484 



HYDRODYNAMICS. 



merits and 

 Kxpcri- 

 ments. 



Hydtostati- either lose its shape, or be broken to pieces ; but if 

 cal Inbtm- t h e f orce w jt|, which tlie body is pressed is applied 

 to every part of the body, it will preserve its form if 

 it is soft, and will not be broken if it is frangible. 

 Hence it follows, that if any body is exposed to a 

 pressure sufficiently powerful to change its shape or 

 crush it to pieces, and if it preserve its form and its 

 integrity under this pressure, we are entitled to infer 

 that the pressure is equal in every direction. 



Let a piece of very soft wax, of an irregular shape, and 

 an egg, be placed in a b.'adder filled with water. Let the 

 bladder be then laid in a brass box, and a cover of 

 brass put upon the bladder, so as to be entirely sup- 

 ported by it. If a hundred or a hundred and fifty 

 pounds weight be laid upon this cover, so as to press 

 upon the bladder, this enormous force, though propagat- 

 ed through the fluid, and acting upon the soft wax and 

 egg, will produce no effect. The egg will not be bro- 

 ken, nor will the wax change its figure. 



Apparatus 

 for illustra- 

 ting the 

 doctrine of 

 pec. ric gra- 

 vities. 



PLATE 

 CCCXVII. 



Fig 8. 



6. Apparatus for Illuslr>iling the Doctrine of Specific 

 Gravities. 



In order to shew that when a solid body is immersed in 

 a fluid, the loss of weight which it sustains is equal to 

 the weight of the water which it displaces, or of a 

 quantity of water of the same bulk with the body, 

 the following very simple apparatus has been em- 

 ployed. 



A cylindrical or cubical body of any kind, either en- 

 tirely solid, or made hollow and loaded within, so as 

 to sink in the fluid, is exactly fitted to a hollow cylinder 

 or cubical vessel, so that the solid contents of the hollow 

 cylinder or cubical vessel is exactly equal to the solid con- 

 tents of the cylindrical or cubical solid. The cylindrical 

 or cubical vessel is then suspended to the hook of a hy- 

 drostatic balance, or any other balance, and the solid cy- 

 linder or cube is suspended to a hook in the bottom of 

 the cylindrical or cubical vessel. Weights are now put 

 into the opposite scale of the balance till an equilibri- 

 um is produced in air. Every thing remaining in this 

 situation, the solid cylinder or cube is completely im- 

 mersed under water, and consequently the equilibrium 

 is destroyed ; that is, the scale of the balance to which 

 the apparatus is suspended will require to have added 

 to it a weight equal to the loss of weight sustained by 

 the solid, in order to restore this equilibrium. By fill- 

 ing with water, therefore, the cylindrical or cubical 

 vessel, it will be found that the equilibrium is exactly 

 restored. Hence it is obvious to the eye, that the loss 

 of weight sustained by the solid is exactly equal to the 

 weight of water displaced. 



7. To make a Body lighter than Water lie at the bottom 

 oj a Vessel Jltted with Water. 



To make a We have seen in Prop. IV. p. 430, that when a body 



erth-in wa~ ^ a ^ ess s P ec ^ c gravity than a fluid, it will float upon 



ter lie at the tne sur f a ce of the fluid, as it is pressed upwards with 



bottom of a a force greater than its own weight. If by any means, 



vessel HUed however, we can prevent the upward pressure from 



with water, acting upon the lighter body, it is manifest that it must 



remain at the bottom of the vessel in the same manner 



as it would rest upon any other body in the open air, 



for the body is not only pressed down by its own weight 



but by the weight of the superincumbent fluid. 



In order to shew how to prevent the upward pres- 

 sure from acting upon the solid, let us take two pieces 

 f wood planed perfectly flat and smooth, so that no wa- 



lixperi- 



na-iits. 



ter can get in between them when their smooth surfaces, Hydrostati- 

 are put together. If one of the pieces of wood is ce- cal Ill5t "- 

 mented to the bottom of a glass vessel, so as to have its " 

 smooth side uppermost, and if the other piece is pla- 

 ced above it, and held in that situation till the vessel is 

 filled with water, it will be found to lie as quietly and 

 firmly as if it were a plate of lead or stone. If the 

 edge of the upper plate, however, is raised in the 

 slightest degree, so as to allow the water to insinuate 

 itself between the plates, the wood will instantly spring 

 to the surface. 



This experiment is sometimes made in a different 

 manner. A flat and smooth brass plate is fixed at 

 the bottom of the vessel, and a large mass of cork has 

 a thin smooth brass plate fixed to its bottom, so that 

 the specific gravity of the cork and its brass base may be 

 much less than that of water. The brass plate on which 

 the cork rests is then placed on the fixed brass plate ; 

 and when water is poured into the vessel, the cork will 

 remain at the bottom. The two brass plates should be 

 oiled a little on their touching surfaces, and should be 

 ground upon one another, but not very accurately, for 

 in this case the force of cohesion would prevent their 

 separation, independent of the weight of the superincum- 

 bent pressure of the fluid ; as it is well known that one 

 brass plate can lift another in the open air, even when 

 it is two or three pounds weight. The experiment as 

 made with the brass plates is therefore not so satisfac- 

 tory as the one with pieces of wood, for the reason which 

 we have now assigned ; and though we are satisfied that 

 the cork and the brass plate are together lighter than 

 water, yet the result appears less striking, as we are al- 

 ways in the habit of seeing brass sink to the bottom. 



A similar result may also be obtained by fixing a 

 glass plate at the bottom of a gkss vessel, using a plate 

 of ivory instead of wood, and pouring mercury into the 

 vessel in place of water. 



8. Experiment for illustrating the parabolic form of a> 

 fluid surface influenced by a centrifugal force. 



Experiment 

 for illustra- 

 ting the pa- 

 rabolic form 

 of a fluid 

 surface in- 

 fluenced by 

 a centrifugal 

 force. 

 PLATE 

 CCCXIII. 

 Fig 3. 



In order to shew that a horizontal surface of water 

 assumes a parabolic form when it is acted upon by a 

 centrifugal force, along with the force of gravity, we 

 have only to take a bucket containing water, whose 

 surface c d is of course horizontal when the bucket is 

 at rest. If by means of a rope R, however, fastened to 

 the handle AB, we give the bucket a rotatory motion 

 round a vertical line, the surface will lose its horizontal 

 form, and the water becoming concave in the centre, will 

 rise round the sides of the vessel, and have its surface 

 of the form of a parabolic conoid, whose section m n o 

 is a parabola. See Chap. I. Prop. 1. cor. p. 427. 



9. Desertion of Dr Hooke's Semicylindrical Counter* 

 poise. 



The principal object of this ingenious contrivance Hooke's H- 

 was to keep a vessel always full of water, or any other micyliudri. 

 fluid, but as it is not only of use in hydrostatical experi- ca 

 ments, but also illustrative of the principles of the equi- *" 

 librium of fluids, we have thought it necessary to give a cccxVii. 

 drawing and description of it in this place. In Fig. 9- p; g .' 9. 

 ABG is a vessel of any form. Upon a horizontal axis 

 C, a semicylinder or a hemisphere, whose section is 

 DEF, is made to revolve, and the weight of the gemi- 

 cylinder is so adjusted that it is exactly equal to the 

 weight of a portion of the fluid of half its magnitude. 

 When the vessel is filled with water, the semicylinder 



