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reduced to powder in an agate mortar. An alkaline silicate placing a wire of platinum in the axis of a bar of silver, and then is formed when this powder is heated with three times its weight in the usual way-that is, by drawing it through holes in a steel of sodium or potassium carbonate. If this be added to an plate---procured a very fine wire, the centre of which was one much excess of diluted hydrochloric acid, the acid combines with the finer of platinum. By melting the silver off with nitric acid this metal, and although the silica is thus ejected from its combina- was exposed, and found to be 0.. th of an inch in diameter. The tion, it does not precipitate; but if heat be now applied, when foregoing qualities are greatly dependent on the texture of the the solution has reached a certain point of concentration, the metal, and the requisite texture, by various manipulations, may silex is again rendered insoluble, and becomes a gelatinous mass. be procured. Thus cast-iron is brittle, so is hard steel; yet By still continuing the heat until much of the water is driven steel is capable of being made into watch-springs, and iron can off, then the chloride of the metal may be washed out, and the be drawn into very fine wire. pure silex again remains in its insoluble form. When rendered Specific Gravity is the relation which the weight a body bears &nhydrous, it is a white, light powder.
to the weight of an equal volume of water. The metals differ All spring or well waters contain silicn, either in a free state greatly in their specific gravities :or in solution as an alkaline silicate, and by this means it enters Platinum, 21.5. Silver, 10:53. Arsenic, 5.96.' into many vegetable and animal organisms.
suagnesia, 1874. pound, tuis is got he beating cilica mixed with carbon in a car
Sodium, 0-972. rent of chlorine. It is a liquid, and has the same remarkable Mercury, 13:59, Iron, 7.84.
Potassium, 0.865. action with water as the boron chloride, being decomposed into
Lithium, 0.593, hydrochloric acid and silicic acid.
Zinc, 7.14, Silicic Fluoride (SiF,) is the gas by the formation of which, The lightest metals are the most easily attacked by oxygen. with hydrofluoric acid, the etching of glass is effected.
Fusibility.-—The following table gives the “melting points” There is also a sulphide of silicon, which is a solid. When of the chief metals :thrown into water it decomposes, sulphuretted hydrogen
Tin, 28 escapes, and soluble silicio acid is taken up by the water.
Copper, 1091o Potassium, 580
Gold, 1102" METALS.
while platinum requires the intense heat of the oxyhydrogen
blow-pipe. a metalloid and a metal was not very decided. Perhaps the definition of a “metal,” which will be finally adopted, will be off in vapour at certain temperatures. Mercury, arsenic, tellu
Volatility is the property which some metals exhibit of going that it is “a body which, when in solution, is carried with an rium, zinc, cadmium, potassium, sodium, can all be distilled from electric current which traverses that solution;" but on referring
their compounds. to the analysis of water by the voltameter, it will be noticed that hydrogen passes with the current; hence it is necessary,
Alloys.-When metals enter into combination, "alloys" are if
formed. this definition be adopted, to class that gas among the metals.
The_union is now generally considered to be
“chemical." There is no reason for doubting that if hydrogen could be con.
The various alloys will be treated of under their densed into a solid it would exhibit metallic lustre and the metals. Ad “amalgam " is an alloy in which one of the metals other properties common to all metals.
is mercury. The chief properties which characterise metals are
The Appearance of Metals in the Earth's Crust.-Gold, pla. Metallic Lustre. This lastre, however, is not peculiar to the in an uncombined form;
but the last-named three are also found
tinum, silver, mercury, and copper are found "native"—that is, class, for it is shared by iodine and graphite. Moreover, if most metals be procured in a state of fine sub- buted in nature. Lime is the oxide of calcium. The tint of the
Next to silica, metallic oxides are most widely distridivision they are lustreless. This is prominently the case with sandstones is due to the oxide of iron. gold, which, when painted on china, in a chemical solution, and tain many oxides, while the waters of the ocean are rendered
The granite rocks conthen burnt, comes out of the furnace dull green, and the well. known lustre of gold does not appear until the painted portions large quantities we seek from masses of their ores, which are
briny with their salts. But the metals which we require in have been burnished. Opacity.—Metals are usually considered opaque, but this is
found in mineral veins. It often appears that the older rocks not absolutely true, for gold, if not more than oth of an inch have, in the convulsions of Nature, been rent into fissures. thick, permits green light to pass through it, and other metals with molten basalt, trap, etc., thus forming dykes, they have
When these openings have not been filled up from below exhibit a similar imperfect opacity when reduced to very thin been filled up with metallic ores, which seem to have been leaves.
Hardness. ---Steel, which is a compound of carbon and iron, is usually deposited from above. These constitute “lodes." The the hardest of the metals, and the rest pass through every degree lodes of a neighbourhood generally run in the
same direction, down to potassium, which may be moulded by the fingers as if and, strange to say, if this direction be altered, the ore geneit were putty. The hardness of a metal may be greatly in- rally alters its character, and frequently its chemical constitucreased if its temperature be raised to a certain point and then
tion. This and other reasons have led to the belief that suddenly cooled by plunging it into water. Many of the hard electricity has been the chief agent in depositing metallic veins. metals are sufficiently elastic to be sonorous when struck.
It sometimes happens, as in the case of the iron beds in our Brittleness and tenacity are closely connected. Many of the
own country, that the ore is found in strata, occupying the metals, such as bismuth, antimony, arsenic, are so brittle as to position of a layer of rock. admit of being pounded in a mortar, and many, such as steel,
DIVISIONS OF THE METALS. iron, copper, can be made brittle by suddenly reducing their
1. Metals of the Alkalies. temperature. Others, again, exhibit this quality only at certain
Lithium, temperatures : for instance, zinc, which cannot be bent without danger of cracking, is readily worked at a temperature of about
2. Metals of the Alkaline Earths. 115o Cent. ; and on the other hand, brass-an alloy of zinc and
Calcium. copper-becomes brittle as it approaches a red heat.
Magnesium. Tenacity is the property which gives to metals their power of
3. Metals of the Earths. supporting a strain. Iron possesses it in the most eminent
Erbium. degree, hence the great value of this metal.
Glucinum. Melleability and Ductility.--Possessing the one property, the
Cerium. metal may be beaten or rolled into very thin leaves ; with the
Lanthanum. other, it admits of being drawn into wire. Gold, silver, copper,
Didymium. and platinum are very malleable. Gold may be beaten out into
4. The Metals Proper, leaves so thin that 280,000 only make an inch. These metals, The last division is subdivided into classes of metals which and iron, are the five which are notably ductile. Wollaston, by exhibit certain similar features.
SKETCHING FROM NATURE.-I. whether it is easier or more difficult depends upon the inclination
of the mind, the practical experience, or, speaking more exactly, ! MATERIALS—CHOICE OF SUBJECTS, ETC.
the kind of experience the pupil has been accustomed to. If the Is our Lessons in Drawing, to be found in the previous pages grammar of the art has been well learned, the pupil will find of the POPULAR EDUCATOR, we have endeavoured to place that a very considerable amount of the knowledge he has before our pupils the general principles which belong to and acquired whilst drawing from the flat will be of the greatest are applicable to the practice of drawing from the flat (that is, service when drawing from nature. from copies), and also those principles which guide us in drawing We have frequently met with portrait painters who have had frem the object. We now undertake a more direct application of to make duplicates of their pictures, and who have said they the instruction therein given, for the purpose of introducing our would much rather paint them again from the sitter than copy popils to that very interesting and delightful practice of them from the original picture : only those who have experienced drawing, usually termed “sketching from nature ; we mean it can fully understand how much more feeling and life can be by this, the taking up a few simple materials and seeking our imparted to the work when nature is the guide, than when they sabjects out of doors. The phrase "sketching from nature” have to depend upon the limited expression of a copy. So with is & very convenient one, and is generally understood, therefore landscape: we have frequently been more pleased with the
we will retain it, although we prefer the expression “ drawing "original sketch," taken upon the spot, than with the finished from nature," as it implios greater care and attention to details picture painted from it in the studio at home. Although the than the term sketching in its usual sense. A loose habit of "original sketch” was not so highly finished as the picture, drawing may be called sketching, and if this were all that is yet it had the stamp of nature and freshness upon it, which understood by it, the practice would be a dangerous one for a could best be caught from the scene itself, and which it is diffi. beginner ; but as we have already given sufficient cautions upon cult to impart at second hand. As the eye of the student this point in the lessons upon Drawing, we will only repeat one becomes more and more accustomed to Nature, and keener to piece of advice and pass on—" Learn to draw first; sketch detect and appreciate her beauties, he will discover much of afterwards.” In the course of these lessons we shall find it which a common observer has but an imperfect perception; to necessary occasionally to refer back to the lessons in Drawing the latter, a landscape is the same to-day as it was yesterday, already given, as our object is to apply practically the principles he can only soo trees, buildings, and other objects abstractedly which have been there stated. How many times has the ques. through one and the same medium ; while the eye of the artist tion been asked, “Do you draw?" And what is the reply in is continually discovering something fresh, perhaps principally the great majority of cases ? “ Yes, but only from copies ; I caused by the successive changes of light, or from the positions have never attempted to do anything from nature, having always of objects in relation to each other, and their contrasts in both considered it so much more difficult.” Now, there are those colour and form. The tree before him in the morning may who maintain the reverse, namely, that drawing from nature is certainly be the same that he sees in the evening, but how very cazier than copying pictures. Certainly the former is much different is the effect, and what a multitude of details, with ail more pleasant, and more satisfactory, as all must acknowledge; their beanties, which were imperceptible in the morning, are
brought out by the change of light. We have no doubt that there is no escape, but at the cost of much discouragement. many of our pupils, when they have conquered their early diffi- All must acknowledge that, whatever may be the extent of the culties, will discover with pleasure and surprise that drawing subject they propose to draw, it is essentially composed of several from nature has a charm about it which cannot be realised by particular objects, each of which requires a separate and careful copying only.
study. Now the first question every one must ask himself The necessary materials are simple :- A block, that is, a solid should be, "Can I copy any one of these objects, independently mass of paper composed of several layers bound together only of the rest ?" If he cannot, let us assuro him it would be use. at the edges, so that when a drawing is completed we have only less to attempt the whole together. All who have reached any to slip a penknife between it and the next paper, pass it round, eminence in the art have found from experience the advantage remove the drawing, and underneath will be found another sur- of overcoming the difficulties connected with single objects first. face like the one already filled, ready for use. The kind of paper Our pupils will clearly see from these remarks that the simpler for pencil drawing ought not to be very rough, a slight grain will the subject the better for a first trial, so that as their strength assist the pencil to mark freely, but on very rough paper it is and confidence increase they will find themselves capable of impossible to give a very high finish to the work; rough papers enlarging their subjects, of entering more closely into their are better adapted for colours. A few pencils, H, HB, and B, and numerous details, and as they proceed a proportionate amount a portable sketching stool, will be all that is requisite for our of increasing satisfaction will be gained, and the art itself will first essay. Being now prepared, let us suppose that we are on become more and more interesting. our way in search of a subject, and in the meantime we will Fig. 1 will give some idea of the class subject for a first make a few observations which especially apply to beginners. attempt, and the manner of treating it, which need not be much No one who has been accustomed to copy pictures only, can beyond a carefully arranged and cleanly drawn outline; the altogether comprehend what a very different thing it is to draw shadows might be slightly marked in by a few parallel lines from nature until he has made the attempt, when he will discover | under the projecting parts, down the shadowed sides of the posts, there are several reasons for the difference. One is, that all the to define and to bring forward the branch of a tree. In this objects in the picture are reduced for him, probably to the simple arrangement of a few posts and weeds, there are no exact size he wishes to make them; another is, the outline upon important retiring lines, consequently there will be no necessity the paper has a more definite effect than the general form in for vanishing points, a subject for our consideration in another nature, which admits of no actual boundary line, but presents lesson. The distance of the station point, or the position of only the mass discoverable from other objects by colour, and the draughtsman from an object of this class and extent, might light and shade ; another reason is, that objects in nature be about a dozen or fourteen yards, because at that distance all advance or recede from one another, whilst in a picture they are contained within its outer limits will be considerably within an all arranged upon one plane or surface; and thus we are led to angle of 60°. See" Lessons in Drawing,” Fig. 25, and the remarks acknowledge the necessity of knowing something both of lineal upon it (Vol. I., page 72). Subjects of the class we have selected and aërial perspective. It is true many depend upon the eye are very common: a stile, a bridge over a brook, and many more alone for the proportions of the retiring parts as they recede, of the same kind, are to be found almost everywhere. We have and consequently are liable to make frequent and serious mis- just said that the drawing need not be more than a carefully takes, which a little acquaintance with perspective would arranged outline. If for some time the pupil will confine himprevent; but we intend to take up this part of our subject self to outline, and use no more shadow than is necessary to again.
assist in making the form clear and intelligible, it will be an We will now pass on to another consideration with reference advantage, because it is doing one thing at a time, and he is to the choice of subject for the first attempt of a beginner. not overpowering himself with difficulties; besides, shading We well know the feelings with which most beginners go out bad outlines is a waste of time, as shading cannot improve the for the first time to draw from nature; their enthusiasm drawing, nor can it be successfully practised without the poires would persuade them to attempt great things; nothing short of of correct drawing, as it is only an additional help to represent some extensive prospect, hill and dale, woods, rivers, buildings, the form marked out by the outline. There are other important in short, a whole country side. Upon this point we wish to considerations to be attended to. The pupil must remember, caution our pupils. It is one of the first and greatest mistakes when he is seated, that the few moments before he puts his wliich young painters make when they begin to draw from pencil on the paper are very important. First, he must decide nature; nearly all, without exception, sit down to take somo how much of the subject he intends to draw; that being deterextensive view, without a question as to its composition, and mined, he must fix upon the centre of the subject to be arranged without any inquiry whether they will be able to go through in the centre of his paper, and as in most cases the eye will be with it. The principal reason they give for their choice is "the considerably below the centre, there will then be sufficient room beauty of the scene.” We knew a case some years ago of a for the sky above, and the foreground below the object. Proyoung student in the Royal Academy, who copied in the painting bably a single trial will induce him to make this a general rule school an elaborate landscape by an old master; succeeding until experience has taught him to arrange this matter for beyond his expectations, he felt a strong desire to paint a picture himself according to his position and the nature of the subject from nature, having now, as he thought, acquired sufficient he is drawing. The next piece of advice we would give him power to justify the attempt. Accordingly, he went to the top before he begins, is to fix his whole attention upon what he of Highgate Hill, and commenced a picture of the entire pros- is about to draw; he must examine not only of what it is compect looking northward; he worked hard for several days, but posed, but he must attentively ob rve how the several parts found he was alternately painting in and rubbing out; the are arranged with regard to each other, and what are the rules constant changes of sunshine and shade, as they passed over the and principles he has at command for his purpose.
As he is landscape, perfectly bewildered him, and the result was that ho about to draw it as it appears to him, without attempting any gave it up quite disheartened. He resolved, however, to show effect which does not strictly belong to it, he must take up one the little he had done to the late Mr. Constable (the painter of principle at a time; the first will be form--this refers, in the first "The Corn-field” in the South Kensington Museum), and ask instance, to the shape and character of the subjeet as a whole ; his advice. Mr. Constable looked first at the picture and then then the position of the parts relative to each other; all at the youth, and in a quiet way, though with unmistakable important particulars must be carefully oxamined, his eye and meaning, said, “ My young friend, go and draw a gate-post, his mind must become familiar with everything; this will and when you have done that draw two posts, and go on till strengthen his confidence, so that when he begins to draw, the you can manage a dozen; afterwards add a cottage, then a acquaintance he has made with his subject will be of the greatest tree, and proceed in this way until you have power to do value. In practice, it is quite allowable to determine the something more elaborate before you think of painting relative heights of the parts with one another by placing the snch a subject as this. You have made precisely the samo pencil horizontally before the eye, having its edge ou a level mistake that I made when I was your age; you have begun at with any particular point, and by looking along the remain. the wrong end."
ing portion of the pencil when thus placed, the pupil will be The above excellent advice needs very little comment from able to see at once which other portions are on the samo level,
It is exceedingly valuable, and forcibly suggests the folly which are above, and which below; he must notice where lines of rushing headlong into a multitude of difficulties from which if produced would cut other lines already drawn, and also where
one part is over or under another. We have drawn dotted lines
EXERCISE 59. in the illustration (Fig. 1) to show the various directions in which
15. 103. the pencil might be held between the eye and the object, and the
16. The first. result it gives in deciding how the parts are placed in connection 3. 4..
10. £6,947 18s. 40. 17. £52 10s. with each other.
4. In the Three per 11. £13 108. 10d. 18. £51,350 103. Cents.
12. £19 16s. sd. less ; 19. £818 8s. 5. 4; 41.
M'u per cent. less. 20. £77 28. 437d. LESSONS IN ARITHMETIC.-XXXIX. 6. In the Three and 13, 90 and £33 68. 8d. 21. £475, FELLOWSHIP, AVERAGES,
a Half per Cents. 14. 91/763341, or 91.28 MIXTURES IN CERTAIN
7. 100. PROPORTIONS, ETC.
nearly. 1. Ir several partners have invested different sums in an undertaking, it is manifest that the profits or losses must be divided
HYDROSTATICS.–V. among them in proportion to the capital each has invested in
EQUILIBRIUM OF FLOATING BODIES METACENTRE-CAPILthe business, if the capital of each has been in use for the same
LARY ATTRACTION-HYDRAULIC MACHINES-WATER-WHEELS. time.
The method by which the share of each is determined in this WE have now examined at some length the effects produced on case is called Simple Fellowship. It is manifestly the same as bodies by immersion in liquids, and have seen that one of the that given in Lessons in Arithmetic, XX., on Ratio and Propor-conditions of equilibrium is that the weight of the diaplaced tion, Arts. 7, 8 (Vol. I., page 343), where a given number is fuid shall be equal to that of the body immersed. This, howdivided in proportion to certain others.
ever, is not the only condition that must be complied with in EXANPLE.--A, B, and C put into a business £300, £500, order to ensure equilibrium. Suppose, for instance, that we and L800 respectively. At the end of a year they have gained have a solid of the shape of A B in the an.
A 2400. What is the share of each ?
nexed figure, and that the end B has a piece We have to divide £400 in the proportion of 300, 500, 800, or, what of lead affixed to it, so as to render it
B is the same thing, in the proportion 3, 5, 8.
heavier than the other. Let us now see According to Lessons in Arithmetic-XX, Art. 7, since 3 + 5 + 8 = what are the forces acting on this body, 16, we divide 400 into 16 equal parts, each of which is £25.
One force is its own weight, which acts The respective sbares of A, B, and C will be £75, £125, and £200.
through its centre of gravity G, and as the 2. If the sum invested by each partier is not used for the end B is heavier than the other, this point same period of time, so that we have to take into account not is nearer that end; the other force acting
Fig. 18. only each sum, but the time during which it is employed, the upon it is the buoyancy of the liquid which case is called one of Double or Compound Fellowship.
acts through the centre of gravity of the displaced liquid, that EXAMPLE.—A, B, and C contribute to a business as follows : is, upwards through o'. Now these two forces are equal to one A puts in £1,200 for three months, B £1,000 for six months, another, and act in opposite directions, but their lines of action and C £800 for twelve months. How must they divide a profit do not pass through the same point; and hence, as we saw in of £800 ?
our Lessons on Mechanics, they constitute “a couple," and proA's £1,200 for 3 months is the same as 3 x £1,200, or £3,600 for 1 duce a tendency in the body to twist round. In order, then, month.
that there should be equilibrium, the points G and G' must be in B's £1,000 for 6 months is the same as 6 * £1,000, or £6,000 for 1 the same vertical line.
Now either G or G' may be the higher, and, according to this, C's £800 for 12 months is the same as 12 * £800, or £9,600 for 1
A B is in a state of stable or unstable equilibrium. If the month,
Hence the shares must be in the proportion of 3,600, 6,000, 9,000; centre of gravity of a B be above that of the displaced liquid, Le, of 3, 5, 8.
the body will remain at rest until some disturbing force acts Hence, procceding as in Simple Fellowship, the shares will be tendency to rotate will come
into action, and the body will move
on it; but as soon as it is moved at all from its position, the respectively
further and further from its original position. If, on the other £800, 1. £900, . £800; that is, £150, £250, £100.
hand, G' be above g, and the body be then deflected slightly This example sufficiently explains the following
from its position, the forces acting on it Rule for Compound Fellowship.
will draw it back. Hence it is said to be Multiply each capital by the number of units of time for in a condition of stablo equilibrium. In which it is employed; the shares will be in the proportions of the case of floating bodies, or of vessels these products, and will be determined as in a case of Simple going to sea, it is clearly of the utmost Fellowship.
importance to be sure that they are in this EXERCISE 60.
condition, as otherwise a little wind will 1. A traveller divided 808, among 4 beggars in such a manner that cause them to incline, and they must then 23 often as the first received 10s., the second received 9s., the third 88., turn over. We will see, then, what are the Fig. 19. and the fourth 78. What did each receive ?
conditions requisite to ensure safety. 2. A, B, and C engage in business, putting in respectively £3,500, 15,610, and £0,000. What would be the share of each out of a profit downwards, and it would then remain at rest. Now let it be
The body A B, in Fig. 18, would be found to turn till B was C: 41,000?
3. A, B, and C contribute respectively to a speculation £160, £240, turned a little from its vertical position, as in Fig. 19. The and L180, and they gain £264. What will be the share of each ?
dotted line represents its axis, in which both G and G' were 4 A, B, C, and D embork in a business, and put in respectively situate, but in the new position G' will be at one sido of this 2,000 for 6 months, £1,500 for 9 months, £1,000 for 12 months, and axis. Draw from this point a line vertically upwards to repre2759 for 15 months. If at the end of 15 months the profits are found sent the buoyancy of the water, this line will cut the axis in to be £1,000, how must they be divided ?
some point, m. If this point be above , the body is in a stato 5. A and B form a partnership for a year. A contributes £5,000, of stable equilibrium ; if it be below, the body is unstable. to which at the end of 6 months he adds £1,000 more; B contributes This point m is called the metacentre. Hence, if the metacentre L,), and at the end of 9 months withdraws £2,000 from the busiHow must they divide a profit of £1,500 at the end of the
year? Now from this
we learn several important things. The first is,
bo above the centre of gravity, the vessel will float in safety. 6. A, B, and C form a partuership ; A contributing £1,000, B £2,000, 13d C £3,000. After 9 monthg C withdraws, and after 3 months more that in a vessel the centre of gravity should be as low down as D is admitted to the partnership, contributing £1,500.
At the end possible. A captain accordingly arranges to stow the heaviest of 18 months, the partnership being dissolved, the profits are found part of his cargo in the lowest part of the hold ; and for the to be £W. How must they be equitably divided ?
same reason, in a ship almost empty, or in a pleasure-boat, a
large amount of heavy material, such as clay or pig-iron, KEY TO EXERCISES IN ARITHMETIC.-XXXVIII. is stowed away as ballast. If the lower part were left empty, EXERCISE 58.
or filled with light cargo, and heavy goods placed on the deck, 1. (^) 314 years. () 37 years.
3. 69!; days.
the centre of gravity would be raised dangerously high, and the 2 () 1111's m. (*) 113 m. 4. 5 years.
vessel, in all probability, would capsize. Forgetfulness of this
fact is a fruitful source of danger to passengers in rowing or and thus we can ascertain how high it rises for each different
vessels is to have the cargo so stowed, We have now noticed the main points in the first branch of
which it flowg. Fig. 20.
We now pass on to notice another If we have a vessel of the shape shown in Fig. 22, with
property of liquids, known as capillary several jets inserted at different points along the side, which attraction. If we procure several glass tubes (Fig. 20) of small can be opened or closed at pleasure, we can ascertain how but different diameters, and dip them into water, we shall find much flows from each, and from this the velocity with which it an apparent exception to the rule that liquids maintain issues. It is, however, necessary to maintain the water at the their level, for the water will rise in them to a height which same level during the experiment, and therefore a spout is made varies with the size of the tube. This height increases in. at A, and the vessel so placed that a stream versely as the diameter. The name, "capillary attraction," or of water from a tap runs in rather more capillarity, is derived from the Latin word capilla, which rapidly than it issues from any of the jets. means "a hair," and was so used because this effect was The surplus water will escape by the spout, B first observed in tubes almost as fine as a hair. We see and thus maintain a uniform level and presa great many common things which afford illustrations of sure. By a series of experiments conducted this fact. A lump of sugar consists of a large number of in this way Torricelli arrived at the conclusmall crystals held together so as almost to touch, and they sion that if the distance of any jet, E, below leave small tubes or passages between them. Hence, if wo the surface is four times as great as that of just dip a corner into a cup of tea, we see that the tea rises at any other, B, the velocity with which the water once and wets the whole lump. A better illustration is to pro- will issue from the first is twice as great as g cure a tall lump of salt, and set it in a plate filled with some from the other; that is, that the velocity coloured fluid, as water and red ink; the line produced by the varies as the square root of the height of the rise of the liquid is then very clearly seen. If a towel or piece water. Further experiments point out that of linen be placed in a vessel of water, a portion being allowed this velocity is just that which, under tine
Fig. 22. to hang over one side, it will in the same way draw up the water laws of gravity, the liquid would acquire in in its interstices and allow it to drip from the lower corner, thus falling from the surface to the opening. Thus, if the jet be emptying the vessel.
one foot below the surface, the liquid will issue with a velocity A practical application is made of this principle in quarries of eight feet per second, that being the velocity a body acquires where millstones are obtained.
in falling through a space of one foot. If, then, the aperture A block of stone is roughly trimmed to a cylindrical form. have an area of 1 square inch, 96 cubic inches ought to Grooves are then cut round it at distances regulated by the flow out in one second, but on trying the experiment we find thickness of the stones. Into these grooves wedges of dry hard that only about 60 cubic inches actually flow, or about 62 per wood are firmly driven, and the damp of the air is so power cent. of the calculated amount. This discrepancy seems at fully attracted into their pores that they swell and split off the first sight to show the inaccuracy of the law, but on further stones from the block.
examination it only confirms it. On the same principle a candle burns. The heat of the flame If we make an opening in the bottom of a vessel (Fig. 23), and
melts the tallow or composition, carefully observe the water as it issues from it, we shall notice that and forms a cup filled with the the stream is not the same size throughout, but narrows consimelted portion; this rises in the derably just beyond the orifice, so that the smallest area is a wick by capillary attraction, and little way below the opening. Thus, if A B be the aperture, the there it is converted into a gas, and part of the stream with the smallest sectional area will be at consumed, while it gives light. a b. The particles of water, in flowing along towards the open
In all these cases we have sup- ing, acquire an onward motion, which they retain as they flow posed the solid has been of such out, and this narrows the stream. Now the section at a b is a nature as to be wetted by the found to be just of that at A B, but tho actual effus we found liquid. If, however, this be not was actually this fraction of the theoretical. If, then, we take the case, the liquid in the tube as the arca through which the water flows, not that of the aperwill stand at a lower level than ture, but that of the section at a b, the actual flow will just that without. This may be tried correspond with the calculated amount. with a glass tube dipped into mer. The diminished stream at a b is called the vena contracta, or
cury, when the mercury within the contracted vein, and in all their calculations allowance is made Fig. 21.
tube will be seen to be at a lower by hydraulic engineers for the existence of this.
We have thus far supposed the water to flow from a hole These effects are accounted for by the attraction or repulsion made in the side of the vessel ; the actual amount that escapes of the surface of the tube for the liquid, and may be seen is, however, very much varied by inserting a jet or pipe from well by immersing a sheet of glass in the liquid, or, better still, which the water may issue. If a straight pipe, whose length is by taking two glass plates and moving them different distances about three times its diameter, be inserted in the opening, the apart. If we arrange them, as shown at Fig. 21, so that the flow from it will be increased to about 82 per cent. of the theoedges at one side meet, while at the other they are a small dis- retical amount; if this pipe be slightly tapering outwards, the tance apart, the liquid will rise between them and form a curve, issue will be still greater, while, if it taper inwards, the external