BRIDGE. 



511 



of the current just under the bridge. But if a body 



fall 11 feet in a second of time, it acquires a vel.ieity 

 of la feet per second, and the heights are as the 

 squares of the velocities; wherefore, in order to pro- 

 duce the velocity r, we must suppose a fall from a 



>'* r' . , 



height = or expressing v in reel, and neglect- 

 ing that small fraction, whereby the fall of a heavy 

 body in one second exceeds 16 feet. 



But when water is forced from a larger channel 

 through a smaller passage, it is observed, that the 

 stream thani.;!i this pa-.sageis contracted. This con- 

 traction has been variously stated. It isprobable, that 

 the ratio of the diameter of the contracted stream to 

 that of the passage, is that of 4 to 5, or .8 to 1, ac- 

 cording to Bossut, Michelotti, and Venturi. 

 Buat gives - (i to !>, or .66$ to 1. 

 And Newton 21 to 2.1, or .84 to 1. 



Consequently, iff express the breadth of the wa- 

 ter-way between the piers, yC is the water-way 

 contracted ; take b the breadth of the channel, 



.5 h 

 *c:o::v: -7 v the velocity in the contraction ; 



and to produce this velocity, we need a height, or 

 fall, of - 



4c 



64, and the difference between that 

 and the former, or that which produces the original 

 velocity v, will be j-^- ~ the fall sought ; or 



4.8. c 



l) sl will also be a theorem for it, which 



in H) !>r thu - rxplr 



Add uni- fourth lii the lirrndth of tin- river, anil di- 

 vide tli>- sum In/ I/if leiitfr-irii / /. / I/if tirc/ir* ; fnnn 

 the xi/iiiiif of t lie i/miiieiit sulilnicl u.iiti/ ; m 



the remainder '// <//r xi/i/m //</// part i,f the 



mean velocity of-tk *in-<ur '</< in feet. 



Upon tlua principle, the following Table is con- 

 structed. It is not so complete as could be wished, 

 for a great deal depends on the depth of the river ; 

 the eikct of which is not so easily ascertained, and 

 the due consideration of it would extend our investi- 

 gations much further than the present subject would 

 warrant. We may find another opportunity to com- 

 municate some further researches on this ^natter ; 

 and, in the mean time, what we give here will, we 

 think, be of no s.mall value to the engineer and 

 practical bridge-builder. We have given a separate 

 column for the usual designation of the stream, and 

 for the nature of the bottom, which will just bear 

 the velocities expressed in the first column, that the 

 use of the Table may be extended and facilitated. 

 For, by this means, a look at the bottom will deter- 

 mine the state and velocity of the river, without the 

 necessity of measuring it. We next give the head 

 or fall produced by various obstructions, and the ve- 

 locity thereby acquired, from whence we are enabled 

 to form an idea of the action likely to take place up- 

 on the bottom. 



Theory. 



The rise of Water produced by Obstructions to the Current, as square ended Piers, or abrupt Projections. 



