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th, D and 3, and they will be pushed outwardly with a pres. I the direction in P, may be decomposed into two forces, the one fede of 20 pounds, if their surfaces be each equal to that of the Q, acting in the direction me perpendicular to the surface A B,
and the other F, acting in the direction M F Or B A. The first Fig. 20.
force Q will be counteracted by the resistance of the liquid mass, and the second F will urge the particle m in the direction,
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 B
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 direc
tion of gravity is then the same. This is not the case, howpiston A; but if their surfaces be twice, thrice, or four times ever, in the surface of a liquid of great extent, such as that of that of the piston A, the pressure communicated will be 40, 60, the sea. For the surface of the sea being everywhere perpenor 80 pounds accordingly; that is, the pressure communicated dicular to the direction of gravity, and this direction varying increases proportionally to the surface.
in different places considerably apart from each other, it is The principle of equality of pressure is generally considered plain that the surface of the sea changes its direction with as a consequence of the constitution of liquids. It can be that of gravity; and the latter being constantly directed to proved by the following experiment that the pressure is the centre of the earth, the former causes the sea sensibly to really communicated in all directions; but it does not prove assume a spherical form, as may be observed in the phenomena that it is equally so. A cylinder, fig. 21, in which a piston of a ship approaching to, or receding from, the shore. Fig. 21.
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.
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 con. moves, is fixed to a hollow globe on which are placed a num- sideration of the pressure on the bottom of vessels. ber of small cylindric pipes, all perpendicular to the surface. Vertical Pressure Upwards.---The downward pressure of the The globe and the cylinder being filled with water, if the pis- upper layers of a liquid upon those which are below them, ton be pushed inwards the water will spout through all the produces in the latter a reaction which is equal and contrary, orifices or pipes, and not through that only which is opposite in consequence of the principle of the communication of to the piston. The reason why the principle of equality of pressure in all directions. This upward pressure is denomipressure, or, as it has been elegantly termed, the Quaquaversal nated the resistance of liquids. It is very sensible when we Pressure, cannot be perfectly proved, is that in our experiments push our hand into a liquid, especially if it be one of great we cannot take away weight from the liquids, nor friction from density, such as mercury. the pistons which communicate pressure to them.
Fig. 23. 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 en instant the direction B A, fig. 22, inclined to the horizon, the
We wie pravity P on any particle m of this surface having
To prove this fact by experiment, we employ a glass tube the quantity of liquid which it contains, As to the bottom open at both ends, fig. 23. To the lower end of this tube is of the vessel, it is evidently the same in the two cases, that is, applied a disk of glass B, which serves as a stopper, and which the surface of the mercury in the tube A C. is supported in its position by means of a thread A which is
From this law, it is evident that by means of a very small fastened to it. This apparatus being immersed in a glass quantity of water very considerable pressures may be obtained. vessel nearly full of water, the hand is removed from the For this purpose, we have only to fix in the side of a closed thread and the disk is left free. This disk then remains as avessel full of water a tube of very small diameter and of great stopper applied to the tube, indicating that it is supported by height; this tube being filled with water, the pressure comthe upward pressure of the water, which is greater than the municated to the side of the vessel is equal to the weight of downward pressure of its weight. Now, if water be slowly the column of water which has this side for its base, and whose poured into the tube, the disk will continue to support this height is equal to the height of the tube, Thus the pressure water until the level of the water within the tube is nearly of the water on the side of the vessel may be indefinitely the same as that without, when the disk will fall to the boto increased. In this manner, a narrow pipe of water of the tom of the vessel. This experiment proves that the downward height of 33 feet has burst a strong and well-constructed pressure on the disk is equal to a column of water having for cask. its base the interior section of the tube, and for its height the distance of the disk from the upper surface of the water in exists at the bottom of the sea may be determined. It is
On the principle just proved, the pressure of water which which the tube is immersed. Hence, the resistance or upward known, and will soon be proved, that the pressure of the pressure of liquids, as well as their downward pressure, is atmosphere is equivalent to that of a column of water of 33. proportional to their depth.
feet. Now Davigators have often observed that the sounding Pressure on the Bottom of Vessels. The pressure of a liquid lead does not reach the bottom of the sea at a depth of about on the bottom of the vessel which contains it, is regulated by 13,200 feet. There is therefore a pressure equal to 400 times the same laws as the pressure on any layer of that liquid; that of the atmosphere at the bottom of a sea of the depth of that is, it depends only on the density of the liquid and on its 21 miles. depth, and riot on the form of the vessel. That the pressure on the bottom of vessels is independent of their form is prored gravity in the mass of a liquid is communicated in all directions
Lateral Pressure of Liquids.
The pressure which arises from by the following experiment, the apparatus for which was according to the quaquaversal principle; hence, it follows invented by M. de Haldat.
that the pressures which take place perpendicularly to the This apparatus is composed of a bent tube A CD, fig. 24, on vertical sides of vessels are included in the laws of vertical
which, at A, two vessels m and p can be screwed in succession, | pressure. It has been proved both by analysis and by experiof the same depth, but of different form and capacity, the first ment, that the pressure on a given side of a vessel is equal to being conical and the second cylindrical. The experiment is the weight of a column of water which has that side for its made by pouring mercury into the tube A c, until its level base, and for its height the vertical distance of its centre of nearly reaches the cock A. The vessel is then screwed on gravity from the surface of the water. As to the point of the tube and filled with water ; the water by its weight forces application of this pressure, it is always a little below the the mercury back and causes it to rise in the tube at C H, and centre of gravity. This point is in fact called the centre of its level is marked by means of a slide H, which moves along pressure ; and its position is determined by calculations of the part of the tube cd. The level of the water in the which the following are some results : 1st. The centre of pres, vessel n is marked by means of a moveable rod placed sure of a rectangular side, of which the upper edge is level above it. These levels being noted, the vessel m is emptied by with the water, is situated downwards from that edge at twothe cock at A; it is then unscrewed, and replaced by the vessel thirds of the straight line which joins the middle of its hori. P. Now, on pouring water into this vessel, the mercury which zontal edges. 2nd. The centre of pressure of a triangular side had resumed its original level in the tube at a, is again raised of which the base is level with the upper surface of the water, in the tube at c; and 28 son as the water reaches the same is in the middle of the straight line which joins the vertex of level in the vessel P, which it had in the vessel m (which is the triangle with the middle of the base. 3rd. The centre of preserred by the position of the rod above it), the mercury pressure of a triangle whose vertex is at the level of the water, takes exactly the same level in the tube at #, as it did before, and base horizontal, is at the distance of three-fourths of the this being indicated by the slide H. This pressure is therefore straight line joining the vertex and the middle of the base mdependent of the shape of the vessel, and consequently or from that vertex,
The Hydraulic Tourniquet. - When a liquid is in equilibrium principle of Pascal, the upward pressure of the kquid column, in a vessel, it produces on the opposite sides along each hori- whose section is # EFG, on the annular side of which P GFR is zontal layer pressures equal and contrary in pairs, which a section, is equal to the weight of a column of water which counteract each oiher, so that the existence of these pressures would fill the space of which o PG HEFRI is a section. The is not manifest; they are, however, proved by the Hydraulic effective pressure of the liquid on the body supporting the Tourniquet. This apparatus is composed of a glass vessel, fig. 25, which, resting on a pivot, revolves freely round a vertical Fig. 25.
base, is therefore the weight of the volume of water which fille. the space whose section is OMNI, diminished by that of the water which would be contained in the space whose section is OPGHE FRI, 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. axis. On this vessel, at its lower end, is fixed, perpendicular to its axis, a copper tube bent horizontally at its two ends and in opposite directions, the bottom of the vessel being fixed in the middle of the tube. If the apparatus be filled with water, LESSONS IN BOOKKEEPING.-No. VII. and the tube quite closed at both ends, the interior pressures
HOME TRADE. on the sides of the tube counteract each other, and no motion But if the tube be open at both ends, the liquid
(Continued from page 341, Vol. III.) 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 WAEN you see in a city, such as London, a space of ground the sketch on the right of the figure. The pressure which dug up to a certain depth, and surrounded by a hoard, that is, takes place at A being no longer balanced by the pressure on
in enclosure formed of a collection of boards fastened to posts the opposite point at B, acts upon the tube and on the whole driven into the ground, you then begin to think that a buildvessel so as to produce a motion of rotation in the direction of ing is about to commence, that a superstructure is about to be the arrow, in the sketch to the right of the figure; this motion raised, and that its foundation is in the process of preparation. being more or less rapid in proportion to the height of the You are still more convinced of the fact, when you see cartliquid in the vessel, and to the section of the orifices from loads of stone, brick, and lime deposited within the hoard, and which the water issues. The motion produced in this appara- workmen proceeding to prepare the mortar and stones or tus, is similar to that exhibited in the machine known by the bricks for the foundation. So it is in the system of Bookname of Barker's mill. The lateral pressure of water is applied keeping by Double Entry, which we are about to lay before in a useful and important manner in the construction of the you. We must begin with a series of Transactions in Business, hydraulic machines called Wheels of Reaction.
which are arranged in the exact order of their occurrence, as
the materials to be employed in forming a system or superHydrostatic Paradox.-—We have already seen that the pres- structure which shall constitute a model for your guidance in sure on the bottom of a vessel full of liquid depends neither keeping the books of any Mercantile house in which you may on the form of the vessel nor on the quantity of the liquid, hereafter be engaged. We have selected the supposed transbottom. Now, the pressure on the bottom of the vessel must actions of a particular branch of Home Trade, namely, that of a bottom. Now, the pressure on the bottom of the vessel must Cotton Merchant, as one well adapted, from its simplicity and not be confounded with that of the vessel itself on the body generality, to exemplify the principles which we have exwhich supports it. The latter is always equal to the whole plained in former Lessons. We have arranged these weight of the vessel and of the liquid which it contains ; while transactions in order from January, when we suppose the the former may be greater than this, less than this, or equal business to be commenced, till June, when we suppose a to it, according to the form of che vessel. This curious fact is Balance to be struck, and the Merchant's Real Worth ascercommonly known under the name of the Hydrostatic Paradox, tained. These six months' transactions in the Cotton trade because that, at first sight, it seems to be paradoxical, that is, are interspersed with various Banking, Bill, and Cash transcontrary to received notions.
actions, such as might be supposed to occur in the business To explain this paradox, let Efen, fig. 26, be the vertical of a Cotton Merchant resident in the metropolis ; and the section of a vessel formed of two cylindrical parts in one piece, whole is afterwards entered in the various subsidiary books which but of unequal diameter. Let it be filled with water; then as belong to such a business; then into the Journal; and, lastly, the horizontal pressures balance each other on all its sides, into the Ledger. The General Balance is then taken, and the . these may be left out of consideration. The vertical pressure difference between the Assets and Liabilities, or the Real upon the bottom mn, is equal to the weight of a column of the Worth of the Merchant, is ascertained from the Ledger alone. liquid which has this bottom for its base, and the height om The remarks which it will be necessary to make concerning for its altitude ; that is, this pressure is the same as if the the method of Balancing the Books, a process equivalent to the vessel had M N 10 for its vertical section, and was completely | taking of stock among tradesmen and others, who only use filled with water. This pressure is not wholly communicated Single Entry, we must postpone until we have shown how to to the body which supports the vessel; for according to the l make up the Subsidiary Books of our system,
Bought of White and Co., London,
24 bags of West India Cotton (at 1 mo. credit) Drew out of the London and Westminster Bank £10 00
Net 8476 lbs. at 6d. per Ib.
£229 11 2 5th. Discount at 11 per cent.
3 8 10 Took from Cash for Petty Cash £5 00
£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)
£195 1 4 Discount at 11 per cent.
2 18 6 10th. Took from Cash for Petty Cash 5 0 0
£192 2 10 12th.
Receired of Thomas Watson, London, Bought of Andrews and Co., London, 30 bags of Grenada Cotton (on credit)
My Loan of the 5th instant
£100 00 Net 9240 lbs. at 8 d. per lb. .... £327 5 0
Deposited in the London and Westminster Bank £100 0 0 Drew out of the London and Westminster Bank £985 0 0
Bought of the East India Company, Bought £1000 of Stock in the Three Per Cents.
10 Lots of Madras Cotton (prompt April 25th), viz., Consols, at 98% per cent.
No. 1. containing 12 bales, net 4320lbs. at 4d. per lb. £72 0 0
71 0 0 21st.
68 17 4 Accepted a Bill drawn by Osmond and Co., London,
68 14 No. 1, Payable to their Order, due at 3 months £288 3 3
66 5 4
68 4 0 22nd.
80 12 6 Drew out of the London and Westminster Bank £10 00
78 9 0)
73 1 0 22nd.
75 1 6 Took out of Cash for my Private Account £10 00
£721 12 0 26th,
25th. Bought of Andrews and Co., London,
Due to James Manning, London, 14 bags of Maranham Cotton (on credit) Net 4350 lbs. at 7 d. per lb.
For his Brokerage on £721 12s. at : per cent. £3 12 2 £135 18 9
Drew out of the London and Westminster Bank £120 00 Accepted two Bills drawn by Andrews and Co., London No. 2, Payable to their Order, due at 3 mos. £327 50
26th. , 3, Smith and Co. 4 mos. 135 18 9 Lent to Darling and Co., of London,
£50 00 February 1st.
28th, Sold to Brown and Smith, London,
Paid the East India Company their Deposit on 22 bags of Berbice Cotton (at 1 mo. credit)
10 Lots of Cotton at £6 per Lot
£60 0 0 Net 7280 lbs, at 10d. per lb.
£318 10 0 Discount at li per cent.
4 15 7
28th, Took out of Cash for Petty Cash
£10 0 0 £313 14 5
March 1st. 5th.
Receired of Brown and Smith, London, Drew out of the London and Westminster Bank £100 0 0
For Cotton sold to them February Ist
£313 14 5 5th.
Ist. Lent to Thomas Watson, London
£100 0 0
Deposited in the London and Westminster Bank £300 0 0 10th,
2nd. Bought of White and Co., London,
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 6d. per Ib.
£202 0 10 Discount at li per cento
3 0 7
3rd, Sold 41000 of Stock in the Three Per Cents. £199 0 3 Consols, at 997 per cent
$997 10 0
LESSONS IN ITALIAN GRAMMAR.NO. VIII. Deposited in the London and Westminster Bank £1000 0 0
By CHARLES TAUSENAU, M.D., 5th, Received of Darling and Co., of London,
Of the University of Paria, and Professor of the German and Italian My Loan of the 26th ult.
Languages at the Kensington Proprietary Grammar School, 5th.
(Continued from p. 104.) Lodged in the London and Westminster Bank £50 0 0
7. Gna, Gne, Gni, Gno, Gnu.
£200 0 0 Gnao
Mewing of cats
Grrido Paid White and Co., London,
Gnidus, a town of Caria
nyô-mai For Cotton bought of them February 10th
Nobody, not one
Sign 14 bags of Maranham Cotton (at 1 mo. credit)
£163 2*6 Sogno
Dream Discount 17 per cent.
2 8 11 | Pugno
Fist, cuff, I fight
kôn-byee-to Known Received of Williams and Co., London,
Everybody 14th. Lodged in the London and Westminster Bank £170 00
* Gn is a combination almost as important as gl. G before no 16th.
must never be omitted to be sounded, as in the English words Sold to Thompson and Co., London,
gnaw, gnat, &c., but Englishmen are apt to forget this, and to
sound the combination on in several foreign languages as if nog 24 bags of West India Cotton, for Cash,
was before the n. The combination on must, likewise, never be Net 7460lbs. at 8 d. per lb.
£264 4 2 sounded as gn in the English words signify, malignity, assignation, Discount 23 per cent.
6 12 1 physiognomy, cognisance, and so on. Those who know French will
be able to sound on at once by bearing in mind the correct pro
£257 12 1nunciation of gn in the French words mignon, mignard, peigner, 16th,
oignon, &c., with which the Italian pronunciation of gn exactly Received of Thompson and Co., London,
agrees. Those who do not understand French may form a notion For Cotton sold to them this day,
of the sound, by the same operation pointed out in my explanation £257 12 1
of the sound of gl. They must, as it were, sound the n before the 17th.
9, and change the latter into y; only taking care that the voice
should glide rapidly from 1 to y, and squeeze, as it were, these Paid to White and Co., London,
two letters into one very mild enunciation. Indeed this very mild For Cotton bought of them 17th February £226 24
enunciation of the squeezed sound on is a peculiarity of the Italian 18th.
language, and among foreigners, Germans, who have no correTook from Cash for Private Account
£20 O o sponding sound, rarely arrive at a correct pronunciation of the gn.
The English have words, the pronunciation of which may be said 21st.
to be an approximation to the Italian sound; as, for example, Received of Williams and Co., London,
bagnio, seignior, poignant, poignard, champignon, Spaniard, and, For Cotton sold to them 21st February £192 2 10 perhaps, most of all, in the word cognac; and therefore English
men may, without much difficulty, arrive at a correct pronunciation, 21st.
nerer losing sight of the peculiar squeezed and mild sound of the
Italian on. Deposited in the London and Westminster Bank £200 0 0
I shali try to imitate the sound on by the letters nny in a similar 22nd.
way to that in which I have imitated the sound gl before i and another Sold to Althorpe and Co., London,
vowel by-the letters lly; and where in Italian words the on occurs in. 12 bags of West India Cotton (for cash in a week),
the middle and at the end, the first uz must go in some respect to one Net 4240 lbs. at 8d. per lb.
£141 6 8 syllable, and the second n along with the y to the next; the voice 24th.
rapidly gliding from one of those syllables to the other in the way
I have already stated. For example: campagna (pronounced Bought of Baring, Smith and Co., London,
kahin-páhn-nyah), country; vegnente (ren-nyên-lai), future, next; 30 bags of Demerara Cotton (on credit),
Giugno (joon-nyo), June; gnocchi (nyok-kee), small dumplings, Net 9218lbs. at 7 d. per lb.
£288 1 3 clowns; 'scrigno (skríunnyno), hunch, a coffer; Spagnuolo (Špahn26th.
nyooo--), a Spaniard. I must not omit the remark that foreigners.
in Italian pronunciation, are apt to confound the two combinations Drew out of the London and Westminster Bank £600 0 Ogn and ng as though they were the same. This is not the case. In 26th.
uttering on, the g must be converted into y and sounded after n;
while in uttering ng, the g retains the natural sound depending on Lent White and Co., London,
£600 0 0 the vowel that follows. In urtering gn, the n, which is heard 29th.
before the g, has its natural sound; while in uttering ng, n has a
kind of nasal sound. Further, the combination on always retains Received of Althorpe and Co., London,
iis peculiar sound irrespective of the vowels that may follow, which For Cotton sold to them on the 22nd inst. £141 6 8
is illustrated in the pronouncing table above; while in the com30th.
bination rg, g has the sound of the English g in spent before the Received of White and Co., London.
vowels a, o, and u, and the sound of the English j before the My Loan of the 26th inst.
£600 0 0 vowels e' and i.
For example: giugno (joon-nyo), June, and
giungo (joon-go), I arrive, I join; agnolo (áhn-nyo-lo), anges, and 30th.
angelo (áhn-jai-lo), angel; pugno (poon-nyo), fist, cuti, 1 fight, and Deposited in the London and Westminster Bank £740 0 0. pungo (poon-go), I sting. As a last remark on the gra, I have to
Kot, that when yn is followed by the lettere, it is a sign tnat gni is 31st.
w form a syllable by itself; and the i in such cases is never a Accepted a Bill drawn by Baring, Smith and Co., London, mere auxiliary letter-never a mere soundless, written sign to
No. 4, Payable to their Order, due at. 3 mos. £288 i 3 indicate that yn is to have a squeezed sound, because, as I have ·