HYDROSTATICS. 



27 



them through plants. The juice, it is 

 true, cannot be so carried from a lower 

 to a higher level in a capillary tube, and 

 flow out from the top ; but it may be 

 carried upwards in one, and forwards 

 into others, partially oblique, and 

 from these it may be carried upwards 

 again in a third set of tubes. 



Spongy bodies act in all probability 

 on liquids in the same manner, by 

 means of a great number of extremely 

 small capillary tubes, of which their 

 substance is entirely composed. 



The attraction, by means of which 

 capillary tubes and plates nearly touch- 

 ing, act on fluids, may be seen very 

 easily by placing a drop of water upon 

 any 'surface which, from being oiled, 

 or from any other cause, cannot be 

 easily wette'd. It assumes a round- 

 ish form. If over this you hold any 

 flat surface, easily wetted, you will 

 perceive that, when it is brought near, 

 but not touching, the upper part of the 

 drop rises to meet it, and by moving 

 the surface to a greater distance the 

 drop becomes lengthened out, broader 

 on the two surfaces, and narrow in the 

 middle. If the second surface, instead 

 of being held parallel to the first, is 

 placed upright upon it, and brought 

 near the side of the drop, the water 

 is drawn towards it, and stands up 

 against it in the corner with a hollow 

 surface ; as in a glass containing any 

 liquid formerly mentioned. And in 

 this manner, when any vessel is nearly 

 full, but not overflowing, the liquor 

 may be made to run over, by placing 

 any body upon the top and leaning 

 over the edge, so that it touches the 

 liquor and raises it to that edge. 



CHAPTER IX. 

 Mathematical Illustrations *. 



1. Let A B C D (/^.27.) be the sec- 

 tion of a vessel filled with any liquid ; 

 the pressure of the liquid upon the 

 base B C, is measured by the area 

 of the base multiplied into the alti- 

 tude A B. Thus if the figure is a 

 cube, the pressure is the weight of 

 a bulk of the liquid equal to the cube 



The foregoing Chapters contain the science 

 adapted to readers who are unacquainted with the 

 Mathematics. These may pass over this concluding 

 Chapter. 



of B C : if a rectangular parellelo- 

 piped, the presssure is equal to B C 2 



fiff. 27. 



x A B the depth of the liquid: if a 

 cylinder, it is B C 2 x .7854 x AB : if a 

 cone, whose base and altitude are the 

 same with those of the cylinder, the 

 pressure is the same : if the frustrum 

 of a cone F G B C, or B C O P, the 

 pressure on B C is still the same as 

 that of the cylinder A B C D, as long 

 as B C, the base, and B A, the alti- 

 tude, continue the same. 



2. If there are two vessels of the 

 same figure but of different depths and 

 bases, and filled with different fluids, 

 let D and d be the depths, B and b the 

 area of the bases, G and g the specific 

 gravities of the fluids : then the pres- 

 sure upon B is to that upon b as D x 

 B x G to d x b x g. 



3. If in any vessel there be strata of 

 the thickness F F' F", &c. of fluids, 

 whose densities are D, D', D", &c., the 

 pressure of the whole strata on the 

 area B of the bottom, is equal to B x 

 (D x F + D' x F' + D" x F" + , &c.) 



4. Let there be a perpendicular- 

 sicled vessel, that is, a vessel whose 

 sides, if planes, are at right angles to 

 the base, and if curvilinear surfaces, 

 have all their tangents in planes at 

 right angles to theT base, and let the 

 vessel be filled with any liquid ; if a be 

 the height of the liquid, p the perimeter 

 of the vessel ; the pressure on the whole 

 perpendicular sides, that is, the whole 

 perpendicular surface, is the weight of 

 a rectangular prism of the liquid 



whose base is a x | and altitude is 



a; therefore the pressure is . If 



the vessel be a cube, the whole la- 

 teral pressure is 2 a 3 , and the pressure 



g3 



on each side , or half the pressure 



on the base. If it be a cylinder, whose 

 diameter is d, the lateral pressure is 



