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set, D and E, and they will be pushed outwardly with a pressure of 20 pounds, if their surfaces be each equal to that of the

Fig. 20.

piston A; but if their surfaces be twice, thrice, or four times that of the piston A, the pressure communicated will be 40, 60. or 80 pounds accordingly ; that is, the pressure communicated increases proportionally to the surface. The principle of equality of pressure is generally considered as a consequence of the constitution of liquids. It can be proved by the following experiment that the pressure is really communicated in all directions; but it does not prove that it is equally so. A cylinder, fig. 21, in which a piston

moves, is fixed to a hollow globe on which are placed a number of small cylindric pipes, all perpendicular to the surface. The globe and the cylinder being filled with water, if the piston be pushed inwards the water will spout through all the orifices or pipes, and not through that only which is opposite to the piston. The reason why the principle of equality of pressure, or, as it has been elegantly termed, the Quaquaversal Pressure, cannot be perfectly proved, is that in our experiments wa cannot take away weight from the liquids, nor friction from the pistons which communicate pressure to them. Direction of the Surface of Liquids.--When a liquid is acted on by the force of gravity, only, its surface always tends to take a direction perpendicular to the direction of that force. Thus, suppose that the surface of a liquid, as water, takes for an instant the direction B.A, fig. 22, inclined to the horizon, the

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the direction on P, may be decomposed into two forces, the one Q, acting in the direction on Q perpendicular to the surface A B, and the other F, acting in the direction m F or B.A. The first force Q will be counteracted by the resistance of the liquid mass, and the second F will urge the particle m in the direction, wn F. The same reasoning being applicable to every particle of the liquid surface, it is evident that this surface cannot remain at rest in the direction B A inclined to the horizon, but must assume the horizontal direction, when the force acting in the direction B A becomes zero. If the liquid be acted upon by other forces besides that of gravity, its surface will tend to take a direction perpendicular to that of the resultant of all these forces, as will be seen in the case of the phenomena of capillary attraction. According to the principle explained above, when a liquid is contained in a vessel or basin of small extent, its free surface is plane and horizontal, seeing that at every point of that surface the direction of gravity is then the same. This is not the case, however, in the surface of a liquid of great extent, such as that of the sea. For the surface of the sea being everywhere perpendicular to the direction of gravity, and this direction varying in different places considerably apart from each other, it is plain that the surface of the sea changes its direction with that of gravity; and the latter being constantly directed to the centre of the earth, the former causes the sea sensibly to assume a spherical form, as may be observed in the phenomena of a ship approaching to, or receding from, the shore.

PRESSURE IN LIQUIDS RESULTING FROM THE - ACTION OF GRAVITY.

Laws of Vertical Pressure Downwards.-If we suppose a liquid to be in a state of rest in a vessel, and imagine it to be divided into horizontal layers of equal thickness, it is plain that each of these supports the weight of all the layers which are above it. Throughout the liquid mass, therefore, we see that gravity gives rise to pressures which vary from layer to layer, and from point to point. These pressures, which come under our consideration in their effects on the bottom and sides of vessels, are subject to the following general laws :1st. The pressure on every layer is proportional to its depth. - r 2nd. The pressure is the same on all points of the same horizontal layer. 3rd. At the same depth, in different liquids, the pressure is proportional to the density of the liquid. 4th. In the same liquid, the pressure on any layer is independent of the form of the vessel, and only depends on the depth of that layer. Three of these laws may be considered as self-evident; the proof of the fourth will be seen when we come to the consideration of the pressure on the bottom of vessels.

Vertical Pressure Upwards.-The downward pressure of the upper layers of a liquid upon those which are below them, produces in the latter a reaction which is equal and contrary, in consequence of the principle of the communication of pressure in all directions. This upward pressure is denominated the resistance of liquids. It is very sensible when we push our hand into a liquid, especially if it be one of great density, such as mercury.

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To prove this fact by experiment, we employ a glass tube open at both ends, fig. 23. To the lower end of this tube is applied a disk of glass B, which serves as a stopper, and which is supported in its position by means of a thread A which is fastened to it. This apparatus being immersed in a glass vessel nearly full of water, the hand is removed from the thread and the disk is left free. This disk then remains as a stopper applied to the tube, indicating that it is supported by the upward pressure of the water, which is greater than the downward pressure of its weight, Now, if water be slowly poured into the tube, the disk will continue to support this water until the level of the water within the tube is nearly the same as that without, when the disk will fall to the bottom of the vessel. This experiment proves that the downward pressure on the disk is equal to a column of 'water having for its base the interior secticn of the tube, and for its height the distance of the disk from the upper surface of the water in which the tube is immersed. Hence, the resistance or upward pressure of liquids, as well as their downward pressure, is proportional to their depth.

Pressure on the Bottom of Vessels.--The pressure of a liquid on the bottom of the vessel which contains it, is regulated by the same laws as the pressure on any layer of that liquid; that is, it depends only on the density of the liquid and on its depth, and not on the form of the vessel. That the pressure on the bottom of vessels is independent of their form is proved by the following experiment, the apparatus for which was invented by M. de Haldat. i

This apparatus is composed of a bent tube Act, fig. 24, on

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which, at A, two vessels M and P can be screwed in succession, of the same depth, but of different form and capacity, the first being conical and the second cylindrical. The experiment is made by pouring mercury into the tube A c, until its level nearly reaches the cock A. The vessel M is then screwed on the tube and filled with water; the water by its weight forces the mercury back and causes it to rise in the tube at c H, and its level is marked by means of a slide H, which moves along the part of the tube c D. The level of the water in the vessel. M is marked by means of a moveable rod placed above it. These levels being noted, the vessel M is emptied by the gook at A ; it is then unscrewed, and replaced by the vessel P. , Now, on pouring water into this vessel, the mercury which bad resumed its original level in the tube at A, is again raised in the tube at C ; and as soon as the water reaches the same level in the vessèl P, which it had in the vessel M (which is preserved by the position of the rod above it), the mercury takes exactly the same level in the tube at H, as it did before, this being indicated by the slide H. This pressure is thereforé independent of the shape of the vessel, and consequently of

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the quantity of liquid which it contains, As to the bottom of the vessel, it is evidently the same in the two cases, that is, the surface of the mercury in the tube A c.

From this law, it is evident that by means of a very small quantity of water very considerable pressures may be obtained. For this purpose, we have only to fix in the side of a closed vessel full of water a tube of very small diameter and of great height; this tube being filled with water, the pressure communicated to the side of the vessel is equal to the weight of the column of water which has this side for its base, and whose height is equal to the height of the tube, Thus the pressure of the water on the side of the vessel may be indefinitely increased. In this manner, a narrow pipe of water of the o of 33 feet has burst a strong and well-constructed C3 SK,

On the principle just proved, the pressure of water which exists at the bottom of the sea may be determined. It is known, and will soon be proved, that the pressure of the atmosphere is equivalent to that of a column of water of 33. feet. Now navigators have often observed that the sounding lead does not reach the bottom of the sea at a depth of about 13,200 feet. There is therefore a pressure equal to 400 times that of the atmosphere at the bottom of a sea of the depth of 2% miles.

Lateral Pressure of Liquids.-The pressure which arises from gravity in the mass of aliquid is communicated in all directions according to the quaquaversal principle; hence, it follows that the pressures which take place perpendicularly to the vertical sides of vessels are included in the laws of vertical

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pressure. It has been proved both by analysis and by experi

ment, that the pressure on a given side of a vessel is equal to

the weight of a column of water which has that side for its

base, and for its height the vertical distance of its centre of gravity from the surface of the water. As to the point of, application of this pressure, it is always a little below the

centre of gravity. This point is in fact called the centre of pressure; and its position is determined by calculations of which the following are some results: 1st. The centre of pressure of a rectangular side, of which the upper edge is level

with the water, is situated downwards from that edge at two

thirds of the straight line which joins the middle of its hori

zontal edges. 2nd. The centre of pressure of a triangular side of which the base is level with the upper surface of the water, is in the middle of the straight line which joins the vertex of the triangle with the middle of the base. 3rd. The centre of pressure of a triangle whose vertex is at the level of the water,

and base horizontal, is at the distance of three-fourths of the

straight line joining the vertex and the middle of the base from that vertex.

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The Hydraulie Tourniquet.—When a liquid is in equilibrium in a vessel, it produces on the opposite sides along each horizontal layer pressures equal and contrary in pairs, which counteract each other, so that the existence of these pressures is not manifest; they are, however, proved by the Hydraulic Tourniquet. This apparatus is composed of a glass vessel, fig. 25, which, resting on a pivot, revolves freely round a vertical

Fig. 25.

axis. On this vessel, at its lower end, is fixed, perpendicular to its axis, a copper tube bent horizontally at its two ends and * opposite directions, the bottom of the vessel being fixed in e middle of the tube. If the apparatus be filled with water, and the tube quite closed at both ends, the interior pressures on the sides of the tube counteract each other, and no motion ensues. But if the tube be open at both ends, the liquid escapes, and then the pressure no longer acts on the sides at the orifices B, but only on the opposite sides at A, as seen in the sketch on the right of the figure. The pressure which takes place at A being no longer balanced by the pressure on the opposite point at B, acts upon the tube and on the whole vessel so as to produce a motion of rotation in the direction of the arrow, in the sketch to the right of the figure; this motion being more or less rapid in proportion to the height of the liquid in the vessel, and to the section of the orifices from which the water issues. The motion produced in this apparatus, is similar to that exhibited in the machine known by the name of Barker's mill. The lateral pressure of water is applied in a useful and important manner in the construction of the hydraulic machines called Wheels of Reaction.

Bydrostatic Paradow.—We have already seen that the pressure on the bottom of a vessel full of liquid depends neither on the form of the vessel nor on the quantity of the liquid, but only on the height of the level of the liquid above the bottom. Now, the pressure on the bottom of the vessel must not be confounded with that of the vessel itself on the body which supports it. The latter is always equal to the whole weight of the vessel and of the liquid which it contains; while the former may be greater than this, less than this, or equal to it, according to the form of the vessel. This curious fact is commonly known under the name of the Hydrostatic Paradow, loecause that, at first sight, it seems to be paradoscical, that is, contrary to received notions.

To explain this paradox, let E F PN, fig. 26, be the vertical section of a vessel formed of two cylindrical parts in one piece, but of unequal diameter. Let it be filled with water; then as the horizontal pressures balance each other on all its sides, these may be left out of consideration. The vertical pressure upon the bottom M N, is equal to the weight of a column of the liquid which has this bottom for its base, and the height om $or its altitude ; that is, this pressure is the same as if the vessel had M N I o for its vertical section, and was completely filled with water. This pressure is not wholly communicated to the body which supports the vessel; for according to the

principle of Pascal, the upward pressure of the liquid column, whose section is H E F G, on the annular side of which P G F R is. a section, is equal to the weight of a column of water which would fill the space of which o P G H E FR I is a section. The effective pressure of the liquid on the body supporting the

Fig. 26.

base, is therefore the weight of the volume of water which fills, the space whose section is o M N I, diminished by that of the water which would be contained in the space whose section is o P G H E FR I, that is, in fact, the weight of water actually contained in the given vessel.

If the vessel has the same diameter throughout, the water presses with the same force both on the bottom and on the supporting body; if the vessel has a greater diameter at the top than at the bottom, the pressure on the bottom is less than on the supporting body.

LESSONS IN BOOKKEEPING.-No. VII.
HOME TRADE.
(Continued from page 341, Vol. III.)

WHEN you see in a city, such as London, a space of ground dug up to a certain depth, and surrounded by a hoard, that is, an enclosure formed of a collection of boards fastened to posts driven into the ground, you then begin to think that a building is about to commence, that a superstructure is about to be raised, and that its foundation is in the process of preparation. You are still more convinced of the fact, when you see cartloads of stone, brick, and lime deposited within the hoard, and workmen proceeding to prepare the mortar and stones or bricks for the foundation. So it is in the system of Bookkeeping by Double Entry, which we are about to lay before you. We must begin with a series of Transactions in Business, which are arranged in the exact order of their occurrence, as the materials to be employed in forming a system or superstructure which shall constitute a model for your guidance in keeping the books of any Mercantile house in which you may hereafter be engaged. We have selected the supposed transactions of a particular branch of Home Trade, namely, that of a Cotton Merchant, as one well adapted, from its simplicity and generality, to exemplify the principles which we have explained in former Lessons. We have arranged these transactions in order from January, when we suppose the business to be commenced, till June, when we suppose a Balance to be struck, and the Merchant's Real Worth ascertained. These six months’ transactions in the Cotton trade are interspersed with various Banking, Bill, and Cash transactions, such as might be supposed to occur in the business, of a Cotton Merchant resident in the metropolis; and the whole is afterwards entered in the various subsidiary books which belong to such a business; then into the Journal; and, lastly, into the Ledger. The General Balance is then taken, and the difference between the Assets and Liabilities, or the Real. Worth of the Merchant, is ascertained from the Ledger alone. The remarks which it will be necessary to make concerning the method of Balancing the Books, a process equivalent to the taking of stock among tradesmen and others, who only use Single Entry, we must postpone until we have shown how to make up the Subsidiary Books of our system.

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MEMORANDA OF TRANSACTIONS. ^, — 14th. 1st, 1853 Sold to Williams and Co., London, January 1st, s 14 bags of Grenada Cotton (at I mo. credit) JBegan business with a capital of © e G $1200 0 0 Net 4312 lbs. at 9; d. per lb. e - © #170 13 8 Discount at 1% per cent. to o e 4 & © 2 11 2 3rd. *Lodged my Capital in the London and West- #168 2 6 minster Bank e e o to o o e e Q £1200 0 0 — 17th, — 5th. — Boo of White and Co., London, o 24 f e it. Drew out of the London and Westminster Bank £10 0 0 || No." loo Isl(). so ) £229 11 2 - 5th. Discount at 1% per cent. 3 8 10 Took from Cash for Petty Cash #5 0 0 #226 2 4 — 7th. — 21st. Bought of Osmond and Co., London, Sold to Williams and Co., London, 22 bags of Berbice Cotton (on credit) 16 bags of Grenada Cotton (at 1 mo, credit) Net 7280 lbs. at 9%d. per lb. ... © to o £288 3 4 Net 4928 lbs. at 9%d, per lb., . ... £1.95 l 4 Discount at 1% per cent. & E & to o 2 18 6 — 10th. — *Took from Cash for Petty Cash to o to 5 0 0 £192 2 10 12th. 22nd. —— Bought of Andrews and Co., London, Received of Thomas Watson, London, 30 bags of Grenada Cotton (on credit) My Loan of the 5th instant 4:100 0 0 Net 9240 lbs. at 8%d. per lb. o ... £327 5 0 22nd 17th. Deposited in the London and Westminster Bank £100 0 0 1)rew out of the London and Westminster Bank £985 0 0 25th — 17th. Bought of the East India Company, 3Bought £1000 of Stock in the Three Per Cents. Ö 10 Lots of Madras Cotton (prompt April 25th), viz., Consols, at 98% per cent. e - to “ ". "| No. 1. containing 12bales, net4320ibs. at 4d.périb. g72 0 0 21st. 2. , 12 42 $3. 71 0 0 so 3. ,, 12 4132 59 68 17 4 Accepted a Bill drawn by Osmond and Co., London, 4. , , 12 4084 3 y 68 I 4 No. 1, Payable to their Order, due at 3 months £288 3 3 5. 99 12 3976 - 3 y 66 5 4 6. I2 4092 68 4 0 22nd. 7. . i2 4300 % 80 12 6 Drew out of the London and Westminster Bank £10 0 0 S. 3 3 12 4.184 3 * 78 9 () - 9. 2, 12 3896 }} 73 1 0 22nd. 10. 3, 12 4004 3 y 75 : 6 Took out of Cash for my Private Account £10 0 0 w #721 12 0 26th. 25th Bought of Andrews and Co., London, Du & e 9 to e to James Manning, London, 14 bags of Moranho Cotton (on credit) For his Brokerage on £72, Ios, at 3 per cent. £3 12 2 Net 4350 lbs. at 7%d. per lb. ... £135 18 9 \ —26th. 31st. D f the London and Westminster B * Accepted two Bills drawn by Andrews and Co., London rew Out of the London an estminster Bank £120 0 0 No. 2, Payable to their Order, due at 3 mos. 3327 5 0 — 26th. -* 2, 3, ,, Smith and Co. , 4 mos. 185 18 9|Lent to Darling and Co., of London, #50 0 0 February 1st. 28th. —— : Sold to Brown and Smith, London, * o o o 22 bags of Berbice Cotton (at 1 mo. credit) Fo ; go. § ** Deposit on £60 0 0 Net 7280 lbs. at 10%d. per lb. ... . ... £318 10 0 e e - wome Discount at 13 per cent. ... ... to o o 4 15 7 — 28th. * $313 14 5 Took out of Cash for Petty Cash #10 0 0 — 5th to-wo - {- March 1st. o o o Received of Brown and Smith, London, JDrew out of the London and Westminster Bank £100 0 0 For Cotton sold to them February lst ... £313 14 5 — 5th. — 1st. — lent to Thomas Watson, London o e to £100 0 0|D eposited in the London and Westminster Bank £300 0 0 — 10th. —--— - • 2nd. — Bought of White and Co., London, o Paid James Manning, London, 24 bags of West India Cotton (at 1 mo, credit) For his Brokerage on the purchase of Cotton ... $3 12 2 Net 7460 lbs. at 63d, per lb. to o o £202 0 10 JDiscount at 1% per cent. ... " • Q o 3 0 7 — 3rd. — --- Sold £1000 of Stock in the Three Per Cents, £199 0 3 | Consols, at 99% per cent to e e £997 10 0

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— 3rd. — Teposited in the London and Westminster Bank £1000 0 0 5th. —— Received of Darling and Co., of London,

My Loan of the 26th ult. to e o to e O $50 0 () o-oo-oo-oo 5th. -o-o: Iodged in the London and Westminster Bank ... £50 0 0 Drew out of the London and Westminster Bank £200 0 0 - 10th. — Paid White and Co., London, For Cotton bought of them February 10th ... $199 0 3 —— 13th. Sold to Spencer and Co., London, 14 bags of Maranham Cotton (at 1 mo, credit) -oNet 4350lbs. at 9d. per lb. ... to a o £163 2 6 Discount 13 per cent. • * * • * to o o 2 8 11 $160 13 7 14th. — Received of Williams and Co., London, For Cotton sold to them 14th February £168 2 6 — 14th. Lodged in the London and Westminster Bank £170 0 0 16th. Sold to Thompson and Co., London, 24 bags of West India Cotton, for Cash, Net 7460lbs. at 8%d, per lb. e Q & to e e £264 4 2 T)iscount 2% per cent. & Q q • * * e - e. 6 12 1 #257 [2 1 16th. Received of Thompson and Co., London, For Cotton sold to them this day, * @ e £257 12 1 — 17th. Paid to White and Co., London, For Cotton bought of them 17th February $226 2 4 18th. Took from Cash for Private Account to e > $20 0 0 — 21st. * Peceived of Williams and Co., London, Por Cotton sold to them 21st February #192 2 iO 21st. Deposited in the London and Westminster Bank £200 0 0 nd. — Sold to Althorpe and Co., London, 12 bags of West India Cotton (for cash in a week), Net 4240 lbs. at 8d. per lb. is so o ... £141 8 —— 24th. Bought of Baring, Smith and Co., London, 30 bags of Demerara Cotton (on credit), Net 9248lbs. at 7%d. per lb. ... & e & £288 l 3 —— 26th. * I}rew out of the London and Westminster Bank £600 0 - 26th. — Lent White and Co., London, ... £600 0 0 29th. Received of Althorpe and Co., London, For Cotton sold to them on the 22nd inst. £141 6 8 30th. *-* Received of White and Co., London. My Loan of the 26th inst. • e & * * * $600 0 — 30th. Ideposited in the London and Westminster Bank £740 0 0 31st.

Accepted a Bill drawn by Baring, Smith and Co., London,
No. 4, Payable to their Order, due at 3 mos. £288 1

| pungo (poon-go), I sting.

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* Gn is a combination almost as important as gl. & before n must never be omitted to be sounded, as in the English words. ignaw, gnat, &c., but Englishmen are apt to forget this, and to sound the combination gn in several foreign languages as if no g was before the n. The combination gn must, likewise, never be sounded as gn in the English words signify, malignity, assignation, physiognomy, cognisance, and so on. Those who know French will be able to sound gn at once by bearing in mind the correct pronunciation of gn in the French words mignon, mignard, peigner, oignon, &c., with which the Italian pronunciation of gn exactly agrees. Those who do not understand French may form a notion of the sound, by the same operation pointed out in my explanation. of the sound of gl. They must, as it were, sound the n before the g, and change the latter into y; only taking care that the voice should glide rapidly from n to y, and squeeze, as it were, these two letters into one very mild enunciation. Indeed this very mild enunciation of the squeezed sound gn is a peculiarity of the Italian language, and among foreigners, Germans, who have no corresponding sound, rarely arrive at a correct pronunciation of the gn. The English have words, the pronunciation of which may be said to be an approximation to the Italian sound; as, for example, bagnio, seignior, poignant, poignard, champignon, Spaniard, and, perhaps, most of all, in the word cognac; and therefore Englishmen may, without much difficulty, arrive at a correct pronunciation, never losing sight of the peculiar squeezed and mild sound of the Italian gn.

I shall try to imitate the sound gn by the letters nny in a similar way to that in which I have imitated the sound gl before i and another vowel by the letters lly; and where in Italian words the gn occurs in. the middle and at the end, the first n must go in some respect to one syllable, and the second n along with the y to the next; the voice rapidly gliding from one of those syllables to the other in the way I have already stated. For example: campagna (pronounced kahm-pâhn-nyah), country; vegmente *::::::::::: future, next; Giugno (joðn-nyo), June; gnocchi (nyók-kee), small dumplings, clowns; scrigno (skrin-nyno), hunch, a coffer; Spagnuolo (Spahnmyooô-o), a Spaniard. I must not omit the remark that foreigners, in Italian pronunciation, are apt to confound the two combinations gn and ang as though they were the same. This is not the case. In uttering gn, the g must be converted into y and sounded after n ; while in uttering ng, the g retains the natural sound depending on the vowel that follows. In uttering gn, the n, which is heard before the g, has its natural sound; while in uttering ng, n has a kind of nasal sound. Further, the combination gn always retains its peculiar sound irrespective of the vowels that may follow, which is illustrated in the pronouncing table above; while in the combination rig, g has the sound of the English g in got before the vowels a, o, and u, and the sound of the English j before the vowels e and i. For example: giugno (joðn-hyo), June, and giungo (joon-go), I arrive, I join ; agnolo (ähn-nyo-lo), angel, and angelo (ähn-jai-lo), angel ; pugno (poćn-nyo), fist, cuff, I fight, and g. As a last remark on the gn, I have to not that when gn is followed by the letter i, it is a sign to at gni is to form a syllable-by itself; and the in such cases is never a mere auxiliary letter—never a mere soundless, written sign to indicate that gn is to have a squeezed sound, because, as I have

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