2Sx. Lot the surface bo a segment of a sphere, with its vortex down* 

 wards. 



Here y d 2 r tf.r, .*. pressure 2 T r 11. (fi .r). d x *2. <~c r (h x 



f A**) ; and for the whole segment A- k, ,'. pressure = n- rh*. 



4. Upon the principle that fluids press equally in all directions, and in 

 proportion to their perpendicular depths, depends the principle of tho 

 hydrostatical paradox or hydrostatic bellows. 



In the hydrostatic bellows, as the urea of the orifice of the pipe : area 

 of the bellows board : : weight of the water in the pipe above the bellows 

 board I the weight sustained on the board. 



Cor. Supposing a given quantity of fluid to be poured into the tube, to 

 determine how much the weight will rise. 



Let x required height, x and y the area of the sections of the tube 

 and bellows, and let the quantity poured into the tube lx t 



then z ' . 



* 4- y 



5. If two fluids communicate in a bent tube, their perpendicular alti- 

 tudes, above the plane where they meet, are inversely as their specific 

 gravities. 



Hence the same fluid will stand at the same altitude on each sido. 

 Thus water may be conveyed by pipes from a spring on the side of a hill 

 to a reservoir of equal height on another hill. 



For Centre of Pressure, see Centre. 



.A few practical inferences from the foregoing propositions. 



1 . In a vertical gate, dam, or sluice exposed to the pressure of water, 

 the pressure on a square foot at the depth of d feet 1000 d in ounces. 

 And if it be rectangular and b its breadth, and D its depth in feet, the 

 pressure by Art. 2. EJC. 2. = LOOO X | 6. D = .000 X b D* in ounces. 



2. If the transverse section of a canal be in the form of a trapezium, 

 widest at the top, tlu-n if B and 6 be the breadth at; the top and bottom 

 respectively, ;>ih in feet, and it be required to find the pres- 

 bure on agate, which, standing across the car. a!, would darn the water 

 up, we have area of trapez. | B -f- -b. d ; and depth of centre of gra- 



26+~B . d . 6 -4- B ,. 



vity = ^ ~ j . the whole pressure in ounces 500. ~ . d*. 



3. B-f 6 



M. The strongest angle of position for a pair -of gates for the lock of a 



-rsuialor riv<T -- 100. 28'. 

 115 



