HYDROSTATICAL PARADOX, WEIGHT OF THE ATMOSPHERE ETC.. 5 cases. Hence it follows, that a body immersed two inches deep in the sea, will not be pressed on with a greater force than if it were immersed the same depth in a basin of water. I will now endeavour (as briefly as possible) to account for the phenomenon in question.-Let a (in the above figure) be a vessel, be a tube fitted to it, and filled with water to the top, b; the upper stratum of particles, from c to d, will be pressed on with the same force as those from e to c; because the column bc, meeting with these particles at c, presses them outwards or sideways, and, as they cannot escape the pressure, on account of the top and sides of the vessel, they must therefore exert the same force downwards as those from c to e; consequently the bottom, e e, will be pressed on with the same force as it would if the vessel were made of the bulk of e e, ƒƒ, and filled with water to the top. I will now notice the question on the Weight of the Atmosphere (page 332), as it is, in some measure, connected with the foregoing subject; I will also include the following one, and endeavour to answer them both together. How is it that the atmosphere is thicker or more dense in warm weather than in cold, when, from what we know of heat, it possesses the property of rarefying air? To answer these questions I will first give you my opinion of the nature of the heat we receive from the sun. I do not believe that the suu is a body of fire (which is the opinion of many), but that it is an opaque body, like our earth, surrounded by a luminous atmosphere, the rays of light from which, mixing with our atmosphere, produce the heat that we feel; thus, then, the heat we feel, as proceeding from the sun, is not of the * As I never believe any thing, except I am convinced in my own mind of the reasonableness of my belief, I could adduce many arguments in favour of this same nature as the heat proceeding from a fiery body. If we suppose, then, that the rays of the sun, wherever they shine on our earth, possess the property of accumulating the particles of our atmosphere, both questions may be easily answered. In this supposition I must be allowed to differ with C. D. Y., as I think the atmosphere, where the sun shines most, is accumulated, and, consequently, increased both in height and density. I must yet beg a little more room, just to notice the question on the Syphon (page 286). The reason is, because the depth of the water is greater in the long leg than in the short one; it is, therefore, of greater pressure at the extremity of the leg, consequently the fluid descends, because it overbalances the pressure at the extremity of the other leg. As there cannot be a vacuum between the legs, the weight of the atmosphere pressing on the surface of the fluid in which the shorter leg is immersed, supplies the discharge by forcing it up the short leg. If I have stated any thing that is incorrect, nothing would give me greater pleasure than in being set right by some of your better-informed Correspondents. I cannot conclude without bestowing my warmest approbation on your valuable and useful Magazine, for thus encouraging useful and scientific inquiry; for directing the attention of the middling and working classes to subjects which otherwise, perhaps, they would never have thought of; and for affording, to all, a better medium through which to express their wishes, thoughts, and experience, than had existed before its commencement. I remain, Sir, Yours very respectfully, Bath. J. E. COOMBS. SIR, Should the following answers to your Correspondent, + W. X. (p. 285, vol. III.) appear worthy a place in your useful Magazine, I should feel much obliged by their insertion. First. Why an additional pint of water will have the effect of bursting a hogshead filled with that fluid, if introduced by a small tube of sufficient height? No part of any confined body of water (excluding the consideration of its own hypothesis, but will not now take up more of your valuable room than what is necessary to the explanation of the present question; however, should any of your Correspondents deem it requisite, I would gladly resume this subject, and give my reasons and arguments, which would, I think, render the truth of what I have already said beyond a doubt.. 6 HYDROSTATICAL PARADOX, Weight of the ATMOSPHERE, ETC. generally brings with it a quantity of hydrogen, contaminating the whole mine, and preventing the atmospheric current from circulating In these cases, if fire is introduced amongst it before the fresh air is taken from the shaft, an explosion is the inevitable consequence-an explosion of so tremendous a nature, that the 'Land-drainer's strong box,' I am afraid, would not be able to resist it. If I might be allowed to offer a few hints to the ventilators of collieries, they would be your 1. Never allow your air to traverse too great an extent of workings, particularly old ones; but let downcast and upcast shafts be connected by shorter ways than is generally done. Many accidents I could mention have occurred from want of this precaution, and I am afraid the only plea for the neglect that can be made is-the saving of expense. 2. Never trust too much to one furnace. If your mine be foul, divide your air, place two furnaces near your upcast shaft, and keep your two currents from communicating till they have passed over the fire. 3. Make all your air-courses large, Your obedient servant, H- Durham. facts on their minds, before I proceed to the explanation of one of the most singular properties of fluids : of the earth, which constitutes the The force of gravity, or the attraction weight of matter, is only exerted perpendicularly downwards, or in a direction tending towards the centre of the earth; this force produces different effects on a fluid than it does on a solid body, on account of the different property of the particles of which it is composed. The particles of a solid body attract each other (called the attraction of cohesion), and it is this property that constitutes each other; consequently they are unable its solidity, while those of a fluid repel to support themselves, and will, if not confined, extend themselves in every direction till they arrive at a level. : on posed of numerous strata of inconceivably Suppose a body of water to be comminute globular particles (see the above figure) as I have shown that these particles repel each other, the attraction of gravitation must exert itself on each particles of stratum a will press particle, separately; consequently the those of b with their own weight or gravity only, and those of stratum b will press on those of c with the weight of both a and b, and so on to the last stratum, which will support the weight of all the others; each particle of stratum a pressing on the two immediately under it, and each particle in stratum & partially pressed on by the two particles above it, as shown by the figure. Now, any par ticle in any of these strata may be considered as pressing upwards, sideways, &c. with the same force as it is pressed on by the particles above it, on account of the resistance occasioned by the repelling property of that particle, which makes it endeavour to escape the pressure. But when it presses downwards, its own weight or gravity must be added; cousequently it must press downwards the weight of the particle more than it does in any other direction. Hence arises the increased pressure of every stratum from top to the bottom. The horizontal extent of a body of water has nothing to do with this vertical pressure, for, if the first or top stratum extend many square miles, the particles of which it is composed cannot press more on the second stratum than they would in a small tube, because a particle in the second stratum will only be partially pressed on by the two above it, and the weight or gravity of these two particles is the same in both HYDROSTATICAL PARADOX, WEIGHT OF THE ATMOSPHERE, ETC. Let A (fig. 1) represent a tube inserted into a vessel, B, filled with water, the lower end of which tube circumscribes the space of half an inch. Let A (fig. 2), in like manner, be a tube, enclosing, by its lower end, an area of three inches. Now, suppose the two vessels, B, B, to contain equal quantities of water, and that the tubes, A, A, being of equal height, are also filled with that fluid; then, although the tube A (fig. 2) contains six times as much water as the other, the weight of that water being exerted on six times as much space, both vessels must sustain an equal internal pressure. Consequently, if the greater column were only half as light, it could have only half the force of the lesser. But if A (fig. 2) be closed at the bottom, and have a short peg attached to it (as represented in figure 3), the area of the bottom of which peg being half an inch, and it be properly inserted into a vessel of equal size with the two former, then will the internal pressure sustained by such vessel be six times as great as before the space being Contracted five-sixths under the same weight. Also, if any given weight be impressed on the water in the tube of fig. 1, and an equal weight on that in the tube of fig. 2, then will that weight exert itself with six times greater force within the former vessel than within the latter, the space it is impressed upon being five-sixths less. Suppose, again, that the sides of the two first vessels were raised, as represented by the dotted lines, to the height of the tubes, and then filled with water (the tops of the vessels, in the first state, being considered as taken away), the pressure on the bottoms of the vessels and on the sides, as high as they were at first, would be precisely the same as before; nor would it be greater were the horizontal dimensions of the vessels increased six thousand times, or any less if in an equal degree contracted; that is, it would not be any greater or any less on equal spaces at equal heights. For if two columns of water, A and B (fig. 4), communicate at bottom, though A be six times as large as B, yet will B sustain A, because all communicating columns of water will maintain their level; consequently, though B should be made as great as A, it would still do no more than sustain it. The column A, in the first case, not exerting the whole of its weight against the column B, but only that of a column equal to B, its remain ing five equal columns being sustained by the parts of the confining vessel surrounding the bottom of the tube B; yet, on the other hand, the column B, though only a sixth part as large as A, does exert a force equal to the weight of its opposite column, because the force with which it presses upon the sixth part of the greater column is immediately counter-exerted by each of the remaining five parts on the internal surface of the confining vessel surrounding the bottom of the tube B, agreeable to the law before mentioned, that no part of any body of fluid can be made to sustain a greater pressure than each of the remaining equal parts of the same height, if unconfined, nor of any height (excluding the consideration of its own gravity) in a confined state. By the intervention of any solid body, as the peg in fig. 3, between a column of water and any other mass of water in a confined state, though that column, in a state of free communication, would impress only its natural weight, yet, by such intervention of a solid body, its force may be increased or diminished in an infinite degree by the diminution or increase of that part of the solid intervening body which presses on the confined mass of fluid, exactly fitting, as a matter of course, the opening of the confining vessel into which it is introduced, which, however, is only a different modification of the experiment described in the first part of this letter. To conclude (which I beg pardon, Sir, I have not done long ago), it is not diffcult to believe that a sphere of water at the centre, with a sinall column extended to the surface of our earth, need not be comparatively very great to put it in the power of the atom called man, to burst this stupendous world like a bubble, provided the matter enclosing the sphere and projected column te so compact as not to allow any portion of the fluid to insinuate itselfiuto greater space without rending asunder the surrounding mass; probably the weight of the column only would be equal to such an effect; for, taking the semidiameter of our globe at 4000 miles, and deducting 250 miles for the semidiameter of the sphere of water, the column would impress a weight of 9,556,250 pounds upon every inch, and the whole force with which the sphere would be made to exert itself, in order to bring the column within its own circumference, would be 30,130,666,384,896,000,000,000 pounds, or 13,451,190,351,400,000,000 tons; on which grand hydrostatic principle may, probably, be accounted for the present geological appearance of our earth. I trust+W. X. will be able to make make up, by his own reflection, for the brevity with which I am obliged to answer his two remaining questions. It is the change in the centre of gravity that gives preponderance to the pea of a steelyard, on removing it further from the fulcrum, and, to recover the equilibrium, either the fulcrum must be placed in the new centre of gravity, or an additional weight must be suspended at the other PIRE-PROOF AND PLANK FLOORS. end, in order to restore that centre to its old place. The centre of gravity, perhaps + W. X. is aware, is that perpendicular line in any body, the product of the weight and distance on each side of which is equal to the product of the weight and distance on the other; hence what is lost in distance is gained in weight, the reason of which is, that velocity is power; and the further from the fulcrum the extremity of a lever, the greater its velocity, which velocity gradually diminishes to the centre of motion; consequently the nearer the end of the steelyard you suspend the pea, the greater is the velocity by which you have to multiply its weight. It is the pressure of the air, not gravitation, that causes the phenomenon of the syphon; the greater weight of water in the longer leg giving the air pressing on the end of the shorter a proportional advantage over that pressing on the end of the former. It is this, +W. X., that "pulls the water down the good-natured leg." FIRE-PROOF AND PLANK FLOORS. SIR,-The imperfection of the old construction of Floors for the purposes of machinery, has induced some people in this neighbourhood to alter the flooring system altogether; and instead of joists, flooring-boards, tiering underneath, &c. (of which they formerly consisted), two planks, of quite a different nature, have been adopted, viz. fire-proof and plank floors. For the fire-proof floors, the columus and beam are made of cast iron, and are secured in their places with wrought iron bars, that traverse from beam to beam; upon a margin underside the beams spring the arches of brick-work; these are filled to a level on their upper side with rubbish, and are covered with flags or tiles. For plank floors, iron columns and beams are used; but the beams are flat on their upper side for the planks to lay upon; three-inch planks are then jointed and ploughed on the edges, for the purpose of admitting slips of sheet-iron (called tongues) to enter half-way into each plank, so that no dust may get through from the upper side. These are certainly improvements on the old plan, as they possess the advantages of stability, and deprive vermin of their harbours. The advantage of fireproof floors are steadiness, durability, and saving the insurance: but then the first expense is great; they take up more head-room, and the tiles or flags with which they are covered are unhealthful to the operatives, on account of their coldness. The plank-floors, though they are both cheaper and firmer than those on the old plan, have nevertheless their disadvantages; for though the floor may be made, yet let the timber be ever so well seasoned, when the rooms are ready for use, and must be kept up to the required temperarure, the joists will open, and the floor becomes pervious to both dust and water, which, with the tremor produced by the machinery at work, creeps round the dowels or tongue, and the consequences are serious to the machinery underneath. Besides, when the floor has become so deteriorated as to require repairing in the passages, the whole length of the planks must be taken up, from beam to beam, which will be attended with bad consequences to any machinery that may stand upon them, or to any fixtures underneath. These consideratious have induced me to turn my attention to this subject. I propose that, instead of three-inch planks, one and a half shall be used, laid upon iron beams, in two courses, one upon another; they shall both stretch the same way, and the upper boards shall break the joints of the lower; underneath the upper, and above the lower joints, slips of sheet iron, about three inches broad, must be laid, and kept in their places with a few nails: it will be necessary to screw the boards together in several places, to give them firmness. When this floor is finished, the joints will be good, and remain so, whatever temperature they may be exposed to. They will have another advantage over the present plank-floors when the upper course is done, they may be renovated without breaking through the floors. Another improvement may easily be made in the iron columns. Let their diameter be as great as convenient, for the purpose of enlarging their internal capacity, and let each column in every room have a cock, or any other application, for the purpose of emission there must be a cistern on the top of the building (in case of accidents by fire, or for any convenient purposes where water may be wanted), and this cistern must be attached to the lifting-pump of the steam-engine. It will be necessary that each column be connected either at top or bottom, so that the water may flow through the whole, and they must likewise have air-pipes attached to them. Now, suppose the columns to be five inches bore (which is common), and the building six stories high, the average height of the stories nine feet six inches, length ninety feet by forty-eight feet, it will then contain eighteen columns fiftyseven feet long each, making in the whole a column of water one thousand and SKETCH OF THE UNDER PART OF A THREE-WHEELED CARRIAGE. = twenty-six feet long, and five inches diameter. Now, 5 x5x, 7854 = 19,635, area of bore; 19,635 x 57, length of column, 13430,34, contents of one column; and 13430,34 x 18,872, imperial gallon. Here, then, is a capillary supply of water in every part of the building, which may be constantly maintained by feeding the cistern above from the engine. The importance of an immediate and convenient supply of water in every part, and in such extremities, needs no comment. But they may be made useful in another way, viz as ventilators. Let there be openings in each column, near the ceiling in every room, and let the whole of the columns connect with an hori 9 zontal pipe in the roof (made of sheet irou), and of sufficient capacity to give them draft. This pipe may be inserted in the chimney, provided it is made to dip a little before it enters, to prevent sparks or soot descending into the rooms; by this means the rooms may be ventilated from a great portion of dust, impure air, and superfluous heat, without opening the windows. Should this be doubted, let it be remembered that the sum of the orifices of the vertical pipes amounts to no less than 353,43 square inches. I am, Sir, Your most obedient servant, Manchester, Feb. 13th, 1825. R. |