BRIDGE. 



The depth cut in the uniform stratum will not, 

 ' indeed, be quite so great as this ; for the matter ex- 

 cavated will be thrown ap as a bar across the river 

 below the bridge, and will add to the depth by 

 heightening the surface of the water. 



The left pier, then, which is only founded two 

 feet under the bed, may stand well enough, but the 

 right pier is in manifest danger, being undermined 

 nearly eight inches. It must therefore be laid deep- 

 er. It will not be safe, however, in proceeding 

 deeper with the foundation, to expose the smallest 

 part of the clay ; for that will move off with a less 

 velocity of current than the gravel or pebbles, and 

 the pier will be still further endangered. Our Table 

 gfiews us, that it will not bear one-third of the velo- 

 city of this stream, and, consequently, runs the risk 

 of being excavated to a great depth indeed. The 

 only safety is in the gravel rolling into the hole thus 

 formed, and ultimately stopping it, not, however, 

 without leaving the pier in a dangerous situation. 



Suppose further, that the river is liable to floods, 

 and that, from observations of its higher marks, it is 

 thought that the channel may be in that case 200 

 feet wide and 6 feet deep, and the progress of the 

 freshes about S{ miles per hour. What will be the 

 consequence of such an accident happening after the 

 bridge is built over it ? 



If we take the depth of the river at 6 feet on an 

 average, the water-way under the bridge is only ^, 

 and it is probable that the diminution of depth to- 

 wards the shores will be made up by a greater depth 

 in the channel, suppose 9 feet : This would encroach 

 on the crown, and place the bridge in a still more 

 dangerous predicament. Yet adhering to the sup- 

 position of an obstruction of |, we find, that for a 

 velocity of 5 feet (3.4 miles), the head is 3.950, or 

 about 4 feet, and the acquired velocity 16j- feet per 

 second. This will produce an absolute cataract, and 

 will sweep out stones, gravel, and clay, to such a 

 depth, if continued even for a short time, as will un- 

 doubtedly destroy the structure. A pavement, or 

 even an inverted arch, will be an ineffectual preventa- 

 tive, in a case like this. But that we may see the 

 result more distinctly, 



Let us state the general depth 

 Add for obstruction or . . 



"U775 



For contraction J or 2.44 



12.19 

 This gives the depth under the bridge when 



the general velocity is restored, vi/.. 5 feet. 



Add $ to bring it to tenor velocity 8.09 



It will cut in the pebbles till the depth ii . . 20.28 



But there is only 9 



So that it cuts below the bed 11.28 



But as there is only 3 feet of pebbles, it passes to the 

 clay ; and as this will not bear more than f of the 

 common velocity, the river will cut in it until the 

 depth be 60.84, which is far below any security that 

 can be given to the structure, without a total change 

 of the foundation. 



We assumed, for the breadth of the actual water- 

 way in the above Table, a rate of contraction, which 

 is much the same as that observed in the diameter of 

 a jet from an orifice in a thin plate. This may be 

 going too far, but we think it advisable to keep the 

 builder on the safe side of the limits of practicability. 

 Square ended piers, and abrupt projections, are likely 

 to produce as great a degree of contraction, especial- 

 ly when the river runs in floods, the only case that is 

 particularly deserving of attention. 



But the discharge through the arches will be ma- 

 terially improved, by forming the pien with pointed 

 sterlings, and otherwise adapting them to the figure 

 of the stream. In rivers, where the arches are wide 

 in comparison of the depth of water, the contraction 

 does not appear to amount to a fourth of the above, 

 or one twentieth of the whole water-way. And in 

 this, we are confirmed by the experiments of Eytel- 

 wein and Bossut. The former of whom states the 

 contraction, in such a case as this, to be from 8.02 

 to 7.7, or nearly T 'r- 



We have, therefore, calculated the following Table 

 upon the principle of a contraction of $ ; and con- 

 ceive, that when circumstances are most favourable, 

 allowing for the additional friction caused by the ob- 

 struction, &c. it will be found to come exceedingly 

 near the truth. 



The Rise of Water pmduced by Obstructions to the Current, when formed to diminish Contraction, as 



Piers with pointed Sterlings, cj-c. 



