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according to the numbers in the preceding list. - The column marked B. contains the area of each Y-3 ! - - ; g * & SJ; * I a province in square miles, whether single, double, Môlena. , - . # !. “ **. or inclusive, according to the same numbers. . - - The column marked c. contains the population of each province according to the same numbers. The column marked D. contains the number r; inhabitants to every square mile, according to the same numerical arrangement.

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Plorence Ical ^2 A. B. C. | D. offliorno, 1 | 12,268 *ś 17, 2 2,788 147,000 52 3 8,680 99S,000 115 4 10,952 | 1,293,000 | 138 T II E 5 11,109 867,000 78 ' (S. VTN - 6 || 19,953 4,513,000 226 AU.STIRIAN ENIIPIRJEs 7 8,602 | 1,826,000 212 s’ 8 1,988 467,000 235 WITIE THE JRAIL WAYS. 9 33,800 || 4,911,000 | 1.45 10 22, 196 || 1,966,000 S9 to 11 | 69,504 || 8,185,000 | 1 || 7 | English Miles 12 10.902 1,362,000 | 125 So . 13 7,423 887,000 119 : 14 4,927 402,000 81 15 15,138 1,220,000 S0 16 || 17,511 4,803,000 | 274

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Cause of the Curvature of Liquids in Contact with Solids.-The differences in the form of the surface of a liquid in contact with a solid body, arise from the differences in the ratio which exists between the attraction of the solid for the liquid, and of the attraction of the liquid for itself. Suppose, for instance, that a liquid particle m, fig. 54, is in contact with a solid body. This particle is under the action of three forces ; viz., 1st, gravity, which attracts it in the vertical direction m P, 2nd, the attraction of the liquid itself, which acts in the direction m F, and 3rd, the attraction of the solid which acts in the direction in n. Now, according to the intensities of these forces, their resultant will take the three following positions, figs. 54, 55, and 56 :

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Effect of Corvature on Capillary Phenomena.-On the concave or convex form of the meniscus depend the ascent or depression of a liquid in a capillary tube. For example, since, by the preceding statements, the liquid particles of a concave meniscus a b c d, fig. 57, are kept in equilibrium by the forces which act upon them, they exert no attraction on the lower layers of the liquid; but they act, in consequence of molecular attraction, on the layers nearest to them ; whence it follows that upon any layer mon, situated in the interior of the tube, the pressure is less than if there had been no meniscus. Consequently, according to the conditions of the equilibrium of a liquid mentioned in a former lesson, the liquid must rise in the tube until the interior pressure on the layer m n be equal to the pressure represented by op, which acts exteriorly on any point p of the same layer.

In the case of the liquid particles of a convex meniscus, gh th, fig. 58, the equilibrium still exists, in consequence of

Fig. 58.

the molecular forces which act upon the liquid ; but the capillary action of the particles which occupy this space being counteracted, they no longer act upon the lower particles. From this it follows, that the pressure on any layer m n, situated in the interior of the tube, is greater than if the space g hik were full of liquid, for the molecular forces which act within it are more intense than that of gravity. The liquid must therefore sink in the tube until the interior pressure on the layer m n, be the same as that at any point g of this layer, exterior to the tube. f

Cause of the Attraction and Repulsion of light Bodies floating in a Liquid.—We have seen in a former lesson, that the light bodies which float on the surface of water, and which are wetted by that liquid, are drawn towards each other whenever the distance between them is sufficient to admit of capillary action. The same effect is produced between two light bodies which are not wetted by the liquid. And if the liquid wets the one body and not the other, they exhibit a repulsion, which prevents their contact. The following is the explanation of these three cases.

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being robbed over with grease, is not wetted, then, in conseguence of the latter cause, the plate B depresses the level between the plates, and the liquid rises only to q on the adjacent side of the plate A, whereas it rises to p on the other side; whence, the difference of these attracting forces, measured by the difference of level between p and q, will occasion a separation between the plates. Conversely, in consequence of the attraction of the plate A, which raises the level between the plates, the liquid will only sink to go on the adjacent side of the plate B, whereas it sinks to go on the other side; whence, the difference of the pressure of these forces, measured by the difference of level between p' and q', will occasion as before a separation between the plates; and thus the mutual repulsion of the plates, on account of both causes, will be the result.

The theory of capillary action, one of the most difficult in Natural Philosophy, can only be treated fully and completely by the aid of mathematical analysis; and thus has it actually been investigated by the most eminent mathematicians of #. times, especially by MM. Clairault, Laplace, and O1SSOI),

Curious Facts relating to Capillary Action—When a capillary tube is immersed in a liquid which wets it, we find that if we withdraw the tube with care, the liquid column which remains suspended in the tube is greater than that which rose in it when the tube was immersed. The reason of this is that the tube draws after it a drop of liquid which adheres to its lower part, and there forms a convex meniscus whose action unites with that of the concave meniscus at the top, and thereby supports a greater column.

. For a similar reason, when a capillary tube is immersed in a liquid, no issue takes place, although the tube be shorter than the liquid column which would rise in it were it longer. For

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porous.

LESSONS IN BOOKIKEEPING.-No. XII.
THE LEDGER.
(Continued from page 200.)

WE have already said so much on the Ledger, and the manner of posting the Journal into it, in Lesson VI., p. 339, vol. III., that we have now only to refer our students to that Lesson again for the proper explanations, before commencing the study of the Ledger. We shall here, however, repeat emphatically what was there taught in another form, in order to impress their minds with the simplicity of the method of keeping Books by Double Entry. * When an entry in the Journal contains only a single Dr. and a Single Cr., the rule is to Debit the Dr. and Credit the Cr.; this has been explained at p. 341, vol. III. When an entry in the Journal contains a single Dr. and a number of Crs., included in the word Sundries, the rule is to Debit the Dr. and Credit each of the Crs. When an entry in the Journal contains a number of Drs., included under the word Sundries, and and a single Cr., the rule is to Debit each of the Drs. and Credit the Cr. Now, as nothing can be more simple than these rules, we proceed to explain the method of striking a General Balance, that is, of finding out a Merchant’s Assets and Liabiloties, and consequently whether he has gained or lost by trade. In commencing the process of balancing the Ledger by Double Entry, the first thing is to close up all accounts in it, of which the two sides, Dr. and Cr., when added up, are perfectly equal, or balanced by the settlement of account. This will generally be the case in a great number of the personal accounts at the end of a given period, say the close of the year, or at Midsummer. To close up such accounts is merely to add up the sums on each side, to draw lines under the sums exactly opposite each other, to put down the totals, and to draw lines under them also. If there be any space left in the folio under an account thus closed, it may be used for the entries of new transactions under the same account, or with the same party. All the self-balancing accounts being closed up, the Trial Balance is now to be made out; this consists of a list of all the unbalanced accounts in the Ledger, with the total sums of all the entries on each side inserted in Dr. and Cr. columns, for the purpose of easy reference in making out the General Balance, and for the immediate object of ascertaining the accuracy of all the entries in the Ledger. The latter object is at once obtained by adding up both sides of the Trial Balance, viz., the Dr. side and the Cr. side; for if the sum of both sides be the same, the strong presumption is, that the Ledger is correct; and, of course, the Journal, and all the subsidiary Books, equally so. We say the strong presumption only, because there sometimes occurs in a Ledger such a thing as a balance of errors, that is, when a wrong entry on the Dr. side of the Ledger is balanced by a wrong entry of the same amount on the Cr. side. & { In Balancing the Books, as the phrase is, very great trouble is saved in making out the Balance Sheet and Check by Double Entry, in consequence of the admission into the Ledger of all

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the Property and Profit and Loss Accounts, and indeed of 'every

account in any manner affecting the business. In conducting this process, as shown at the end of the Journal, in our last lesson, two new accounts are opened in the Ledger, the one being called Balance Account, which is to be considered the converse of Stock Account as to its Dr. and Cr. sides; for on the Dr. side are contained all the Assets, and on the Cr. side all the Liabilities; the other being called The Profit and Loss Account, which

ontains on the Dr. side the amount of all the Losses experienced in business, and on the Cr. side the amount of all the Gains. By means of these two accounts, all the unclosed accounts in

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