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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 assure him it would be useat 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 of 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 him. prevent; 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 power 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 which 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 some 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 observe 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 he 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 subject 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 examined, 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 such a subject as this. You have made precisely the same pencil horizontally before the eye, having its edge on a level mistake that I made when I was your age; you have begun at with any particular point, and by looking along the remainthe 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 same level

, us. 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

1. 38.
8. £8775

15. 103. the pencil might be held between the eye and the object, and the 2. 331.

9. £33 6s, 8a.

16. The first. result it gives in deciding how the parts are placed in connection

3. 4.

10. £6,947 18s. 4d. 17. £52 10s. with each other.

4. In the Three per 11. £13 10s. 10d. 18. 454,350 103. Cents.

12. £19 16s. 8d. less; 19. £818 8s. 5. 4; 410

to per cent. less. 20. £77 2s. 499d. LESSONS IN ARITHMETIC.-XXXIX. 6. In the Three and 13. 90 and £33 68. 8d. 21. £475. FELLOWSHIP, AVERAGES, MIXTURES IN CERTAIN

a Half per Cents. 14. 91110511, or 91-28

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 the business, if the capital of each has been in use for the same

EQUILIBRIUM OF FLOATING BODIES-METACENTRE-CAPIL time.

LARY ATTRACTION-HYDRAULIC MACHINES—WATER-WHEELS. 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 displaced tion, Arts. 7, 8 (Vol. I., page 343), where a given number is fluid 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 EXAMPLE.-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. 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 A

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 shares 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 partrer 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,

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. month.

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 AB 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, 9,600; centre of gravity of A B be above that of the displaced liquid, il, of 3, 5, 8.

the body will remain at rest until some disturbing force acts Hence, proceeding as in Simple Fellowship, the shares will be on it; but as soon as it is moved at all from its position, the

tendency to rotate will come into action, and the body will move respectively

further and further from its original position. If, on the other * £800, 1:£800, £800; that is, £150, £250, £400,

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 stable 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 80s. 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 8s., 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, 25,000, and £6,000. 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 £1,000 ? 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 £190, and they gain £264. What will be the share of each? dotted line represents its axis, in which both g and ' were

A, B, C, and D embark in a business, and put in respectively situate, but in the new position G' will be at one side of this 22,000 for 6 months, £1,500 for 9 months, £1,000 for 12 months, and axis. Draw from this point a line vertically upwards to repre£750 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 6, the body is in a state 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 28,600, and at the end of 9 months withdraws £2,000 from the busi; be above the centre of gravity, the vessel will float in safety. 6. A, B, and C form a partnership ; A contributing £1,000, B £2,000, Now from this we learn several important things. The first is, sad C 23,600. After 9 months C withdraws, and after 3 months more that in a vessel the centre of gravity should be as low down as Dia 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 £000. 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. (-) 374 years. (*) 31 years. 3. 69743 days.

the centre of gravity would be raised dangerously high, and the 2. (') 11 m. (*) 118 mi.

4. 5 years.

vessel, in all probability, would capsize. Forgetfulness of this

month.

fact is a fruitful source of danger to passengers in rowing or and thus we can ascertain how high it rises for each different
sailing boats. If a squall comes on, or any accident seems im- distance between the plates. The elevation here is found to be
minent, the passengers frequently spring to their feet, and by just one-half of what it is in tubes having a diameter equal to
so doing greatly raise the centre of gravity and increase the this distance.
danger; the wisest and safest plan is for all to sit down--or, These experiments you can try for yourselves, and by doing
better still, to lie down—at the bottom of the boat; the centre of so will be far better able to understand them. Never be satis-
gravity being thus lowered, the danger will be much diminished. fied with reading an account of an experiment, or looking at an
Another thing that should be carefully seen to in sailing illustration of it, if you can try it.

vessels is to have the cargo so stowed, We have now noticed the main points in the first branch of
that the centre of gravity is vertically our science, or Hydrostatics proper, and must pass on to the
over the keel, and also to prevent its second branch, or that which treats of liquids in motion, and of
shifting its position when the vessel the various modes of raising them, or deriving motion from
lurches, as, if it does so, she cannot right them.
herself so well. In paddle-wheel steamers,

HYDRAULICS.
where it is important for the vessel to When a liquid is contained in any vessel it exerts a pressure
be upright, small carriages, filled with against the sides, and this pressure we found to vary with the
chain or other heavy material, are often depth below the surface. If now we make an aperture in any
placed upon the deck, so that when the portion of the side the liquid will rush out; and as the velocity
wind inclines the vessel, these may be with which it flows depends on the pressure, the lower down
moved to the higher side, and thus bring the aperture is situated the greater will be the velocity with
it even again.

which it flows. 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, Bl first observed in tubes almost as fine as a hair. We see and thus maintain a uniform level and presa great many ommon things which afford illustrations of sure. By a series of experiments conducted this fact. À 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 we the surface is four times as great as that of 2 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 cure a tall lump of salt, and set it in a plate filled with some from the other; that is, that the velocity coloured Auid, 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 the

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 low, 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. ab. 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 AB, but the actual efflux 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 area 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.
level than that without.

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 tabe 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

[graphic]

B

part being larger than the opening in the vessel, the flow will This is fixed to a pole, and held in some part of the stream for slightly exceed the calculated amount. These differences are a given time; the velocity at this point is thus noted, and in a partly accounted for by currents which are formed in the water, similar way it may be found at other points and a mean taken. and which by collision with the issuing stream destroy a portion A simpler way, however, is to observe the velocity at the surof its velocity.

face. A substance of nearly the same specific gravity as the When liquids have to be conveyed in pipes care should be water is thrown in, and the time occupied in passing between taken to make the bends even and gradual, and in this way to two points noted; from this we easily find its speed per second.

prevent the formation of eddies and currents. Now the mean velocity is found to vary from about to Z of
It should also be remembered that there is a that at the surface, and tables have been constructed showing
considerable amount of friction between the the mean velocity corresponding to each surface velocity. If
liquid and the sides of the pipe, so that the por. we multiply this mean velocity by the area, we ascertain the
tion in the centre of the pipe flows more rapidly amount of water passing per second.
than that against the sides. In the same way Having thus seen the power there is in a stream, we must
the relocity of a canal or river is greater in the notice the different machines employed to utilise it.
centre than at the sides. This friction in The simplest and most common of these is the water-wheel.
creases with the velocity at which the liquid This consists essentially of a wheel turning on an horizontal
moves, and also with the area of the surfaces axis, and carrying on its circumference a number of floats or

in contact. From all these causes the flow of boards. The water strikes against these, and thus causes the Fig. 23. liquids through pipes is much less than theo- wheel to turn with considerable force, and the motion is by

retically it should be, and hence in laying down means of cog-wheels transmitted from it to the machinery pipes considerable allowance has to be made for this loss. which has to be driven.

In former times the flow of water was used as a means of Water-wheels are divided into three classes, according to the measuring time, the apparatus constructed for this purpose way in which the water acts on them, or rather the point of being called a clepsydra, or water-clock. The water is allowed their circumference at which it is applied. to flow from a jet into a reservoir below, in which is a float rising Sometimes the wheel is placed so that its lower floats just dip with the water and carrying at the top a pointer. The reser- into the stream, and it is then called an undershot wheel (Fig. 24). Foir is made of the same size throughout, so that the addition When the water is confined by an embankment, and allowed to of equal quantities of water causes equal rises in its surface. Alow against the wheel a little below its middle, it is called a breast The water is allowed to flow in for a given time-say, half an wheel; and when the water is received on the upper part, it is hour and the rise noted ; marks are then made at this distance an overshot wheel. The first of these three is the simplest in apart, and by these the time may be told. As, however, the construction, no embankment or artificial channel for the water rate of flow depends upon the pressure, it is necessary in such being absolutely necessary, though a much greater power is an apparatus to maintain the same head of water in the upper gained when the wheel is made to fit into a properly shaped cistern, and this may be accomplished in the way mentioned watercourse, so that no water can pass without turning it. Less above, by letting the water constantly overflow the vessel. power is, however, derived from this than from the other kind

There are, however, better ways of accomplishing this, which of wheel, as the water strikes violently against the floats, and are frequently used. In the boiler of a steam-engine, and other thus expends much of its force uselessly machines, it is frequently very important thus to maintain a in straining the wheel. It is always constant level, and this is attained by means of a ball-cock or found that there is the greatest advan. float. A block of wood, or hollow ball of metal, floats on the tage gained when the water strikes the liquid; this block is either fixed on to a lever or fastened to a wheel with as little velocity as possible, cord, so that when the level of the water becomes lower, and the but"acts merely by its weight and presfloat descends, it opens a valve or turns a tap, and allows the sure. water to enter till the lovel is restored.

At first the floats were arranged to We will now look at the most common hydraulic machines, stand out perpendicularly from the and examine their construction, and the principles on which they wheel, but experience shows that it is act. The simplest division is into three classes, the first em better to let them have an inclination bracing those whose object is to employ the force of falling towards the stream of twenty or thirty Fig. 24. water as a prime mover; the second, those which are intended degrees, as thus they break the violence to raise water to any required elevation; while the third con of the current, and allow it to act more advantageously. tains those which are used to propel vessels through the water, Another matter to be considered is the proportion which should and other machines not included in the previous classes. exist between the speed of the wheel and that of the stream. It

In many districts, especially mountainous ones, there exist is evident that there are two extreme cases which may occur. If many waterfalls and rapid streams. In these there is a large the circumference of the wheel move at exactly the same velocity amount of motive power, which is frequently utilised in giving as the stream, no power can be derived from its motion ; and if motion to the machinery employed in mining and other opera- the motion be reduced to a minimum, nearly all the power would tions. This power would be much more employed than it is, be lost. The greatest amount of work is accomplished when the were it not that sometimes, from long-continued droughts, motion is about midway between these two extremes, that is, the body of water is much diminished. If we take any two when the wheel moves at about half the rate of the stream. points in a stream, we shall find that the one higher up the stream has a greater elevation than the other, and the power

ANSWERS TO EXAMPLES IN LESSON IV. capable of being exerted by the stream between these points is

1. The specific gravity of the silver is 10-359. equal to the power of the body of water there is in the stream

2. 1.694. falling vertically through this distance. If the stream discharge 3. The elm weighs 69.896 oz. ; the limestone 276042; and the lead 1,000 gallons per minute, and the difference in height between 1182-292. the two points be four feet, the power stored up in the water is 4. The specific gravity of the oil is 0.916. 1,000 X 10 X 4, or 40,000 foot pounds per minute, but even 5. The stone weighs in air 26 grains, and it loses 10. grains in in the best machines a large portion of this is lost.

water. Its specific gravity is there

10:59

or 2476. When we want to ascertain the force of a stream, we have first to find the sectional area. This may be done by taking

6. The two together displace 6.84 oz. of water ; of this 1.92 oz. is the depth at intervals of five or six feet from bank to bank, the due to the

metal; the wood therefore displaces 4-92 oz., and its weight

is 3.3. Its specific gravity is therefore 0-670. average of these being the mean depth ; multiply this by the 7. The volume of any body is represented by its weight divided by breadth, and we shall have the area. We must then proceed to

48

8-9 find the average velocity, but as the stream flows more rapidly its specific gravity. Hence the volume of the copper is while that in the middle than at the side, it is rather difficult to ascertain of the zinc is The volume of the compound is therefore

7191 this accurately. An instrument, consisting of several fans, 48 which are turned by the water, and register, by means of clock- Hence 99 + 7-191

26

27

75

sp. gr.

27

and this gives the specific gravity of the work, the number of revolutions they make, is sometimes used. I compound as nearly 8-2.

75 sp. gr.

Pippo

LESSONS IN ITALIAN.-III.

of tz in the word switzer, or dz in the word adze. According to II.-PRONUNCIATION OF VOWELS AND CONSONANTS

modern orthography, the , is generally doubled between two

single vowels in the middle of a word, but not after a consonant (continued).

and not before diphthongs the first vowel of which is i; as, for For further practice in the pronunciation of words in which examples, ia, ie, io, where it must remain single, and has the vowels and mute consonants are combined, the reader's attention hard sound. is directed to the following table as a continuation of the one

Pezzo pê-tzo

Piece. given in the previous lesson.

Pizzo pée-tzo

Moustache. It will be well, before commencing this exercise, to refer to

Pozzo pó-tze

A well. the explanatory notes therein contained. I would especially

Puszo póo-tzo

A bad smell. desire my pupil readers to repeat aloud every word successively, Pagato pah-gáh-to

Paid. until they have made themselves quite familiar with their various Ithaca 6e-tah-kah

Ithaca in Greece. and distinct sounds.

Agape áh-gah-pai

Agape, or Christian love-feast.

Ricamo ree-káh-mo
Italian,

Embroidery.
Pronounced.
English,
Vegeto vê-jai-to

Stout, robust.
Veggo

I see. veg-go

Aceto ah-tchái-to

Vinegar. When the gg's are followed by a, 0, or u, they are pronounced Gaeta gah-ki-tah

Town in Naples. in each syllable like the English g in get.

Cedete tchai-gái-tai

Yield!

Cadice káh-dee-tohni Cadiz.
Oggi od-jee
To-day.

Egida ai-jée-dah

Ægis.
Fuggi food-jee
Fly!

Tacito táh-tchee-to

Tacitus
Pace páh-tchai
Peace.

Vagito vah-jée-to

An infant's cry.
Pece
pái-tchai
Pitch.

Rigore ree-go-rại ! Rigour.
Pino
pée-no
Pine.

Epocha
Little.

e-po-ka Poco

Epoeh pô-ko

Pagode páh-gå-dai

Pagoda.
Puto póo-tai
It has a bad smell.

Jacopo jáh-ko-po

Jacob.
Riparo ree-páh-ro
I repair.

Aguto ah-gốo-to

Nail.
Império im-pé-rée-o
Empire.

Acuto ah-kóo-to

Acute, ingenious.
Tapino tah-pée-no
Wretched.

Cicuta tohee-kóo-tah Water hemlock.
Sapone sah-pó-nai
Soap.

Ceduto tchai-dóo-to

Yielded.
Impune im-poo-nai
Unpunished.

Apogeo ah-po-je-o

Apogee.
Pappa páhp-pah
Pap for children.

Capacitato kah-pah-tchee-táh-to Capacitated.
Peppe pêp-pai
Joseph, Joe.

Educato ai-doo-káh-to Educated.
pep-po
Philip, Phil.

Vocativo Yo-kah-tée-vo Vocative.
Coppa köp-pah
The occiput, goblet.

Zebedeo tzai-bai-dd-o

Zebedee.
Zuppa tzoop-pah
Soup.

Tucidide too-tchée-dee-dai Thucydides.
Tabe táh-bai
Consumption.

Abituato ah-bee-too-áh-to Habituated.
Teco tái-ko
With thee.

Zodiaco dzo-dée-ah-ko Zodiac.
Tipo tée-po
Type (a model).

Agarico ah-gáh-ree-ko Fungus growing on larches,
Topo to-po
Mouse.

Idiota ee-dee-o-tah

An idiot.
Tubo tóo-bo
Tube.

Abigeato ah-bee-jai-áh-to Stealing of cattle.
Altare ahl-táh-rai
Altar.

Vegetativo vai-jai-tah-tée-vo Growing.
Altero ahl-td-ro
Haughty.

Decapitato dai-kah-pee-táh-to Decapitated.
Altira ahl-tée-rai
To mount.

Decaduto dai-kah-doo-to Decayed.
Alloro ahl-lo-ro
Laurel.

Agitato ah-jee-táh-to Agitated.
Altura ahl-tóo-rak Height.

Epicuro ai-pee-k60-ro Epicurus.
áht-to
Act, action,

Pedagogia
Getto

Education and government of

pai-dah-go-jée-ah
Cast, throw.
jet-to

children. Fitto fit-to

Rent. Cotto kot-to Cooked.

III.-THE SEMI-VOWELS.
Tutto tốot-to

All, quite.
Vano váh-no
Vain.

There are six semi-vowels in the Italian language, so called
Vero vai-ro
True.

because in their utterance a vowel must be placed before the Vino vée-no Wine.

consonant. They are not pronounced in one syllable only, as Voto vó-to Vow.

in the case of the mutes, but require the utterance of two sylAvuto ah-vóo-to

Had.

lables, which syllables are substantially the same, though in an Bavaro báh-vah-ro Bavarian.

inverse order. The semi-vowels are Severo sai-vê-ro Severe.

1. Ff, named in the alphabet effe (pronounced in the followDivino dee-vée-no

Divine. Lavoro lah-vo-ro

Labour.

ing manner-of-fai). Dovuto do-vo-to Debt, duty.

2. L l, named in the alphabet elle (pronounced el-lai). It Davvi dáhy-vee

He gives you.

has two sounds--one like the English consonant l; the second Eovi 'év-vee

Is there.

is a peculiar sound, of which I shall have occasion to speak in Udivvi 00-dív-vee He heard you.

the pronouncing tables. Dovvi dôv-vee I give you.

3. M m, named in the alphabet emme (pronounced ém-mai). Fนชษา fóov-vee Was there.

To ensure perfect accuracy in the pronunciation, I may remark Zara tzah-rah

Zara, a town.

that when m is preceded by a vowel with which it forms one Zero dze-ro

Cipher. Zitella

syllable, and a consonant being the next, it must be very tzée-tel-lah

Giri. Zona dzô-nah

softly sounded, and the voice must glide quickly to the next

Zone, girdle. Zugo tzóo-go Omelet.

consonant, almost as if it formed part of the same syllable: Macara mah-tzáh-rah Mazzara in Sicily.

for example, ambizione, ahm-beo-tzee-ó-nai, ambition; empio, In this and a few other cases, I am compelled for the sake of ém-peeo, impious ; ombra, óm-brah, a shadow. completeness of system, to make a slight departure from strict 4. N n, named in the alphabet enne (pronounced en-nai). orthography. This word being properly written Mazzara, with Generally speaking, this letter is pronounced just as in English; two z's, as well as the following words-gazzera, axzimo, bazzotto, but the observation made on the m is equally applicable to r. assulfa.

In similar circumstances, the voice must glide quickly from the Gasera gán-dzai-rah A jay.

n to the succeeding consonant: for example, andare, ahn-dahApimo Ah-dzee-mo

Unleavened. Baroto bab-dzó-to

Hall-cooked.

rai, to go; entrare, en tráh-rai, to enter ; onda, ón-dah, & ware. Azura ah-tzú-fah

He comes to blows.

After g, n has a peculiar sound, which I skall have occasion to Paszo páh-tzo Fool.

explain in the pronouncing tables. Often n is pronounced like There is very little difference between the pronanciation of; m before words commencing with the consonants 6, m, and p; the single - and zz. The us, as well as z, may have the sound as, gran bestia, pronounced grahm bô-steeah, a boorish, insolent

Atto

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