PROFIT AND DISCOUNT. Fig. 1 represents a side view of the machine. AC is a frame, of any convenient size, made of wood; I propose that it shall be six feet long, six feet high, and two feet six inches wide, for the convenience of going up passages in streets and buildings. E is a wheel three feet in diameter, on the circumference of which there is a groove, gradually narrowing to the bottom, and forming an angular indentation, which form is the most suitable to take effectual hold of the band. F is a cylinder made of wood, twelve inches in diameter, and two feet six inches long; at each end is fixed an iron plate, with a square hole to receive iron rods, which are made to slide easily through the centre of the cylinder. Gis a pulley, nine inches in diameter, which acts on two centres in an iron frame; this frame is made to slide in the woodwork, and is acted upon by the screw, H, which tightens or slackens the band as occasion requires. I is an iron rod, six feet long, at the end of which is a spiral bit, made to bore a six-inch hole; the top end is rounded to a centre, and works in a brass socket on the bottom of the box, J. This box is filled with sand or shot, and slides down the two uprights, KK; the box, J, acts as a pressure on the rods, and keeps the cylinder in the centre. On the axle of the great wheel, E, is a cantwheel and arbor, which is made to slide up or down, and is made fast by a thumb-screw at any degree, according to the size of the pinion that may be required to drive the machine. The pinion, L, is fitted on the axle of the flywheel, so that it may be taken off at pleasure to put on a larger or smaller. M is a screw to tighten the great wheel as the centres wear off. N is a flywheel, which is turned by a man, and gives motion to the machine; the line is coiled once round the cylinder, and brought over the pulley and great wheel, as is shown by fig. 2. When the cylinder is worked to the bottom of the frame, it is slided up the rods to its former elevation, and so on until the whole of the rod is worked down. The cylinder is then taken off, and another rod is introduced, which has a square socket to receive the end of the former; a pin is next put through the joint, which fastens them strongly together. O is a crane, provided with a chain, which hangs down, and may be attached to the axle of the 35 fly-wheel to pull up the rods. The first bit, I, is intended to bore any soft substances, as clay, chalk, sand, &c.; and I think such a bit, from its spiral form, would clear its way, and raise the core to the top, where it might be cleared away with a shovel. Fig. 2 shows the bottom of the frame, and wheels in their proper situation. Fig. 3 is an end view of the frame and fly-wheel. Fig. 4 is a bit, to bore through stone, coal, &c. PP are two pieces of steel, made widest at the lower end, and brought to a keen bevel, in favour of the cutting way of them. The end of the rod, Q, is steeled, and made flat in the shape of a drill; about a foot from the end is welded a piece of iron, with a groove at each end to admit the two cutters, PP, to slide up or down. R is a band of iron, made to slide down the rod; it must be long enough to receive the top ends of the cutters, with the two wedges, SS. Now, if you slacken one of those wedges, the cutters are at liberty to be slid up or down, or taken out to be sharpened. T is the core cut out by the drill. We will suppose the core, T, to be cut out of a bed of claystone, 30 or 40 feet below the surface of the earth; it would be difficult to get out, and another bit could advance while this core remained in, as it would constantly turn round with the nose of the bit, and prevent its cutting; to overcome this difficulty, the rods must be drawn up, and fig. 5 introduced; the end is made of steel, with an oblong mortice, in which are fitted two pieces of steel, so that when the rod is forced down, they may shut into the mortice; and when drawn up, they will open and take hold of the stone. Such a machine as the above would be very useful in boring wood, and drilling iron, or any kind of metal. 36 IMPROVED THREE-WHEELED CARRIAGE, ETC. In M. W.'s example, "Suppose an article cost 501., on which it is wished to make 7 per cent. profit, what must the selling price be so as to be able to allow per cent. discount?" The answer he makes out is 557. 412d. Applying the above reasoning, 55.412-55.412 × .03 = N=52.445, and 52.445-52.445 x .075=C-48.512, and not 501., as M. W. has it. To illustrate-Suppose I sell goods which cost me 807. for 1007., my profits are one-fifth, or 20 per cent., and my cost four-fifths, or 80 per cent., the five-fifths being the whole, or the centum. Again, if I sell for 1007. what cost me 20s., M. W. would call this 9900 per cent., but which I should call ma thematical nonsense, for the whole being 100, or the centum, he makes the parts to amount to more than the whole. The solution I propose is, that my profits are 99 per cent., or and the cost 1 per cent., or the parts being added to make the centum. 1009 But what will M. W. say to the profit per cent. upon goods which cost him nothing: here he makes out .0 x .075 0, the amount of profit, and 0 added to this will be the amount of cost and profit, but which is much too abstruse for my apprehension, and I will therefore be content, in this case, with saying, that whatever amount the goods were sold for would be all profit, or cent. per cent. Allow me to propose to gain twenty per cent., and allow ten per cent. discount. Example. - Let the prime cost of goods be 721. 72 x .25 = 18, and 72 +18=90, and 90 x .1111110, and 90+10=100, the selling gross amount. But, to do away with algebra, which is often built upon false assumptions, I will descend to pure or unmixed mathematics, viz. plain arithmetic; and, as a general rule, taking 5 per cent. as an example. Five per Cent. is equal to, equal to supposing the centum divided into 20 parts, the profit will be 1, and the cost 19 of those parts; therefore, dividing the cost by 19 will give the profit of 5 per cent. And, universally, whatever the fraction may be,, 15, 1, 1, 1, 1, the divisor of the cost will be 19, 18, 17, 9, 3, 2, 1, &c. &c. and the quotient will be the profit which is to be added to the cost. The same process, in all respects, will show the discount to be added to the nett amount, making the gross amount of sales. The above is the constant practice of a very large manufacturing district, 11.111 = y IMPROVED THREE-WHEELED CAR- SIR,-I observed, in a late Number of your useful Magazine, a sketch and description of a Three-wheeled Carriage: but, as I cannot perceive any difference between it and the common chairs and carts long in use fective in wear, from the leverage on that principle, always found deaction of the fore-wheel on the revolving spindle, which is so much above the centre and bearing of the wheel; and as the gentleman alludes RAREFACTION OF AIR. to me, from a notice of a new construction of a three-wheeled carriage, of mine, which you favoured with a place in your Magazine a few months back; I beg leave to state, that any person who may be desirous of knowing the novelty of the principle, can obtain every information respecting it by application. I have lately resided in Paris, where several four-wheeled carriages, on a new construction, have been made, and generally admired for their safety, ease, and lightness. The simplicity of the construction admits of their being built for considerably less than the ordinary principle of poney phaetons, and likewise kept in repair, while they can be made to evade whatever duty is imposed on the common four-wheeled vehicles. The mode of attaching the shafts to the car preserves the stability of the machine, in case of the horse falling, &c. I have to inform you of a sixwheeled carriage, on an ingenious and novel principle, lately invented by Sir Sydney Smith, which has been found of considerable utility for invalids and persons unable to bear the motion of the ordinary carriage, from its extreme case on uneven pavements. It is likewise of peculiar advantage for travelling over bad roads, and for crossing open countries, for which purpose it forms an excellent sporting carriage. If you will favour it with a place in your Magazine, I will furnish you with a design and description of it.* Any individual wishing to have a three or four-wheeled carriage, on the new principle, may be furnished with any information they may require by sending their address to No. 25, Bow-street, Long Acre. Likewise for the six-wheeled carriage. I remain, Sir, Your obliged and obedient servant, G. M. RAREFACTION OF AIR. SIR,-Your Correspondents, Mr. T. Hartshorne, page 274, and Phylo * We shall gladly give it a place. 37 Sates, page 423 (vol. 111.), appear to entertain some doubts with regard to the phenomena attendant on the rarefaction of air by heat. They agree in stating that, if the open end of a tube be placed in the fire, and its lower extremity be immersed in a basin of water, that the water will rise so far in the tube; and this rise of the water appears to them a most inexplicable arcanum. Now, without arrogating any degree of superior judgment, I am really compelled to say, that I see no reason why it should be otherwise; for it is an established principle, that the particles of air, when heated, expand or occupy a larger space, that is, they become specifically lighter than the surrounding air; they will, therefore, ascend to such a height in the atmosphere as corresponds to their bulk and density, and the adjacent air rushing in to supply the place they had formerly occupied, will, from this natural effect, prevent any sudden or great derangement of the equilibrium from taking place. Now, this upward current of rarefied particles being incessant, and as the force and velocity in that direction may be increased to any extent, by increasing the heat, it follows that the air flowing in to supply this waste will rush to that point which offers the least resistance to its ingress, and if the lower part of the tube were out of the water, the adjacent air would rush through it; and since air or any other body cannot. move through any aperture without exciting in our minds the idea of force, it necessarily follows, that if a cup of water is placed at the bottom of the tube, that that water will rise upward in it, and continue suspended as long as the same degree of heat continues at the top of the tube. Thus we see that the top of the tube is guarded from the pressure of the superincumbent air by the rapid ascent of the aërial bubbles. As a practical illustration of this subject, suppose a balloon to be placed in a tube so as to embrace its sides in the most perfect manner, and without friction. Let the lower part of the tube be placed in a large vessel of water, inflate the balloon either 338 ON MEASURING THE HEIGHT OF OBJECTS. by heated air or hydrogen gas, and it will instantly struggle to get out of its confinement, in consequence of its being specifically lighter than the air in the tube, and the natural consequence resulting from this will be, the air under the balloon will expand, because it occupies a greater space from the ascent of the balloon, and, in order to restore the equilibrium, the external air will press up the water into the tube to such a height as will balance the tendency of the balloon to ascend; so that the water will rise in the tube in the exact proportion as it would have done, had the air within the tube been rarefied to the same degree of lightness as that in the balloon. The two cases I consider as neurly analogous; the particles of heated air, in the former case, becoming, in fact, little Montgolfiers. One might descant on a great many practical cases to prove the cause of the ascent of the water in the tube. The following appear to be regulated by nearly the same principle: The ascent of the flame in Argand's burner and chimney, ballooning, Dr. Halley's marine gauge, letting foul air out of the diving-bell, air furnaces of every description, ascent of vapours in the atmosphere, water spouts at sea, &c. &c. Mr. H. asks, at the end of his letter, "What subverts the rarefied state of the included and insulated air?" "So that, from the fact of water ascending in consequence of reduced atmospheric pressure, and the scale ascending in consequence of increase of pressure, the inference is nothing less than this paradox-that air, rarefied by fire, has a less and a grester pressure than the atmosphere, as it naturally exists." Here is obviously a direct contradiction, for a thing cannot be greater and less than a given thing at the same time. He speaks, also, of water ascending by reduced pressure, and an inverted cone ascending by an increase of pressure. This last certainly is true; but the water also ascends, because, RELATIVELY, there is an increased atmospheric pressure forcing it up the tube. Should the above remarks dispel the doubts of your Correspondents, I shall consider my time and paper spent to some advantage; and if they only tend to increase those doubts, I shall, in a subsequent Number, attempt to set this subject in a clearer point of view. BUT should THEY prove to me that I have only been raising up "bubbles light as air," then let me conclude with the words of the poet ""Tis hard to say if greater want of Appear in writing, or in judging ill; I answer, leakage. The following To tire our patience than mislead our experiment will prove this:-Take a large wine glass, and fix a piece of paper on its bottom inside; set fire to this paper, and the included air sense. I am, Sir, JAMES YULE. being thus rarefied, or, what is the 63, Red Lion-street, Clerkenwell, same thing, becoming specifically lighter than the surrounding air, the consequence is, the particles are forced out of the glass by their mutual expansion, a partial vacuum being thus formed. If the glass is plunged into a saucer of water, with its mouth downward, the water will rise in the glass (after the internal air collapses), from the external pressure of the atmosphere, and may be retained there for any length of time. Phylo Sates draws a most unphiosophical conclusion, when he says: ON MEASURING THE HEIGHT OF SIR,-As some of your readers, no doubt, would wish to be acquainted with the method of determining the quantity of depression of two distant objects on the surface of the earth, and also the principles upon which that depression is founded, allow me, therefore, to contribute a few lines to your miscellany for furthering this object. STEAM WASHING-BOX. pose; let A and B represent two remote objects; C the centre of the earth, to which all bodies gravitate. Join AB, BC, and produce it to D; draw AF a tangent to the circle, and join AE, AC, AD. Now the converging lines AC, BC, will indicate the direction of the plummet at A and B, and the targent AF will mark the line of the horizon from A. Again the angle, as measured at A, by the instrument, is only the angle FAB, which is less than the true angle EAB by the angle EAF. But by a well-known property of the circle (Euclid, Lib. 3, Prop. 32), the angle EAF is equal to the angle ADB, and this again is equal to half the angle at the centre, viz. ACB. Hence the true angle EAB FAB + half the measure of the intercepted are AE; but as this measure depends upon the curvature of the earth, which is neither uniform nor regular, the measure for each particular place must be deduced from the corresponding degree of latitude. = In ordinary calculations, however, such nicety is unnecessary; we will he sufficiently near the truth if we assume the earth as a perfect sphere, whose circumference is 24856 miles; the arc of a minute upon the meridian will, therefore, be 6076 feet; 39 the correction to be added to the observed vertical angle will, therefore, amount to one second for every 69 yards contained in the intervening distances betweeen the objects. 5280 7912 From what we have stated, the quantity of depression, FE, is easily found; for, from Euclid, Lib. 3, Prop. 36, AF2 = DF, FE, or very nearly DE, EF, and from this equation we conclude that the depression of any object is always proportional to the square of its distance, AF; consequently, in the space of one mile, this depression will amount to 39th parts of a foot, and generally we may express it in feet by two-thirds of the square of the distance in miles; but this depression, arising from the earth's curvature, is modified in a small degree by another cause, arising from the refraction of the rays of light in passing through the atmosphere; and this trajectory may be considered as very nearly the arc of a circle, having for its radius about six times the radius of our globe, or about 23736 miles. Now, in order to correct this error, we have only to diminish the effect of the earth's curvature onesixth, or, what is equivalent, deduct from the vertical angles the twelfth part of the intervening terrestrial are. I am, Sir, Your obedient servant, NICOL DIXON. STEAM WASHING-BOX. Q SIR, I now send you a drawing of a Family Steam Washing Machine, which I promised in my last (page |