ON HYDROSTATIC INSTRUMENTS, AND HYDRAULIC ARCHITECTURE; 313- 



amounts to several feet. But in general, the velocity of a river is sufficient to 

 produce a gradual transfer of the particles of its bed, which are shifted slowly 

 downwards, towards the sea, being occasionally deposited iu those parts 

 where the water has least motion, and serving at last to form the new land, 

 which is always advancing into the sea, on each side of the mouth of a large 

 river. It has been recommended, as a good form for a navigable river or 

 canal, to make the breadth of the horizontal bottom one fifth of that of the 

 surface, and the depth three tenths. (Plate XXI. Fig. aas.) 



If a canal or a reservoir were confined by a perpendicular surface of boards* 

 and it were required to support it by a single prop, the prop should be placed, 

 as we have already seen, at the distance of one third of the whole height 

 from the bottom ; but it would be always more convenient in practice to fix 

 the side of the reservoir at the bottom, than to allow the whole pressure to be 

 supported by the prop, and it might also be strengthened by means of ribs, 

 thicker below than above, so as to produce an equal strength throughout, 

 wherever the prop might be placed: but if the side were formed of a single 

 plank, of unifonn thickness, the strain would be most equally divided by 

 placing the prop very near the middle of its height. 



The strength of the materials employed for flood gates and sluices requires- 

 to be determined according to the principles, which have been laid down, in 

 treating of the passive strength of substances used for purposes simply me- 

 chanical ; but the calculations become in this case much more Intricate. Thus, 

 if we have a circular plate or plank, of a uniform elastic substance, constituting 

 the bottom of a pipe or cistern, and simply supported at the circumference, 

 a very complicated calculation is required for determining the proportion of 

 its strength to that of a square plate of the same breadth, supported only at 

 two opposite ends, since at each point of the circular piece, there are two cur- 

 vatures which require to be considered. The square plate will support a 

 column of fluid twice as heavy as the weight which would break it, if placed at 

 its centre; and if I have been correct in the calculation, a circular plate will 

 support a height of water nearly sixteen sevenths as great as a square plate. But 

 for ordinary purposes, it will be sufficient to consider the strength as derived 

 only from the resistance opposed to the flexure in one direction, since the addi- 

 tional strength, obtained from the lateral supports, may very properly be neg- 



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