ismuch to be preferred to the rectangular, which presents an obstacle almost as great asthe rectangular pier, and is perhaps still more dangerous, the greatest fall takingplace at the angle of the shoulder, whilst in the rectangular pier it is a little removedfrom it; if right faces are used, the equilateral triangle must be preferred, with theprecaution of rounding the angle opposed to the current, if there be any fear for its solidity ;the most preferable of all is the equilateral triangle mixtilinear; it unites the advantagesof producing the least contraction and the least undermining possible, with that of presentingsufficient solidity to the projecting angle, since this angle is measured by the third of itscircumference; the oval pier is the only one which occasions a less considerable contraction,and which may be preferred on this account.
The above experiments were made on a current where the rapidity was 3 metres9 centimetres per second: as rivers have still greater in their overflows, two otherexperiments with a velocity of 4 metres 87 centimetres were made.
In the first (fig. 2760.) the base of the starling was formed by two arcs equal to the sixthof the circumference. The eddy produced at the meeting of the pier rose to a heightnearly twice as great as that which had taken place for the rapidity of 3 metres 9 cen-timetres, and although there was no fall, the inclination formed along the faces of the pierswas much more rapid: it did not, however, extend beyond the extremity of the squarebody, as may be judged by the profile eagf; this singular effect, which is observed in allsimilar circumstances, arises from the water being forced to flow, first with a considerable-in-clination, in virtue of which it can attain a velocity relative to the diminution of the sectionwhich the body of the pier causes it to experience, and when, on arriving below the bridge,the section widens, the velocity becomes what it was, and the water remounts almost tothe level it had at first, so that for each point the inclination of the fluid has precisely thevalue which agrees with the corresponding velocity.
This experiment agrees with an observation made at the Bridge de la Drome by M.Montluisant, engineer of the Pouts et Chaussees. He marked the trace left by the waters onthe surface of the piers on the starlings on each side after a flood, and found that the water,which had risen to nearly the same height on both starlings, was lowered about 1 metre 5centimetres, at the angle of the shoulder of the one against the stream, and along the square