UTILITY OF HYDROSTATICS. 



tiori of the hydrostatical paradox, namely, &quot; that 

 a quantity of fluid, however small, may be made 

 to counterpoise a quantity, however great.&quot; 

 Thus, if to a wide vessel AB, we attach a tube 

 CD, communicating with the vessel, and pour 



Fig. 4. 



water into it, the water will run into the larger 

 vessel AB, and will stand at the same height C 

 and G in both. If we affix an inclined tube EF, 

 likewise communicating with the large vessel, 

 the water will also stand at E, at the same height 

 is in the other two ; the perpendicular altitude 

 eing the same in all the three tubes, however 

 imall the one may be in proportion to the other. 

 This experiment clearly proves that the small co 

 lumn of water balances and supports the large 

 column, which it could not do if the lateral pres 

 sures at bottom were not equal to each other. 



Whatever be the inclination of the tube EF, still 

 the perpendicular altitude will be the same as 

 that of the other tubes, although the column of 

 water must be much longer than those in the up 

 right tubes. Hence it is evident, that a small 

 quantity of a fluid may, under certain circum 

 stances, counterbalance any quantity of the same 

 fluid. Hence also the truth of the principle in 

 hydrostatics, that &quot; in tubes which have a commu 

 nication, wlielher they be equator unequal, short or 

 oblique, the. fluid always rises to the same height.&quot; 

 From these facts it follows, that water cannot be 

 conveyed by means of a pipe that is laid in a re 

 servoir to any place that is higher than the reser 

 voir. 



These principles point out the mode of con 

 veying water across valleys without those expen 

 sive aqueducts which were erected by the an 

 cients for this purpose. A pipe, conforming to 

 the shape of the valley, will answer every pur 

 pose of an aqueduct. Suppose the spring at A, 

 fig. 5, and water is wanted on the other side of 

 the valley to supply the house H, a pipe of lead 

 or iron laid from the spring -head across the val 

 ley will convey the water up to the level of (he 

 spring-head ; and if the house stand a little lower 

 than the spring-head, a constant stream will pour 

 into the cisterns and ponds where it is required, 

 as if the house had stood on the other side of the 

 valley ; and, consequently, will save the expense 

 of the arches BB, by which the ancient Romans 

 conducted water from one hill to another. But, 

 if the valley be very deep, *he pipes must be 

 made very strong near its bottom, otherwise they 

 will be apt to burst ; as the pressure of water 

 increases in the rapid ratio of 1, 3, 5, 7, 9, &c. 

 and is always in proportion to its perpendicular 

 height. 



3. Fluids press in all directions, laterally and 

 upwards, as well as downwards. That fluids 

 press laterally may be seen by boring a hole in 

 the side of a cask containing any liquid, when 

 the liquid will run out in consequence of the 

 lateral pressure. The upward pressure is not 

 so obvious, but is clearly proved by the following 

 experiment, with an instrument generally termed 

 the hydrostatic bellows : This machine con 



sists of two thick oval boafds. about 13 inches 

 long and 16 inches broad, united to each other 

 by leather, so as to open and shut like a pair of 

 common bellows, but without valves. . Into this 

 instrument a pipe B, several feet high, is fixed 

 at D. If we pour water into the pipe at its top 

 C, it will run into the bellows and separate the 

 boards a little. If we then lay three weights, 

 each weighing 100 pounds, upon the upper 



