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PROFIT AND DISCOUNT. one of my own inventing, which I Hy-wheel to pull up thé rods. The first hope will be found serviceable to the bit, l, is intended to bore any soft sub

stances, as clay, chalk, sand, &c.; and I

think such a bit, from its spiral form, I am, Sir,

would clear its way, and raise the core Yours sincerely,

to the top, where it might be cleared M. MONNOM. . away with a shovel. Broadway.

Fig. 2 shows the bottom of the frame, Description.

and wheels in their proper situation. Fig. 1 represents a side view of the

Fig. 3 is an end view of the frame and machine. AC is a frame, of any conve

fly-wheel. vient size, made of wood; I propose that

e made of wood? I propose that Fig. 4 is a bit, to bore through stone. it shall be six feet long, six feet high, coal, &c. PP are two pieces of steel, and two feet six inches wide, for the made widest at the lower end, and convenience of going up passages in brought to a keen bevel, in favour of the streets and buildings. E is a wheel three cutting way of them. The end of the feet in diameter, on the circumference rod, Q, is steeled, and made flat in the of which there is a groove, gradually nar- shape of a drill; about a foot from the rowing to the bottom, and forming an end is welded a piece of iron, with a angular indentation, which form is the groove at each end to admit the two cut. most suitable to take effectual hold of ters, PP, to slide up or down. Ris a band the band. F is a cylinder made of wood, of iron, made to slide down the rod; it twelve inches in diameter, and two feet must be long enough to receive the top six inches long; at each end is fixed an ends of the cutters, with the two wedges, iron plate, with a square hole to receive SS. Now, if you slacken one of those irou rods, which are made to slide easily wedges, the cutters are at liberty to be through the centre of the cylinder. Gis slid up or down, or taken out to be a pulley, nine inches in diameter, which sharpened. T is the core cut out by the acts on two centres in an iron frame: drill. We will suppose the core, T, to this frame is made to slide in the wood be cut out of a bed of clavstone, 30 or 40 work, and is acted upon by the screw, feet below the surface of the earth; it H, which tightens or slackens the band would be difficult to get out, and another as occasion requires. I is 'an iron rod, bit could advance while this core resix feet long, at the end of which mained in, as it would constantly turn is a spiral bit, made to bore a six-inch round with the nose of the bit, and prehole; the top end is rounded to a vent its cutting ; to overcome this dithcentre, and works in a brass socket culty, the rods must be drawn up, and on the bottom of the box, J. This fig. 5 introduced; the end is made of box is filled with sand or shot, and steel, with an oblong mortice, in which slides down the two uprights, KK; the are fitted two pieces of steel, so that when box, J, acts as a pressure on the rods, the rod is forced down, they may shut and keeps the cylinder in the centre. On into the mortice; and when drawn up, the axle of the great wheel, E, is a cant- they will open and take hold of the stone. wheel and arbor, which is made to slide Such a machine as the above would be up or down, and is made fast hy a very useful iu boring wood, and drilling thumb-screw at any degree, according to iron, or any kind of metal. 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

PROFIT AND DISCOUNT. pleasure to put on a larger or smaller. M is a screw to tighten the great wheel S IR,-Conceiving your friend M.W.. as the centres wear off. Ñ is a fly- on' Profit and Discount,' in your 78th wheel, which is turned by a man, and Number, page 342, to be in an error, gives motion to the machine; the line is I will take his advice, by “ amusing' coiled once round the cylinder, and myself with trying the cause, Common brought over the pulley and great wheel, Sense versus Mathematicus, beginning as is shown by fig. 2. When the eylinder with M. Wi's own weapons. is worked to the bottom of the frame, it is slided up the rods to its former eleva- Let S represent the gross amount ; tion, and so on until the whole of the D, the rate of discount : rod is worked down. The cylinder is then taken off, and another rod is in

N, the nett amount; troduced, which has a square socket to R, the rate of profit; receive the end of the former; a pin is next put through the joint, which fastens ' C, the prime eost. them strongly together. O is a crane,

Then S-SD - N, provided with a chain, which hangs down, and may be attached to the axle of thé . . and N-NR =€...

36

IMPROVED THREE-WHEELED CARRIAGE, ETC. In M. W.'s example, “ Suppese an thematical nonsense, for the whole article cost 501., on which it is wished being 100, or the centum, he makes to make 7£ per ceot. profit, what must the parts to amount to more than the the selling price be so as to be able to whole. The solution I propose is, that allow 3 per cent. discount?"

my profits are 99 per cent., or 4., and The answer he makes out is 551. 412d. the cost I per cent., or too, the parts

* being added to make the centum. Applying the above reasoning,

But what will M.W. say to the profit 55.412-55.412 x.03 = N = 52.445, and per cent. upon goods which cost him 52.445-52.445 x 075-C-48.512. and nothing : here he makes out .0 x .075 not 501., as M. W. has it.

= 0, the amount of profit, and 0 added

to this will be the amount of cost and To illustrate-Suppose I sell gocds profit, but which is much too abstruse which cost me 801. for 1001., my profits

for my apprehension, and I will thereare one-fifth, or 20 per cent., and my fore be content, in this case, with saycost four-fifths, or 80 per cent., the ing, that whatever amount the goods five-fifths being the whole, or the were sold for would be all profit, or centum.

cent. per cent. Again, if I sell for 1001. what cost Allow me to propose to gain twenty me 20s., M. W. would call this 9900 per cent., and allow ten per cent. per cent., but which I should call ma- discount.

[blocks in formation]

Example. Let the prime cost of and I should not have troubled you but goods be 721.

for the gross blunders frequently met 72 x.25 = 18, and 72 +18 –90, and with in the daily papers when speaking 90 x.11111 =10, and 90 +10=100, the of pronts. .. selling gross amount.

"I am, Sir,

. But, to do away with algebra, which

Your obedient servant, is often built upon false assumptions, I

I AN OLD MANUFACTURER, will descend to pure or unmixed mathe. Birmingham, March 15, 1825. matics, viz. plain arithmetic; and, as a general rule, taking 5 per cent. as an example.

Five per Cent, is equal to ho, equal IMPROVED THREE-WHEELED CARto ; supposing the centum divided RIAGE-NOTICE, ALSO, OF A SIXinto 20 parts, the profit will be l, and WHEELED CARRIAGE, INVENTED the cost 19 of those parts; therefore,

BY SIR SIDNEY SMITH. dividing the cost by 19 will give the profit of 5 per cent.

Sir, I observed, in a late Number And, universally, whatever the frac- of your useful Magazine, a sketch tion may be, a, i, , to, 1, }, , and description of a Three-wheeled the divisor of the cost will be 19, 18, Carriage : but, as I cannot perceive 17, 9, 3, 2, 1, &c. &c. and the quotient

any difference between it and the will be the profit which is to be added

common chairs and carts long in use to the cost. The same process, in all respects,

on that principle, always found dewill show the discount to be added to

fective in wear, from the leverage the nett amount, making the gross

action of the fore-wheel on the reamount of sales.

volving spindle, which is so, inuch The above is the constant practice of above the centre and bearing of the a very large manufacturing district, wheel; and as the gentleman alludes

RAREFACTION OF AIR.

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to me, from a notice of a new con- Sates, page 423 (vol. 111.), appear to struction of a three-wheeled carriage entertain some doubts with regard of mine, which you favoured with a' to the phenomena attendant on the place in your Magazine a few months rarefaction of air by heat. They back; I beg leave to state, that any agree in stating that, if the open person who may be desirous of know- end of a tube be placed in the fire, ing the novelty of the principle, can and its lower extremity be immersed obtain every information respecting in a basin of water, that the water it by application.

will rise so far in the tube; and this I have lately resided in Paris, where rise of the water appears to them a several four-wheeled carriages, on a most inexplicable arcanum. Now, new construction, have been made, without arrogating any degree of suand generally admired for their perior judgment, I am really compelsafety, ease, and lightness. The sim- led to say, that I see no reason why it plicity of the construction admits of should be otherwise ; for it is an their being built for considerably established principle, that the parless than the ordinary principle of ticles of air, when heated, expand or poney phaetons, and likewise kept occupy a larger space, that is, they in repair, while they can be made to become specifically lighter than the evade whatever duty is imposed on surrounding air; they will, therefore, the common four-wheeled vehicles. ascend to such a height in the atThe mode of attaching the shafts mosphere as corresponds to their to the car preserves the stability of bulk and density, and the adjacent the machine, in case of the horse air rushing in to supply the place falling, &c.

they had formerly occupied, will, I have to inform you of a six- froin this natural effect, prevent any wheeled carriage, on an ingenious sudden or great derangement of the and novel principle, lately invented equilibriuin from taking place. Now, by Sir Sydney Smith, which has been this upward current of rarefied parfound of considerable utility for in- ticles being incessant, and as the valids and persons unable to bear force and velocity in that direction the motion of the ordinary carriage, may be increased to any extent, by from its extreme ease on uneven increasing the heat, it follows that pavements. It is likewise of pecu- the air flowing in to supply this liar advantage for travelling over bad waste will rush to that point which roads, and for crossing open coun- offers the least resistance to its intries, for which purpose it forms an gress, and if the lower part of the excellent sporting carriage. If you tube were out of the water, the adjawill favour it with a place in your cent air would rush through it ; and Magazine, I will furnish you with a since air or any other body cannot desigu and description of it.* move through any aperture without

Any individual wishing to have a exciting in our minds the idea of three or four-wheeled carriage, on force, it necessarily follows, that if a the new principle, may be furnished: cup of water is placed at the bottom with any information they may re- of the tube, that that water will rise quire by sending their address to upward in it, and continue suspended No. 25, Bow-street, Long Acre. as long as the same degree of heat Likewise for the six-wheeled car- continues at the top of the tube. riage.

Thus we see that the top of the tube I remain, Sir,

is guarded from the pressure of the Your obliged and obedient servant, superincumbent air by the rapid

G. M. ascent of the aërial bubbles.

As a practical illustration of this

subject, suppose a balloon to be placed RAREFACTION OF AIR..

in a tube so as to embrace its sides _SIR,-Your Correspondents, Mr. in the most perfect manner, and withT. Hartshorne, page 274, and Phylo out friction. Let the lower part of

the tube be placed in a large vessel * We shall gladly give it a place of water, intiate the balloon either

38 :

ON MEASURING THE HEIGHT OF OBJECTS. by heated air or hydrogen gas, and “ So that, from the fact of water it will instantly struggle to get out of ascending in consequence of reduced its confinement, in consequence of atmospheric pressure, and the scale its being specifically lighter than the ascending in consequence of increase air in the tube, and the natural con- of pressure, the inference is nothing sequence resulting from this will be, less than this paradox - that air, the air under the balloon will expand, rarefied by fire, has a less and a because it occupies a greater space greater pressure than the atmosphere, from the ascent of the balloon, and, as it naturally exists.Here is obin order to restore the equilibrium, viously a direct contradiction, for a the external air will press up the thing cannot be greater and less than water into the tube to such a height a given thing at the same time. He as will balance the tendency of the speaks, also, of water ascending by balloon to ascend ; so that the water reduced pressure, and an inverted will rise in the tube in the exact pro- cone ascending by an increase of portion as it would have done, had pressure. This last certainly is true; the air within the tube been rarefied but the water also ascends, because, to the same degree of lightness as RELATIVELY, there is an increased that in the balloon. The two cases atmospheric pressure forcing it up I consider as neurly analogous; the the tube. particles of heated air, in the former. Should the above remarks dispel case, becoming, in fact, little Mont- the doubts of your Correspondents, golfers.

I shall consider my time and paper One might descant on a great many spent to some advantage ; and if practical cases to prove the cause of they only tend to increase those the ascent of the water in the tube. doubts, I shall, in a subsequent The following appear to be regu- Number, attempt to set this subject lated by nearly the same principle: in a clearer point of view. But The ascent of the flame in Argand's should they prove to me that I have burner and chimney, ballooning, only been raising up “ bubbles light Dr. Halley's marine gauge, letting as air,” then let me conclude with foul air out of the diving-bell, air the words of the poetfurnaces of every description, ascentóc "Tis hard to say if greater want of of vapours in the atmosphere, wuter skill spouts at sea, &c. &c. Mr. H. asks, at the end of his letter,

Appear in writing, or in judging ill; «« What subverts the rarefied state But, of the two, less dangerous is th' of the included and insulated air ?”

offence, I answer, leakage. The following To tire our patience than mislead our experiment will prove this:- Take a sense." large wine glass, and fix a piece of;

I am, Sir, paper on its bottom inside ; set fire

Your humble servant, to this paper, and the included air

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 ON MEASURING THE HEIGHT OF mutual expansion, a partial vacuum

OBJECTS. being thus formed. If the glass is SIR, -As some of your readers, plunged into a saucer of water, with no doubt, would wish to be acits mouth downward, the water will quainted with the method of deterrise in the glass (after the internal mining the quantity of depression of air collapses), from the external pres-, two distant objects on the surface of sure of the atmosphere, and may the earth, and also the principles upon be retained there for any length which that depression is founded, of time.

allow me, therefore, to contribute a Phylo Sates draws a most unphi- few lines to your miscellany for furosophical conclusion, when he says: thering this object. '

39

STEAM WASHING-BOX. In measuring the height of any the correction to be added to the object, the angles are usually deter- observed vertical angle will, theremined by the application of spirit fore, amount to one second for every levels to the angular instrument, or, 69 yards contained in the intervening simply, by the plummet; but when distances betweeen the objects. the objects are very distant, it is From what we have stated, the evident that this method will require quantity of depression, FE, is easily some correction, and, for this pur found; for, from Euclid, Lib. 3,

Prop. 36, AF2 = DF, FE, or very nearly DE, EF, and from this equa

tion we conclude that the depression A

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 1919 th parts of a foot, and gene. rally we inay 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 pose; let A and B represent two very nearly the arc of a circle, having remote objects; C the centre of the for its radius about six times the earth, to which all bodies gravitate. radius of our globe, or about 23736 Join AB, BC, and produce it to D; miles. Now, in order to correct this draw AF a tangent to the circle, error, we have only to diminish the and join AE, AC, AD. Now the effect of the earth's curvature oneconverging lines AC, BC, will indi. sixth, or, what is equivalent, deduct cate the direction of the plummet at from the vertical axes the twelfth À and B, and the tar gent AF will part of the intervening terrestrial are. mark the line of the horizon from A. Again the angle, as measured at A, . . . I am, Sir, by the instrument, is only the angle !

Your obedient servant, FAB, which is less tian the true angle EAB by the angle EAF. But

Nicol Dixon. 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

STEAM WASHING-BOX. the angle at the centre, viz. ACB. Hence the true angle EAB = FAB+ half the measure of the intercepted arc AE; but as this measure depends upon the curvature of the earth, which is neither uniform nor regular, the ineasure for each particular place must be deduced from the corresponding degree of latitude. I

In ordinary calculations, however, such nicety is unnecessary; we will be sufficiently near the truth if we assume the earth as a perfect sphere,. whose circumference is 24856 miles; SIP.,--I now send you a drawing the arc of a minute upon the ineri. of a Family Steam Washing Machine, dian will, therefore, be 6076 feet; which I promised in my last (page

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