50lbs., could have preserved the equilibrium; consequently the amount of pressure on the fulcrum must also remain the same. A B CD, fig. 3, represents a strong frame or box, in the inside of which are several levers, bc, de, fg, hi, jk, lm, and no, all of the same length, and the ends of all of them at equal distances from the fixed centres or fulcræ, upon which the said levers are moveable, which centres are represented by the letters r, s, t, u, v, w, and x. There is also a number of columns, Nos. 1, 2, 3, 4, 5, 6, 7, and 8, all of the same length and width, connecting the ends of the levers with those on the opposite side of the frame or box. The use of this arrangement of levers, &c., is to communicate any degree of pressure (that may be applied to the end a of column No. 1) to the end b of the same column, and from thence through the whole of the levers and columns to the end p of the last column (No. 8), which may be done in the following manner. Suppose a pressure equal to 100 lbs. be applied to the end a of column No. 1, the direction of the force being towards b, the lever b c being moveable on its centre of motion r, communicates the same degree of pressure to co lumn No. 2, in an opposite direction, from c to d; the lever de then reverses, and communicates the same degree of pressure (by means of the column No. 3) to f; the lever fg will, in a similar manner, transfer the same degree of pressure to h; and so on, each lever communicating the same degree of pressure (by means of the next column directly attached to it) to the next lever on the opposite side of the frame or box, until it is finally communicated to the end p of the last column No. 8, resting upwards against the immoveable part q of the frame, and pressing on it with the same degree of force of 100 lbs., there not being any gain or loss of leverage (in the communication of the pressure to q) by any of the parts concerned in the communication. The motion of the end p of the last column, No. 8, being resisted by the fixed part q of the frame, causes a strain equal to 100 lbs. on p, and consequently on the ends of all the other columns and levers within the frame or box. The lever bc, in transferring the pressure to the opposite side of the frame, &c. (by means of the column No. 2), causes a pressure on its fulcrum or centre of motion r equal to 200 lbs. towards the outside of the frame, which amount of pressure is exactly equal to that on both ends of the lever bc, as in figs. 1 and 2, and also on the ends of the two columns concerned in the communication, viz., 1001 bs. each. And as the same degree of pressure is in a similar manner transferred to the opposite side of the frame, &c., by all the levers (by means of the columns directly attached to them), there must be the same amount of pressure, viz., 200 lbs. on the fulcrum of every lever within the frame or box; therefore the pressure sustained by the outside of the frame will be equal to 200 lbs. repeated as many times as the pressure is thus transferred: consequently the total amount of pressure outwards on both sides of the frame, &c., is equal to 100 lbs. multiplied by the number of columns communicating with both sides of the frame, which would be exactly the same if the columns were fluid, and the ends of them in actual contact with the outside of the frame or box. The only difference is in the manner of communicating the pressure. Instead of the columns being fluid, and the ends of them in actual contact with the outside of the frame or box, and pressing separately upon it with the force of 100 lbs. each, the pressure of both, viz., 200 lbs., is transferred together from the centre of motion through the fulcrum Y to the outside of the frame. In fig. 3 there are seven columns communicating with the side A of the frame; the amount of pressure, therefore, on it is equal to 700lbs.; and as there are eight columns on the opposite side, the amount of pressure on it must be equal to 800 lbs., or 1,500 lbs. on the whole. As the same amount of pressure would take place on the opposite sides of the box, were it filled with a fluid instead of the solid levers, &c., the arrangement described may serve to illustrate the principle of the hydrostatic pressure. The frame, and consequently the columns, &c., are supposed to be in a horizontal position, so that the weight of them would not cause any difference of pressure on the opposite sides of the frame, &c. To illustrate the pressure produced by the gravity or weight of a fluid, place the frame or box so that the columns therein may be in a perpendicular position; they will thereby represent a series of fluid columns, the column ab weighing exactly 100 lbs., each of all the other columns weighing the same. Now it is evident, by inspection of the figure, that the whole of them must be in equilibrio. 20000 N1 ANALOGY BETWEEN THE PRESSURE OF FLUIDS AND SOLIDS. 359 The columns attached to each end of the same lever being equal in weight, there will not be any pressure upwards from the tops of any of them, and the pressure on the bottom of the box will be equal to the amount of weight of all the columns within the box, viz., 100 lbs. each. And as there are eight columns in the figure, the amount of pressure on the bottom will, of course, be equal to 800 lbs. Therefore, this arrangement will serve to represent the amount of pressure when a vessel is filled with fluid, the pressure on the bottom being equal to the sum of the pressure on all the columns contained in the vessel, each column being equal in height and weight to the column a b, and there being no pressure upwards at the top. To represent the amount of pressure on the top and bottom of a box, when there is a tube or pipe carried above the top, and the other part of the top is quite closed: make the column No. 1 double the height, and consequently it will represent a column of double the weight also. This column will (similar to a fluid column) cause a pressure upwards at the top of the box, equal to the weight (of that part of the column only which is carried above the level of the top) multiplied by the number of columns communicating with the top of the box, and the amount of pressure on the bottom will be the same as if the box and pipe were filled with a fluid, that is, twice the amount of that, when the column No. 1 was not higher than the top of the box; consequently the amount of pressure on the bottom will be identically the same, if the top of the box were removed, and all the columns therein were carried up to the same height as the column bax in the small tube. This is as much a paradox as that which is caused by the pressure of a fluid, or that which is commonly called the hydrostatic paradoxthe increase of pressure on the bottom being always proportional to the increase of the highest column ba x. If the top of the box were of any other form than that represented in fig. 3, whether it be an inclined plane, a curve, or any other irregular figure, the pressure on the bottom would be exactly the same, as it entirely depends on the height of the column carried above the top, which may easily be traced by re a ferring to fig. 4. Suppose the column No. 1 (which is carried above the top) to weigh 100 lbs., this, of course, presses with the same force on the end b of the lever bc; this lever transfers the same pressure upwards on the bottom of column No. 2. The transferring of this pressure (as in fig. 3) causes pressure on the fulcrum equal to the amount of that on both ends of the lever bc, viz. 200 lbs. This is communicated by the fulcrum to the outside of the box. Deduct the weight of column No. 2, which is equal to 20 lbs., and the remaining pressure upwards on d will be equal to 80 lbs. The lever de transfers this pressure downwards on column No. 3, and at the same time communicates the sum of the pressure on both ends of the lever as before, through the fulcrum to the outside, viz. 160 lbs. Add the weight of column No. 3, which is equal to 20 lbs., and the pressure on the lever at the bottom will again be equal to 100 lbs. This lever transfers it to the bottom of column No. 4. Deduct the weight of this column, which is equal to 10 lbs., and the remaining pressure upwards on h will be equal to 90 lbs. This is trans C ferred to the top of column No. 5: add the weight of this column, which is 10 lbs., and the pressure on the lever at the bottom will again be equal to 100 lbs. This being communicated to column No. 6, deduct the weight of this column, which is 30 lbs., and the remaining pressure upwards will be equal to 70 lbs. Again, this pressure being communicated to the top of column No. 7, add the weight of this column, which is 30 lbs., and the pressure downwards on the lever at the bottom will still be equal to 100 lbs. This being communicated to column No. 8, deduct the weight of this column, which is equal to 40 lbs., and the remaining pressure upwards of column No. 8, at the top of the box, will be equal to 60 lbs. The whole of the top of the box not being on the same level, the pressure of course on the different parts of it (as described in fig. 4), will not be the same on any given part, it will be equal to the weight of that part only of column No. 1, which stands above the level of that particular part, multiplied by the number of columns communicating with that same part— the pressure in all parts of the top and bottom depending entirely on the height MODE OF PROPELLING STEAM-VESSELS WITHOUT PADDLEs. 361 of the highest column No. 1. I do not mean to say that the weight of the columns, as represented in fig. 4, is as much as if the whole of them were equal in height to the highest column No. 1, as a spring could be forced in a box, which is capable of producing a pressure equal to several pounds (tending to force open the box), although the box and spring together do not weigh more than a few ounces. The small spaces between each column are left for the purpose of showing the communication of pressure more distinctly than if (like fluid columns) they had been in actual contact. The pressure produced by the weight of column No. 1, may be communicated at once to the seven columns within the box, considering them as one column of seven times the width; and this may be done by placing those parts of the two columns, which are directly under the centre of gravity of each, on the two ends of a lever, placed on a fulcrum exactly over the centre of the bottom of the box. This arrangement will communicate the same amount of pressure on the top and bottom of the box, as the arrangement in fig. 3. Column No. 1, fig. 5, is supposed to weigh 200 lbs., and consequently presses with the same force on the end b of the lever bc, which causes a pressure upwards on the other end c of this lever, and on the bottom of column No. 2, equal to 1,400 lbs., in consequence of the end b of the lever being seven times the distance of the end a from the fulcrum. Deduct the weight of column No. 2, which is equal to 700 lbs., and the remaining pressure upwards at the top will be, as in fig. 3, equal to 700 lbs., and the pressure communicated from the fulcrum to the bottom of the box will be equal to the amount of pressure on both ends of the lever, viz. 1,600 lbs., as before. If the re-action of the top of the box is taken away by removing it, and if column No. 2 is carried up to the same height as column No. 1, the pressure on the bottom, as in fig. 3, will still remain the same, which also appears as much a paradox as that which is caused by the pressure of a fluid. Lastly, fig. 6 represents a horizontal arrangement of levers and inflexible bars, instead of columns, which latter would to e. have made the figure appear confused. This arrangement will communicate and multiply the pressure that may be applied (to one bar only) to all the four sides of the frame, A B C D, as follows: -A pressure of 100 lbs. is applied to the end a of the bar a b; this is transferred in the same manner as in fig. 3, till it is communicated to the rightangled lever c d, which transfers the pressure to the side D of the frame, from which it is finally communicated Now it is evident, on inspection of the figure, what the amount of pressure will be on each of the four sides. There are seven bars communicating with each of the three sides, A, B, and D, therefore the pressure on each is equal to 700 lbs.; and as there are eight bars communicating with the side C, the pressure on it must be equal to 800 lbs., or 2,900 lbs. on the four sides: so that the apparent paradox, which is produced by the pressure of fluids, does not appear to be any greater than that which is produced by the pressure of solids. An arrangement might also be made to show the different degrees of lateral pressure at different heights in the sides D and B, when in a perpendicular position, which would, of course, require a much more complicated figure than any of the foregoing, and which I suppose will not be thought necessary after what has already been said on the subject. I did not think it necessary to make any allowance for friction, as I believe it is not customary in explaining the principle of any arrangement of mechanical powers. Sun Fire Office, Cornhill, J. R. A. MODE OF PROPELLING STEAM-VESSELS Sir,If you should think the enclosed plan for propelling steam-vessels worthy of a place in your Miscellany, I' shall feel obliged if you will insert it at your earliest opportunity. It has been intimated to me, that a plan for propelling steam-vessels, by a principle which is very similar to this, has been fre quently attempted without success; but I suspect that the two methods, though agreeing in principle, are nevertheless very |