ON HYDROSTATIC INSTRUMENTS, &c. 239 



tice 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 uniform 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 

 mechanical ; 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 curvatures 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 additional strength, obtained from the 

 lateral supports, may very properly be neglected, as only assisting in afford- 

 ing that additional security which is always necessary, to compensate for 

 any accidental defects of the materials. It has been asserted that the 

 strength of a square plate is doubled when it is supported on both sides ; 

 but this appears to be a mistake. 



We may, therefore, be contented with determining the strain on the ma- 

 terials in that direction in which they afford the greatest resistance, either 

 from the shorter distance between the supports, or by the disposition of the 

 fibres ; and it will be always most eligible to combine these circumstances, 

 so that the fibres of the wood may be arranged in the direction of the short- 

 est dimensions of the sluice. If a sluice be supported above and below 

 only, the greatest strain will be at the distance of about three sevenths of 

 its height from the bottom ; and it is at this point that the greatest strength 

 is required. But if the boards forming the sluice be fixed across it, in hori- 

 zontal directions, their strength must be greatest at the bottom. (Plate 

 XXI. Fig. 283.) 



In the construction of flood gates, the principles of carpentry must be ap- 

 plied in a manner nearly similar to that which serves for the determination 

 of the best forms of roofs. The flood gates, if they are double, without a 

 solid obstacle between them, must meet at an angle : and when this angle 

 is very open, the thrust against the walls or hinges must necessarily be very 

 great. If, however, the angle were too acute, the flood gates would require 

 to be lengthened, and in this case their strength would be far more dimi- 

 nj^hed than that of a roof similarly elevated, since the hydrostatic pressure 

 acts always with full force in a perpendicular direction. The thickness 



