H I 



515 



product, d is '_>.G7'-'.~j, ami velocity 1 ! fret per 

 |t "" itcuiid, which would rt quire ;l bottom as firm 



liil rock. With good workmanship, however, the 

 pavement would stand a considerable time, especially 

 if the joints were so crretully closed t! mild 



not readily penetrate, and work out tin: liner mute- 

 rials in which the pavement was bcd<l( d : For, al- 

 though the water passes through the arch vvitli this 

 great rapidity, yet the genera! river being in a diflc- 

 t train, and running with a much smaller velocity, 

 will not bring along wilh it much heavier materials 

 than the gravel and pebbles of th~ bed, and t 

 will not be very injurious to the artificial bed at the 

 bridge : For we are of opinion, that it is by no means 

 the action of the water, but rather the attrition, or 

 battering and rubbing of the boulderstones, gravel, 

 and sand, brought down by it, that renders the hard- 

 est rock liable to be cut up by the force of a swift 

 running stream. It is, nevertheless, extremely dif- 

 ficult so to iecure a pavement, or inverted arch, in a 

 river, that the water will not ultimately carry it 

 away, even when the river does not run foul in its 

 freshc?. The great velocity which has been commu- 

 nicated to the river, cannot be supposed instanta- 

 neously to change upon passing the obstruction. 

 Instead of that, we sec a swift current shooting along 

 in the line of the arches for a great way below the 

 bridge, while powerful eddies run up in the line of 

 the piers, casting up at length banks or shoals behind 

 them, which tend, in their turn, to strengthen and 

 prolong the original current and eddy. Whatever 

 pains, therefore, we take to secure the pavement or 

 inverted arch, thisstrong current mustcut up and carry 

 away the materials of the bed behind them ; an ope- 

 ration which, if once begun, must constantly go on 

 with increasing force. The water will have a fall 

 over the lower end of the pavement, and will gradually 

 wash out the foundation of the outer course of 

 stones, which being immersed in water, will not be 

 difficult to move. A few stones dropping out will 

 add to the power of the stream, by roughening the 

 bottom. Course will loosen after course, until the 

 whole presents only a loose mass, ready to be torn 

 up and swept away by the first ensuing flood in the 

 river. 



We could wish that what we have said here may 

 induce persons properly Qualified to turn their at- 

 tention to the subject. We are convinced it is one 

 of the most important departments of the art of 

 bridge-building. Mathematicians have bestowed much 

 time and pains on the equilibration of arches, a 

 matter about which the common bridge builder sel- 

 dom seems very solicitous. We have seen that, in 

 reality, the usual speculations of that kind have hither- 

 to led to no one useful practical result. Nay, if the 

 deductions of the theory were to be followed too im- 

 plicitly, they may lead, as in the case of the catenaria, 

 and even the flat arch, to the proposing of weak- 

 lies; instead of strength, and craziness instead of sta- 

 bility. 



But the security of the foundation is that about 

 which the practical man is, with reason, most so- 

 licitc.-u;:. 1 1 knows that it demands his greatest care. 

 An error in that is irremediable, and there it is that 

 his work generally fails. Give the ancient mechani- 

 cian only a place to stand on, and he would have moved 



the woild; give the modern engineer only a mire I 

 foundation) lie will i HUV as durable astlie v~ -' 



! i.d . (it whi.'h it is i 



OF THE STERLINGS on EXTHF.MITIES OF TIIK Pi, 



The reader must before- this have seen, that there of the 

 would be a great impropriety in forming the ends of sterling, 

 our piers into planes at right angles to the stream ; 

 the water which is thereby shot off abruptly to each 

 side, obstructs the general current by contracting the 

 section, makes an increase of velocity neiv.-.sary, v. !, 

 at the same time increases the action on the bottom, 

 and hastens the downfall ol the structure. 



The bridge builder, therefore, has in all ages en- 

 deavoured to obviate or diminish this contraction, bv 

 building projecting sterlings, or breakwaters, towards 

 the stream, with the intention, as it were, of splitting 

 the current, and conveying the waters more quietly 

 under the arches. Those which point down thir 

 stream in rivers without reflux, were at first perhaps 

 built only for the sake of uniformity ; for although 

 probably little less important than the other, they do 

 not, as they are generally formed, seem calculated to 

 serve any good purpose. 



The form of the sterling has given rise to some 

 discussion, 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 tri- 

 angle in the horizontal plan, having the right angle 

 facing the stream ; from a notion, perhaps pretty 

 general among workmen, that this 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 or- 

 nament, need not be mentioned here. At other times, 

 the plans of these cutwaters or sterlings have been PLATE 

 farmed into two arches, of 60 each, described from I. XXXI. 

 the two angles of the pier, into a semicircle, or serni- ' ; 'o- ' 

 ellipse, on the conjugate ; or into other and probably 

 far.ciful figures, as in 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 semi- 

 circle and scmiellipse, are best calculated to resist the 

 shock of a loaded barge, or the like ; and the Gothic 

 intersecting arches, combine in some degree the ad- 

 vantages of both. But it is evident, we think, that 

 if there be any form, which really deserves a prefer- 

 ence over all others, it must be that which is adapted 

 to the figure of the contracted stream ; and which 

 delivers the water in such a manner, as totally to fill 

 the breadth of the archway. Unfortunately, how- 

 ever, our notions of the motions of fluids, are yet so 

 iYr from being precise, tiiat it is a matter of no small 

 difficulty to discover what figure is best adapted to 

 the purpose in view. 



That we may have the clearer conception of 

 matter, 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 F.F (Fig. 8.) I 1 ' AT* 

 would strike the pi'T with the 't kXXXL 



the end of the pier was in the line AC, and the num- '"' 

 ber of these particles will be as AD ; but when the 

 end is formed into the triangle ABC, the effect of 



