HYDROSTATICS. 



13 



perpendicular to them, the whole sur- 

 face in each case will be supported. 

 Now we have found before that the 

 whole pressure upon any rectangular 

 figure upright in the water, is the weight 

 of a bulk of water equal to the surface, 

 multiplied by half its depth below water. 

 We can, therefore, see at once the force 

 required to balance the water, and the 

 point where it must be applied. Multi- 

 ply the height of the surface by its 

 breadth, and the product by half the 

 height, (the water being supposed to 

 stand as high as the upper edge of 

 the surface ;) then apply a force or a 

 resistance equal to this weight of wa- 

 ter, in a horizontal line against a point 

 situated two-thirds down the per- 

 pendicular, from the middle point of 

 the upper edge of the surface, the 

 whole pressure of the water will be ba- 

 lanced. Suppose the height and breadth 

 of the sluice or floodgate are equal, it 

 being a square of six feet ; the pressure 

 on it will be 108 cubic feet of water, or 

 about three tons. Aforceofthis amount, 

 then, applied on the back of the sluice, 

 in the middle line, and four feet from 

 the top, will be sufficient to counteract 

 the pressure of the water, without any 

 assistance from the hinges or sides of 

 the gate. 



The strain which the water exerts 

 upon the hinges of the floodgate is the 

 pressure to make it turn round on its 

 lower side ; and it is found by multi- 

 plying one-sixth of the breadth of the 

 gate into the cube of the height, and 

 taking a bulk of water equal to the pro- 

 duct. The pressure which the water ex- 

 erts to open the sate, or make it move 

 round on its hinges, is found by multi- 

 plying one-fourth of the square of the 

 height into the square of the breadth, 

 and taking a bulk of water equal to the 

 product. The proportions of these 

 two pressures may therefore be easily 

 found. They are to one another as 

 one-sixth of 'the breadth multiplied by 

 the cube of the height, to one-fourth of 

 the squares, of height and breadth mul- 

 tiplied together : that is, as one-sixth of 

 the height to one-fourth of the breadth, 

 or as twice the height to thrice the 

 breadth. When, therefore, the gate is 

 a square, the height and breadth being 

 equal, the pressures are as two to 

 three ; and the same gate at the same 

 time has half as much more force 

 exerted to make it open on its hinges, 

 as to make it turn over on its base ; 

 supposing that there Avere either no 



resistance from the hinges, or that 

 there were hinges at the base. Thus, 

 if the gate is a square of six feet, the 

 pressure to turn it on its bottom is 

 one-sixth of 1296 cubic feet of water, or 

 216 feet; and to turn it on its hinge, 

 one-fourth of 1296, or 324 feet. There- 

 fore there will be a force of six tons 

 pressing it round on its bottom, and 

 nine tons pressing it open on its hinges. 



CHAPTER V. 



Specific Gravity The Hydrometer 

 and Areometer. 



WHEX a solid body is plunged in any 

 liquid, it must displace a quantity of 

 that liquid exactly equal to its own 

 bulk. Hence, by measuring the bulk 

 of the liquid so displaced, we can ascer- 

 tain precisely the bulk of the body ; for 

 the liquid can be put into any shape, 

 as that of cubical feet or inches, by be- 

 ing poured into a vessel of that shape, 

 divided into equal parts ; or the vessel 

 in which the body is plunged may be of 

 that shape, and so divided. If the 

 width of the vessel is four inches by 

 three, or twelve square inches, and 

 divided on the upright side into twelfths 

 of an inch when a body of an irre- 

 gular shape, as a bit of rough gold 

 or silver, is plunged in it, every di- 

 vision that the water rises will show 

 that one-twelfth of twelve cubic inches, 

 or one cubic inch of water, has been dis- 

 placed ; so that if it rises two divisions, 

 the body contains exactly two solid 

 inches of metal. And this is by far the 

 easiest way of measuring the solid con- 

 tents of irregular bodies. 



When a body is so plunged, it will 

 remain in whatever place of the fluid it 

 is put in, if it be of the same weight 

 with the fluid, that is, if the bulk of the 

 body weighs as much as the same bulk 

 of the fluid ; for in this case it will be 

 the same thing as if the fluid were not 

 displaced ; and as an equal quantity of 

 the fluid would have remained at rest 

 there, beins; equally pressed on all 

 sides, so will the solid body : it will 

 be pressed from below with the same 

 weight of fluid as from above. But if 

 the body be heavier than the fluid, bulk 

 for bulk, this balance will be destroyed, 

 and the weight of the fluid pressing 

 from above, will be greater than that 

 pressing from below, by the weight of 

 the solid body, which will therefore 



