We could wish that what we have said here may in duce persons properly qualified to turn their attention to the subject. We are convinced it is one of the most important departments of the art of bridge-building. INlathematicians have bestowed much time and pains on the equilibration of arches,—a matter about which the common bridge-builder seldom seems very solicitous. We have seen that, in reality, the usual speculations of that kind have hitherto led to no one useful practical result. Nay, if the deductions of the theory were to be followed too implicitly, they may lead, as in the case of the catenaria, and even the flat arch, to the proposing of weakness instead of strength, and craziness instead of stability.
But the security of the foundation is that about which the practical man is, with reason, most solicitous. He knows that it demands his greatest care. An error in that is irremediable, and there it is that his work gene rally fails. Give the ancient mechanician only a place to atand on, and he would have moved the world ; give the mealern engineer only a sure foundation, he will raise a as durable as the materials of which it is composed.
OF TilE STERLING:. OR EXTREMITIES OF THE PIERS The reader must before this have seen, that there would be a great impropriet, in forming the ends of our piers into planes at right angles to the stream ; the water which is thereby shot off atubtly to each side, obstructs the general current by contizcting the section, makes an increase of velocity necessary, which at the same time increases the action on the bottom, and has tens the downfall of the structure.
The bridge-builder, therefore, has in all ages endea voured to obviate or diminish this contraction, by build ing projecting starlings, or breakwaters, towards the stream, the intention, as it were, of splitting the current, and conveying the waters more quietly under the arches. Those which point down the stream, in rivers without reflux, were at first perhaps built only for the sake of uniformity ; for although probably little less im portant than the other, they do not, as they are gene rally formed, seem calculated to serve any good pur pose.
The form of the sterling has given rise to some diS cutsion, and bridge builders do not yet seem agreed on what is the best. For the most part, they have been formed into an isosceles right angled triangle in the horizontal plan, having the right angle facing the stream; from a notion, perhaps pretty general among workmen, that thls is of all angles the strongest. The projecting edge rises perpendicularly till above the surface of the water, and the spring of the arch ; what is higher being merely matter of ornament, need not be mentioned here. At other times, the plans of these cutwaters or sterlings have been lormed into two arches, of 60° each, describ ed from the two angles of the pier, into a semicircle, or sctmellipse, on the conjugate ; or into other and proba bly fanciful figures, as in Plate LXXXI. Fig. 7. Nor
are these different methods without their advocates. Thus it is said for the right angle, that it divides the stream best, and a more acute angle would be too weak ; that the semicircle and semiellipse, are best calculated to resist the shock of a loaded barge, or the like ; and the Gothic intersecting arches, combine in some degree the advantages of both. But it is evident, we think, that if there be any form, which really deserves a pre ference over all others, it must be that which is adapted to the figure of the contracted stream ; and which deli vers the water in such a manner, as totally to fill the breadth of the archway. Unfortunately however, our notions of the motions of fluids are yet so far from being precise, that it is a matter of no small difficulty to dis cover what figure is best adapted to the purpose in view.
That we may have the clearer conception of this mat ter, let us attend a little to the way in which a fluid in motion may be supposed to act upon any obstacle.
The particle moving in the direction EF (Plate LXXXI. Fig. 8.) would strike the pier with the whole of its force, if the end of the pier was in the line AC, and the number of these particles will be as AD ; but when the end is formed into the triangle ABC, the effect of each particle on the plane AB is diminished in the pro portion of the sine of its incidence EFB ; and the ac tion on the face being given, the effect of it in the direc tion BD, or parallel to the axis, will be found by still further diminishing it in the ratio of the sine of obli quity. In the common case then, when the length of the pier is in the line of the stream, the resistance of the pier will be as the square of the sine of incidence, or it will be inversely as the square of the length of the face AB of the pier, that being a straight line. Otherwise, EF represent the absolute force of any particle, draw the perpendiculars, FG, EG, and GH, then FG exhibits the impulse perpendicular to the force AB, and FH the effect of that impulse in the direction of the axis BD ; where, by the way, it may be observed, that if the angles DAB and DBA be equal, that is, if ABC be a right angle, then are FG and GE equal, also FII and HE; so that the absolute impulse on the sides of a rectangular wedge is just half the impulse on its base. NVc might pursue this mode of reasoning much further. We should find among other things, that the absolute im pulse on right lined triangles, is less than on any cur vilineal figure ; that the impulse on cylinders, or the front of half cylinders, is just two thirds of the direct impulse on the base ; that in all other curves, the near er they approach to the right lined triangle, the less is the impulse upon them ; and it is sufficiently evident, that the impulse will be always the less the more acute we make the vertex of that triangle, that is, the greater projection, and the sharper a point we give to the pies'.