properly represent them according to the circumstances under which they are placed, may certainly claim the title of a draughtsman in its fullest meaning. In arranging the positions of the head and features, we must bear in mind that the general form of the head is oval. This figure may be applied with great advantage in two ways, both of which we will consider. As the oval which represents the form of the head is a solid, and the several lines which we are about to draw, to determine the proportions and positions of the features, are supposed to be drawn on the surface, therefore the perpendicular line drawn throughout the length in Fig. 129, Lesson XXI., will decide the position of the face to be parallel, that is, a full face. In a retiring view this same line will be a curve, as A B in Fig. 136, upon which the features must be arranged as in Fig. 137. When the head is looking up or down, then all the lines which are straight in Fig. 129 become curved in proportion to the extent of the inclination of the head. Figs. 138, 139 will illustrate these positions, and show that the use made of the curved lines is the same as that employed in the full face. Regarding the treatment of the details, more especially the peculiarities belonging to each feature, the pupil must be left in a great measure to his own observation and practice from nature and from casts. In the details no two faces are alike; consequently, there can be no special rules in reference to them. We must treat the subject as a whole, and use those rules only which are applicable to all, with regard to proportion and position. We may say, for instance, that the length of the mouth is equal to the width between the eyes; that the centre of the mouth is one-third from the bottom of the nose to the lower part of the chin. These and other regulations may be useful where a classical head only is attempted, and it is right to know them; but Nature does not always carry out these exact dimensions, otherwise we should lose that individual character so admirable, and in most cases indispensable to real beauty. The knowledge of these proportions will help us to avoid extreme deformity, and many absurdities; it will likewise quicken our perception when studying the characteristic differences existing amongst heads; consequently, this knowledge, coupled with close observation regarding the angles of the face, and of the features one with another, and more minutely those angles which constitute the form of each feature singly, will together enable the pupil very quickly to acquire a power of giving cha racter and individuality to his subject, either in portraiture or when engaged on an ideal head representing some passion or emotion of the mind. What rule could be furnished for drawing a Roman or a snub nose, beyond that of marking the angle which gives character to the shape of the nose? Nothing would prevent originality of drawing and a true feeling for Nature more effectually, than confining the practice in all cases to set rules for details. Because Nature is varied in her details, therefore it is in generalities only that rules are useful, and where it would be unwise to reject them. LESSONS IN ENGLISH.-XXVI. THE learning of a new language is like the acquisition of a new sense. This is true, if only because a new language affords a new set of means for the expression of our ideas. The capacity of the human mind is greater than is the power of expression possessed by any vocabulary. That greater capacity finds a new channel, and a new outlet, in a new language. Besides, language is a medium for conveying ideas to a recipient, as well as an instrument for the expression of ideas already enter tained. With words, then, you gain ideas. The increase of a man's vocabulary is the augmentation of his mental treasures. New knowledge must run into the old moulds. If it be truc that no idea no word, equally is it true that no word no idea. You may, indeed, make a word contain more than it does contain. You may transmute brass into silver, and silver into gold; but out of nothing comes nothing. There are, then, two ways by which I may impart knowledge; I may give a new idea by giving a new word, and I may increase the value of the word you have. Equally may I aid the development of your mind, and augment at once its knowledge and its power, by supplying you with a fresh term, or a fresh series of terms, as a means for the expression of your thoughts and feelings. These remarks find verification in the study even of the remnants of Greek which form part of our English speech. If ours is a rich language, if ours is an expressive language, we owe a large debt of gratitude to the Greek. By the aid which it affords, we express thoughts which we could not otherwise have expressed; and we acquire ideas, and modifications of ideas, the sources of which are found only in its literature. In exemplification, it suffices to refer to the single domain of theology. The creed of Christendom wears the shape and the hue which it received from the Greek language, in which the Gospel was promulgated to the world, and by which it was planted in the mind of all the most civilised nations. The aid which the Greek language affords to the student in making. exact verbal distinctions is illustrated in orthoepy, which is, by its derivation, seen to designate right speaking, as orthography is right writing; the first, therefore, refers to pronunciation, the second to spelling. "The epic poem is a discourse invented by art to form the manners by such instructions as are disguised under the allegories of some one important action, which is related in verse after a probable, diverting, and surprising manner."--Pope. The three great epics are Homer's "Iliad,” Virgil's “ Æneid," and Milton's "Paradise Lost." Such is the perfection of these poems that they form a class by themselves. "Three poets, in three distant ages born, Greece, Italy, and England did adorn." The formation of our hermit, from the Greek purJ (e-re'-mi-tees), illustrates the change which words undergo in passing from one language to another. Metallurgy, an incomprehensible term to the ordinary English student, discloses its meaning by its own act to those who know the import of its component parts. Metallurgy is, in general, the art of working metals-that is, the extraction of metal from the ore. Ethics is the science of morals-that is, of right feeling and right doing. The word ethics resembles the word morals in origin. They both signify customs, and they intimate that with the ancient Greeks and Romans, what is customary was what is right. At the bottom of such a notion there must have been a low standard of morality. Thus does a knowledge of language open to our eyes the character of nations. The termination of ethics, like physics, mathematics, etc., denotes a science. Ethics is the science of morals. Evangelist is, according to the derivation, the bearer of good news. The Greek word for gospel-namely, evayyeλiov (en-angel'-i-on)-means good news. (Luke ii. 10.) "The gastric juice, or the liquor which digests the food in the stomach of animals, is of all menstrua the most active, the most univeral.”Paley, "Natural Theology." In Greek, when two g's come together, the first sounds like n. "Oxygen is a principle existing in the air, of which it forms the respirable part, and which is also necessary to combustion. Oxygen, by combining with bodies, makes them acid, whence its name, signifying generator of acids."-Todd's Johnson, Hydrogen is water-producer. Hudor (wp), in its form hydro, is found also in hydrocephalous (Greek, kepaλn, keph'-a-le, the head), having water in the head (the brain) and in hydrophobia (Greek poßos, phob-os, fear), water-madness. Hydropsy, water-sickness, is shortened into our dropsy. "Soft, swollen, and pale, here lay the hydropsy, hecatombs of most happy desires, praying all things may prove prosperous unto you."—Drummond. Isothermal lines are lines of equal heat in different parts of the globe. Iso is also found in isosceles (σkeλos, skel'-os, a leg), applied to a triangle which has its two sides of the same length. most distant from the sun; perihelion is that point in which it Aphelion is that point of the orbit of a planet in which it is is nearest to the sun. Anything whose duration or existence is very short is termed ephemeral, or lasting for a day. Thus, insects that spring into life at sunrise and perish at sunset are styled ephemera. "There are certain flies that are called ephemera, that live but a day."-Bacon. Thomson, "Castle of Indolence." Hydrography is properly the opposite of geography; for as the latter, considered in its component parts, is a description of the land, so the former is a description of the water. By usage account of daily transactions. Ephemerides (the plural of ephe An ephemeris is properly a journal (French, jour, day), an these significations are modified, so that geography, signifying ameris) denote a set of astronomical tables, showing the state of description of the surface of the earth, comprises hydrography, the heavens for every day. which describes, by maps, charts, etc., the surface of the water, and especially the sea-coast, with its rocks, islands, shoals, and shallows. By derivation, grammar is the science of letters. This is not an incorrect definition, for the science of letters, considered in all its relations, is the science of language, of which letters are the elementary portions. "Letters" is often used, however, for systematic knowledge, or the results of a high and varied education. So we speak of "a man of letters." In this sense the term is used in the question, "How knoweth this man letters, having never learned ?" (John vii. 15.) The hostile questioner took Jesus to be ignorant (Acts iv. 13)—that is, as in the original, dicerns (id-i-o'-tees), idiot, untaught—such as Peter and John were accounted. "I made it both in forme and matter to emulate the kind of poeme which was called epithalamium, and by the ancients used to be sung when the bride was led into her chamber."-Ben Jonson, "Masques." Stems. English Words. hagio hagiography. Meanings. holy hundred Greek Words. 'Αγιος Εκατον Pronunciation. Ήλιος Περι he'-li-os per'-i helion peri Απο ap'-o from ap apology. Ημερα he'-mer-a a day homer ephemeral. of Geometry," in reference to lines and angles that correspond The expression homologous is used by Euclid in his "Elements in relative position, proportion, or structure: hence any two forms or expressions that exactly correspond in position, proportion, formation, or value, may be said to be homologous. "Comparing the homologous or correspondent members on both sides, we find that the first member of the expression," etc.-Bishop Berkeley, "Analyst." Apocalypse, by its very derivation, signifies uncovering; in Latin it is unveiling-that is, revelation. In apocrypha we have another theological term, which is interpreted to mean a hidden writing, from ano (ap-o), from, and KPUTTE, krup-tine (cryph), to hide. But why should not the apo here have the same meaning as in apocalyse, and so reverse the import of kryptein (English crypt), to hide, and thus signify the disclosed, discovered, or detected writing? Any way, apocryphal is equivalent to spurious, and opposed to canonical or authentic. "Now, beside the Scriptures, the bookes which they called ecclesiasticall were thought not unworthy sometimes to bee brought into publicke audience; and with that name they intituled the bookes which we term apocryphal."-Hooker, "Ecclesiastical Polity." Laity denotes the people as contradistinguished from the clergy. In ancient times the laity were ignorant, the clergy learned. Hence arose a broad contrast, exhibiting the people as wicked as well as untaught, and the clergy (clerks) no less holy than instructed. These usages are found in the substance of our language, and still linger amongst us in both thought and feeling. "He entended (intended) to set forth Luther's heresy, teaching that presthed (priesthood) is no sacrament, but the office of a lay-man or a lay-woman appointed by the people to preache."—Sir T. More. "No wonder though the people grew profane, When churchmen's lives gavo laymen leave to fall."-Drayton. Synthesis is properly the putting together, as analysis (ava, an'-a, up; and Ave, lu'-ein, to undo, to loosen) is the undoing. A watchmaker performs an act of analysis when he takes a watch to pieces, and an act of synthesis when he puts the parts together again. "Synthesis consists in assuming the causes discovered and established as principles, and by them explaining the phenomena proceeding from them, and proving the explanations."-Newton, "Optics." "Analysis consists in making experiments and observations, and in drawing general conclusions from them by induction."-Ibid. Analysis is the way of discovery, synthesis is the way of teaching or communication. By synthesis men put together and exhibit what they have ascertained by analysis. Metamorphosis denotes a change of form. "Thus men (my lord) be metamorphosed From seemly shape to byrds and ougly beasts."-Gascoigne. Metempsychosis (uera, meta, change; ev, en, in; and yʊxn, psu'-ke, the soul) has for its Latin equivalent transmigration (trans, over; migro, I change my place). "The sages of old live again in us, and in opinions there is a metempsychosis. We are our re-animated ancestors, and antedate their resurrection."-Glanvill. Metathesis is a change of position or a transposition. Thus what we write bird was formerly bryd, thei and the r changing "And here, sir, she offers by me to the altar of your glory, whole places. Mythology is the science of fable, and is applied to the religion of the Greeks, the Romans, the Hindoos, etc., in opposition to the pure religion of the Gospel. German philosophy has introduced amongst us the new term myth, as denoting a legend, or a version of facts, shaped and coloured by opinion, fancy, preju-| dice, by the workings of the intellect, the workings of the imagination, or the workings of the heart. In origin, myth, fable, and legend are one, for the words severally denote a word, something spoken, something narrated. But as old stories soon lose their primitive form, and acquire new shapes and hues, so words pass into legends, and legends are corrupted into fables. Necromancy is the fancied art of learning and disclosing facts by communication with the dead. The witch of Endor dealt necromantically with Samuel at the request of Saul. (1 Sam. xxviii. 7; compare Deut. xviii. 9.) A pedagogue is a term of Greek origin, equivalent to our schoolmaster. Pedagogue is a word which is now used contemptuously. In an oligarchy the interests of a few predominate. In a democracy the interests of the many prevail. The real and the apparent interests of men are sometimes very different. A polemical spirit is undesirable. Polemical writings are occasionally required. The character of the apostle Paul is very noble. Apostolical virtues are rare. The apostles received their mission immediately from Christ. Without enthusiasm the best of causes cannot be carried forward Enthusiasm is in danger of degenerating into fanaticism. HYDROSTATICS.-II. PRESSURE OF LIQUIDS AKISING FROM THEIR WEIGHTCENTRE OF PRESSURE-LEVELS-SPRINGS AND ARTESIAN WELLS. HAVING now mastered the principle of the equal transmission of pressure in all directions, we must pass on to notice the pressure which is produced by the weight of the liquid itself. Water, in common with all other substances, possesses weight, and this weight must cause pressure on the sides of the vessel containing it. If we have an upright cylindrical vessel with straight sides, and place in it a cylinder just fitting, it will press on the bottom of the vessel with a force equal to its own weight. If now we replace the solid by a liquid having the same weight, the pressure on the bottom of the vessel will remain the same as before, but, in addition to this, every part of the sides of the vessel will sustain an outward pressure. This is clear from the fact that, if we remove the side, or any portion of it, the liquid will no longer retain its shape, but will spread AL K 8 itself out as widely as possible. E L F The first fact we have to notice about this pressure is that it increases with the depth of the liquid, and in the same proportion, but is perfectly independent of the shape of the Fig. 4. vessel containing it. In the proof of this and other propositions, we shall make the following assumption-that any portion of a bulk of fluid may be supposed to become solid without making any difference in the state of equilibrium of the liquid, or in the forces which act upon it. A moment's thought makes this fact self-evident. Let ABCD (Fig. 4) represent a vessel filled with water to the level A B. Take in it any horizontal layer, EF, and in this let a portion, GH, having an area of 1 square inch, be supposed to become solid. It is now kept at rest by two equal 瓜 and opposite forces-the weight of the water above it, and the upward pressure of that below it. Now the former is clearly equal to the weight of a column of water having, like G H, an area of 1 square inch, and whose height is equal to G K. If G H be now sunk to a lower level, it will have to sustain the weight of a longer column, and therefore of the pressure of the water on it will be greater. We see thus, that the pressure increases with the depth. If we take a number of bags of flour or sugar, and pile them one on the top of the other, the lower ones have to sustain the weight of those above, and will accordingly be compressed to a greater extent than those which are higher up in the pile, and therefore have to sustain the weight of fewer. P Just in this way each layer of liquid has to sustain the weight of all above it, and thus the lower layers are more powerfully compressed. An illustration of the great pressure thus exerted is seen in the fact that if a tightly-corked bottle be sunk to a depth in the sea it will be broken, or else the cork will be driven into it. IN Fig. 5. We have now to show that this pressure is quite independent of the shape of the vessel. Instead of that shown in Fig. 4, let us have one made in the shape of a small tube fitted into the top of a larger one, as shown in section in Fig. 5. The pressure on the part directly under H E will, as before, depend on the height of the column of water above it. But every part of the base, M N, must sustain the same pressure, for otherwise there would not be equilibrium, but the liquid would move towards that part where the pressure was least. Every part of a horizontal layer sustains then exactly the same pressure. We thus arrive at the apparently strange result, that if the vessels represented in Figs. 4 and 5 be filled to the same height, and the areas of their bases be equal, the pressure on each base will be the same, although one contains a much larger quantity of water than the other. We must not, however, suppose that, since the pressures are equal, the vessels, if placed in opposite pans of a pair of scales, would balance each other. This paradox is easily explained. Suppose we have a box, the lid of whieh fastens down by a catch, and we place a spiral spring inside, so that when the lid is closed the spring is powerfully compressed, the pressure on the bottom is manifestly much greater when the box is closed than when it is open, and yet it weighs no more. The fact is, the spring presses the top of the box upwards with exactly the same force as it presses the bottom downwards, and these two forces neutralise each other. So in the vessel shown in Fig. 5, the pressure of the liquid, being transmitted in all directions, presses up against the surface PGF R, and balances a part of the pressure on the base, and the pressure on the scale pan will be the difference between these two, the upward pressure on PR being exactly 1 h b Fig. 6. equal to the weight of the ring of water required to make up the quantity there is in the other vessel. The following experiment affords a proof of this principle of the pressure being dependent alone on the area of the surface and the depth of liquid. Procure three vessels of the shapes represented in Fig. 6, and let their bases be made of exactly the same size, and arranged so as to open like trap-doors by means of hinges. To a similar part of the base of each attach a string, and let these pass over pulleys and have equal weights affixed to their ends, so as to keep the bottoms closed. If now water be poured into each vessel it will be found that the bottoms will open, not, as might be supposed, when as equal weight of water has been poured in, but when the water stands at the same level in each. We see thus, that when filled to the same height the bases sustain exactly the same pressure, and this pressure is equal to the weight of the fluid in the middle vessel. Having thus seen that pressuro is proportional to the depth, we can examine the variations in it at the different parts of the sides of any vessel or of an embankment. If we have a column of water having a base 1 square inch in area, tho pressure on a layer of it at a depth of 1 inch will be equal to the weight of a cubic inch of water, or 252-5 grains; and at a depth of 2 inches the pressure will be equal to the weight of 2 cubic inches, and so on, varying in direct proportion to the depth. We see thus, that an embankment or sea-wall should also increase in thickness in the same proportion. The pressure against such an embankment is, it may be observed, quite independent of the extent of the body of water it sustains. The same strength is required to resist the pressure on the side of a narrow mill-stream as in a sea-wall, provided the depth be the same in each case. If we divide the side of a rectangular vessel into any number of equal divisions, the pressures at these divisions will be in the proportion of the consecutive numbers 1, 2, 3, etc. Let these divisions be one foot apart. Then at the first, the pressure on any portion will be equal to the weight of a column of water one foot high. The pressure on a square foot at this depth will therefore be equal to the weight of a cubic foot of water. We must not, however, suppose that this will be the pressure on a square foot of the side extending from the surface to the first division, for at the surface the pressure is nothing, and it gradually increases with the depth. The mean pressure on the square foot is therefore equal to that at a depth of 6 inches, and the total pressure is equal to the weight of a column of water of this height. So if we want to know the pressure on the rectangular side of a vessel, we must ascertain its area, and multiply this by half the depth; we shall thus find the number of cubic feet of water to which the pressure is equal. An example will make this clear. Suppose we have a vessel 5 feet long and 4 broad, and it be filled with water to a depth of 4 feet, what is the pressure on the four sides, and what on the bottom? We will take the sides first; each of these is 5 feet by 4, and has therefore an area of 20 square feet; each of the ends has also an area of 4 feet by 4, or 16 square feet. The total area of the two sides and the two ends is therefore 40 + 32, or 72 square feet. Now the depth of the water being 4 feet, the mean pressure is found at a depth of 2 feet, and thus the total pressure on the sides is equal to a column of water 72 feet in area and 2 feet in height; that is, to the weight of 144 cubic feet of water. In these calculations we must remember the following weights: A cubic foot of water weighs about 1,000 ounces, or 62 pounds. A cubic fathom weighs 6 tons. The total pressure on the sides is therefore 144 × 62) = 9,000 pounds, or rather over 4 tons. The pressure on the bottom is 5 x 4 x 4, or 80 cubic feet of water. This is equal to 80 x 624 or 5,000 pounds, which is nearly 2 tons. Sometimes the surface on which we want to ascertain the pressure is not a rectangle, but we may always take the mean depth as that of the centre of gravity of the surface, and, multiplying this by the area, we obtain, as before, the pressure. We thus see that when water has to be confined by a wall or embankment, the safest plan is to spread it out as widely as possible so as to diminish the depth, and also to let the edges gradually slope down to the middle. If the depth against the embankment be great and a small leak occur-as it may, from the hole of a rat or some similar cause-the water, when once it has found a way, soon wears a larger hole, and the upward pressure of the water is often so great as to blow up the bank. It is on account of the great pressure thus produced by a body of water that lock-gates have to be made so strong; and to enable then to stand better, they are usually made so that when closed they are in the form of an arch, the convex side being turned in the direction in which the water is highest. When the gates are large, a sliding panel, worked by a screw, is introduced near the bottom, and through this opening the water flows till it stands at the same level on each side. With out this the pressure would be too great to allow of the gates being opened. AL Fig. 7. Now, although the mean pressure is that at the centre of gravity, we must not imagine that this point is the centre of pressure-that is, that a support placed behind this would balance the pressure. If we suppose the surface divided into layers, there will, if it be rectangular, be as many layers above the centre of gravity as below it; but, since the pressure is greater on the lower layers than on those higher up, the larger part of the pressure will be below the centre of gravity. The centre of pressure is therefore below this point. Its position varies with the shape of the surface, but in a rectangular surface is situate at about two-thirds of the depth. This fact should be borne in mind in the construction of lock-gates, for if a hinge be placed near the top, and a pivot and socket at the bottom, an undue pressure is thrown on the lower support, and thus there is a tendency to wring or twist the gates. The sup ports should be arranged as nearly as possible equi-distant from the centre of pressure, one being near the bottom, and the other about a third of the way from the top, as then the pressure is equally distributed. There is another property of liquids which results from the facts already noticed, and that is, that the surface always maintains its level and forms an horizontal plane. This fact is familiar to us by every-day experience, and the reason of it is easily seen. Let A B C D (Fig. 7) be a vessel containing liquid, and let the surface be supposed to have the figure AGH B. Take any layer, E F, in the fluid, and imagining it to become solid, let us see what is the pressure at each end of it. At E it is equal to that of a column of water having the height & E; at Fit is equal only to the column F H. The former of these is obviously greater, and therefore equilibrium cannot exist till this difference is removed. The particles of fluid will therefore move from E towards F until the surface becomes even. M Fig. 8. Exactly the same result will occur if, instead of one vossel, we have any number communicating with each other, no matter what their shape may be. The apparatus usually used for the proof of this is shown in Fig. 8. A number of glass vessels, varying greatly in size and shape, but all having the same height, are arranged so as to communicate freely with each other. If now water be poured into any one of them, all will be filled, and the water will rise in each of them to the same height; or, if a stopcock be fitted at the bottom of each, and they be filled to different levels, immediately on the taps being turned, the level will become the same in all. The mass of water in M is many times greater than in N, yet it will stand at exactly the same height in each. Familiar illustrations are seen in tea-pots, or other vessels used to pour liquids from. The spout is always so arranged that the open end of it is at least as high as the surface of the liquid within. Fig. 9. The practical applications of this principle are numerous and important. The most common is the level, which is such an important instrument in surveying operations. In making roads or railways, or still more in canals, it is necessary that all parts should have as nearly as possible the same elevation, so as to avoid inclines. It is desirable, too, to do this with as little labour as possible, and therefore that route is chosen which will require least cutting or embankment. To ascertain this, levelling is required. The form of level which shows best the |
