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WHY IS A CARRIAGE LIGHTER WHEN IN MOTION THAN AT REST? 135 the end of two seconds it will be found at diately return to their figure by their natwenty feet froni the cliff, and sixty-four tural elasticity. feet below it: and thus it will appear, For instance, if a body, B, whose vethat both powers operate without either locity is 12, impinge against A, in a state diminishing the other. If any one will of rest, and whose mass is to that of B examine thin ice breaking under too as 3:1, the direction of the inotion oriheary pressure, he will perceive that it ginally impressed upon the body, B, will is a progressive, and not an instantaneous be changed after the stroke, and it will action. It bends first to a considerable return with the velocity of 6. In this inextent, and receives an additional sup- stance we suppose B and A to be perport from the water thus displaced underfectly elastic; but as we are unacquainted it, like a shallow boat; the pressure con- with any bodies possessing this quality in tinuing, it begins to crack in lines, ra- so perfect a degree, allowance must, of diating from the point where the force course, be made in speaking of natural is exerted; when these have proceeded bodies; those which approach the nearest to a sufficient extent to have leverage to this perfect state of elasticity.

state of elasticity, admitenough, notwithstanding the counter- ting inore immediately of the application acting increase of width of the pieces in- of the general rule. tercepted between these radii, the whole We will endeavour to apply this rule breaks in by a fracture nearly circular. to the question under consideration. In proportion as there is a greater dispa- When the ball is in a state of rest upon rity between the force applied and the the weigh-bridge, the latter body, after resistance, this process goes on with the elasticity generated by the first immore rapidity; when the powers are pression (viz. the impression exerted by nearly balanced, I have seen ice sustain the ball in the act of being placed upon weights for a second or two that it broke the bridge) has subsided, is then acted in with; in fact, the process of break upon only by the force of gravity, which ing occupied this time. Hence, if a man acts equally and every moment of time skating over ice too thin to sustain his weight resting long upon it, quits his If the ball be thrown down upon the place continually before the process is bridge with the velocity of 12, the mass completed, he does pass over ice that of the bridge beiug to the mass of the ball may be said to be too weak to sustain as 3:1, the ball will rebound, and rehis weight; but the fact arises from the turn with the velocity 6 (supposing the slow, counteracting process, and no force of gravity suspended); but supother cause. Time is a necessary ele- posing the force of gravity existing, 'it ment iv all calculations of force. A shot must be subtracted from the last-menwill cut a piece out of a board suspended tioned velocity. by a string, and scarcely stir the board; In this case it is evident, that immethus the firm attraction of the particles diately after the stroke, and during the of the wood give way, apparently with- action of elasticity, not only is the force out effort, because attraction is a thing of gravity insensible, but absolutely overmeasured by the time it operates ; but it come, and a motion impressed upon the is equally effective during every portion ball in a direction contrary to the first. of it, and the amount of the whole in a This case is easily applicable to that of given time is a given sum. If a carriage the ball rolling over the bridge, the mooccupy one second in going over the flat tion of which may be considered as a sucboard of a weighing-uachine, it will cession of strokes, the momentum of distribute as much pressure over the each being equal to the force of gravity. whole length as it would have applied to If the velocity of the ball generated by any one point of it, on which it stood gravity, for argument sake, be supposed still during the same time. Hence I con- equal to 12, and the masses bearing the ceive the Carriage Question may as well same proportion as above, gravity would rest as be kept going.

then, of course, be insensible, and the I am, Sir,

bridge would be under no impression: Your obedient servant,

but as neither of the masses bear this 'G. C. proportion, or the velocity of the ball

the same as above, the general result

must, of course, be different. ON THE SAME QUESTION.

It is upon this principle that a carriage From another Correspondent.

suspended on springs moves with less

resistance over a road, than would a carSIR.-It is a well-known principle in riage of like bulk without springs. mechanics, that when two bodies impinge against each other, the mutual ac

I am, Sir, tions of one body against the other are

Your obedient servant, invariably equal. By this action the parts of the bodies yield inwards, but imme

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H. W. B. N.

Woolwich.

( 136 )

.. PLAN OF A SIMPLE STEAMWHEE L.

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SIR, -I send you the plan of a curred on that occasion. Whilst the Steam-Wheel, the model of which I engine was at work, Mr. Boulton set to work in Mr. Boulton's labora- was called out of the room; on his tory, at Soho, about twenty years return, he informed me that he had ago. A remarkable coincidence oc- been requested by an American gen

IMPROVEMENT OF WHEEL CARRIAGES.

137 tleman to give his advice on the same the hot water, in some degree, but it invention, and that one of us must may easily be restored again, by have borrowed it from the other. melting the oxide under tallow.When This, however, proved not to be the water only is used, the whole machine case; and, on more minute examina- niay be made of wood, in the form of tion, there appeared a considerable a common bucket water-wheel; a difference in the mode of constructing steam pipe is introduced through the the American engine, though acting bottom of the trough, just under the on the same general principle as my side of the wheel where the buckets own. From that time to this, I believe are inverted, when they become filled neither of these engines have ever with steam in succession, and thus a been applied to any use, though a streain of steam effects as much, patent was obtained for the American bulk for bulk, as a stream of water. engine, which was, I think, the best This is the form of the American of the two, if used with water only. engine. I conceive, however, that these en Fig. 2 is a plan for admitting the gines are so simple in principle, and steam into the pipes leading to the so cheap and durable, that, on many cells, but many better modes might occasions, if generally known, they be adopted; this is, however, suffiwould be applied with great advan- cient to explain my engine. It is tage. The power of them is derived scarcely necessary to mention, that from the tendency of light bodies to the steam tubes should be covered up float when immersed in heavy fluids, by circular plates on each side of the or, to speak inore correctly, of the wheel, to obviate the resistance in heavy fluids to displace them. passing through the fluid. Fig. 1 exhibits a wheel divided into

I remain, Sir, cells, and placed under heated mer.

Your obliged servant, cury, or that mixture, of eight parts

G. C. of bismuth, five lead, and three tin, which is fluid at the temperature of 2120; or, where waste of fuel and loss of space are no great objects,

IMPROVEMENT OF WHEEL CARplaced only under boiling water. Each

RIAGES. of these cells is connected by any SIR, Your Correspondent signappropriate means with a steam pipe, ing himself R. E. (p. 103, vol. iy.) so that each receives the steam; inquires, whether any benefit would when at the bottom, the floating be derived by a horse in drawing a power then brings the other cells in gig by shafts, connected to the other succession to be filled with steam, part of the carriage by a resisting and the wheel is thus put into full spring, in order, as your Correaction. Where the expansive force spondent says, “ to relieve him at only is used, the steam escapes from starting, and on meeting with any the top of the trough; but if this be obstructions on the road.” Now, connected with a condenser and air. Sir, I apprehend the very reverse of pumps, as usual, the full power will ease would be the consequence of be obtained with the metallic fluids. such an alteration; as the horse Each cubic foot of steam, in water, would then have to overcome the rewill give about 60 pounds of power; sistance of the spring, in addition to in the metallic mixture, about 600 that of the carriage, and his whole pounds; and the velocity with which labour would be further increased by this supply can be afforded, and the the unsteady purchase it would height it can rise, will give the re- create. My ideas for an improvemaining elements for calculating the ment in the draught of gigs, would power of the engine. As the steam suggest an immediate connexion of will expand as it rises up in the the shafts to the axle-trees, thus disbuckets, no more should be allowed pensing with traces; and by allowto enter than will fill them when at ing the line of draught to be quite the top of the wheel. The metallic straight, and at a proper angle, it mixture is subject to oxidation by would tend to prevent much useless

THE

138

ON CEMENTING WATER AND STEAM-PIPE JOINTS. labour to the animal, and much pipes would, when laid down, remain unnecessary strain upon the wood. fixed and immoveable. There were vawork.

rious forks in some of the pipes, on the

right and left sides, in case a supply of While upon this subject, I am anxi. water should afterwards have been ous to know the opinion of some of wanted in those directions; those were your Correspondents upon double plugged, and never used; the water was or under-springed carriages. They taken from the pipes at three different seem to me well calculated to pre

places, about 100 feet apart, by orifices

left in the upper surfaces of the pipes. serve the carriage part, but I think,

What jar or shake the pipes could feel besides the extra weight, that they from the velocity of the water passing add to the difficulty of draught; in through them, I am quite at a loss to asmuch as any person sitting in the find out, as the pipes would always reinside of the chariot will perceive,

maiu full, except when water was draw

ing from thein ; aud as that was from upon passing any obstacle, that he

lead pipes, and cocks of about an inch in is subjected to a second rocking or

diameter, it would be scarcely felt on undulation before the first has pipes of three inches bore. Your Bow ceased, and that the horses have in Engineer states, that he uses iron borings creased labour till they receive their

pounded, which must be difficult to be steady pull. This inconvenience

got in most places (I fear he means to might, perhaps, be dirninished by

bore your Henley inquirer). To be sure,

iron filings can be got in most country having the under-springs longer, so smiths' shops; but then these cannot that they, as well as the whip. need pounding. The place where my springs, might get into action, and pipes were laid down was very near to again become quiescent at the same

the yard of a shipwright, who did a good

deal of work, and for more than thirty time.

years I was very frequently in the yard, I am, Sir,

viewing vessels building and caulking, Your most obedient servant,

and I have some little idea how the latter

work is done, but I can form no concepD. P. BUNGY. tion how such a substance, as your Bow

Engineer describes, can be caulked into the ends of the joints of iron pipes. I

am certain it cannot be by what the REPLY OF DIR. WAY, ON CEMENTING

caulkers call their art and mystery,

namely, drive and go; if it is, cast iron WATER AND STEAM-PIPE JOINTS.

pipes would soon go to atoms. I cannot SIR,-Your nameless Correspondent, here lay my hand on the directions given who writes from Bow (p. 389, vol. III.), me hy the agent of the Neath Abbey ironcalls himself a 6 Practical Engineer" foundry for a luting, where that is rebut without better authority thau his lét- quisite, and at this distance of time I ter, I should doubt his claiin to the title cannot remember all the materials of he assumes. When I had stated so dis- which it was composed: borax was one tinctly, that the water was pumped into of the principal articles, but I am certain a reservoir, about 900 feet from the there were rio iron borings in it, as regreatest extent to which the water was commended by your Correspondent. Bebrought that pipes of three inches in tween us, however, I dare say we shall diameter were used; that part were afford sutlicient information for the purtlanged, and part spiggot and faucet; pose of your Henley Correspondeut." In and that the water was raised in my my letter, I certainly had no idea of house from the pipes, through lead ones, giving information to real practicul engia height of about eight feet; if he had neers, being well aware that they were becil what he pretends to be, he would too well informed for any thing I could have required no other information to write to be of the slightest use to them; enable him to calculate the pressure of I cousidered (as I stated nothing but water upon the joints; which, for nic, plain facts, avd those in the plainest who am not a practical evgineer, might way) that if they found a place in your possibly have proved a more difficult task. very valuable publication, they might He must also, I think, have been aware afford some useful hints to persons in that, as the easiest way to fill the reser- the same situation in which I was placed. voir, the water would be pumped into it as well as to such sort of mechanics as I at the top, on the side nearest the well; then employed. aud that, for the sake of economy, it The friend who supplied me with the would be conveyed into the pipes, by fix. Roman cement I used, has been dead ing them at the bottom of the reservoir, some years; but I have before me a letnearest the house, and, of course, not ter from his only surviving son, dated connected with the pump; and that the the 7th of March, referring me to your

CALCULATION OF INTEREST AT FIVE PER CENT.

139 Magazine for a description of an engine But the first thing wbich strikes the he meant to examine," which (he adds) scientific observer's eye is, the first I see, by a letter in a Number of last antecedent is equal to the first consemonth, you occasionally look into. Tho- . quent, and therefore may be both inas Everett came into the counting

exterminated without altering the house one day, and I gave it him to read.

proportionality of the analogy as to He is highly pleased to find his name in print. I have employed him for several

numberyears, and I do not think there is a more days.

. . days. . honest man in existence, nor one that 365 . 25 :: 219 has your interest more at heart while working for you." This gentleman was

To meet my view of the true prinborn, and has always lived, in the parish ciples of proportion, we must make an in which my pipes are laid down.

alteration in the relative positions of · I am, Sir, yours, &c.

the above remaining terms, viz.A CONSTANT READER AND SUBSCRIBER.

days.

days. l. 365

219 :: 25

25 CALCULATION OF INTEREST AT

1095 FIVE PER CENT.

438 Multiply the sum by the days, and . divide the product by 365, the quotient will be the answer in shillings. Query,

365) 5475 (15 Why is it so ? ..

1825
I days. I. 2. days. s.
100.. 365 .. 5 :: 25..219 ..15
365 . . 219 .

It is here very evident that the quo-
36500
1095

tient 15, found as above, must be 151. 438

sterling, therefore cannot be the true interest sought; but as some sensible

gentleman may have discovered that 5475

the true answer was 15 shillings, he very shrewdly suggested, as a short cut,

15 = 15; therefore call the quotient 36500) 27375 (0 shillings, and you will be right."

This being a mechanical mode of

obtaining scientific results, induced me Here we find the product of the an- to think it may be particularly applitecedents greater than that of the con- cable to your widely-circulating and sequents, and we must proceed to bring useful publication; allow me, therethe latter into the next lower denomi- fore, to endeavour to explain all this pation, which, being shillings, we mul- to you. Let x equal the interest of tiply by 20.

one hundred pounds for one day; if the 27,375

one hundred pounds be forborne for ten

days, the interest will be ten times x. 20

If ten hundred' pounds be forborne for

one day, and that the interest of one 365,00) 547,500 (15s. true ans. hundred pounds for one day equals x, 1825

ten times x must be the interest, the same as in the case of one hundred pounds for ten days, and we at once obtain the following corollary :--If any

number of pounds be multiplied by We first multiplied the product of 1

any number of days, the product will

be a sum, the interest of which for the sum and days by the factor 5, and one day will be equal to the interest then multiplied that product by 20, of the given suin for the given days. but x x 5 x 20 = x x 100; therefore, re

Now, on referring to our last analogy, ferring to our original statement, we

we may read it thus:--As the whole may make a new one, as follows:

year is to the number of days forborne, days." shillings. l. days. so is the principal sum to the fourth 100., 365 .. 100 :: 25., 219 proportional, which shall be the sum,

5

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