А may be done by making a wire-rather less than the tube-red- | Flasks with flat bottoms are required, and these may be had for hot, and then burning a hole through the cork. But by far the 4s. 6d. a dozen, having a capacity of 12 oz., 60. less a dozen for best plan is to buy" cork-borers," which are pieces of thin brass each 2 oz. less in capacity, and 6d. more for every additional 4 oz. tubing, the edge of One of these latter which is sharpened at flasks may make a one end. They are very useful apparatus made in sets which fit -a wash bottle (Fig. into each other. A d 11 b). By blowing set of two costs 10d.; down the open pipe at three, Is. 2d. There A, a jet of water issues are sets of six, but from the other at B, those of two or three which is a convenient answer every practical mode of filling a test purpose. tube, or adding a little Test tubes are in con water to a solution. stant requisition; their To make this bottle sizes range from two will be a good begininches in length and a ning for a student, as quarter of an inch in the tubes and cork diameter, to eight must fit tightly. inches in length and A Ring Stand (Fig. one and a-half inches 11 c), with three rings, diameter. Their prices is 5s., and is indisvary usually from 48. pensable in the laboa dozen to 3s. ratory. They may be When they have Fig. 12. had larger, but this is been used as with all quite sufficient. chemical apparatus—they should be cleaned. This is best effected Evaporating Basins (Fig. 11 d) are shallow basins of Berlin by a round brush, made of bristles held in twisted wire, which porcelain. A nest of seven, containing from 1} oz. to 18 oz., costs 3d., or a piece of tow at the end of a wire will answer the may be had for 6s. 5d. same purpose. Thuringian porcelain is thinner, and basins of this, more It is convenient to have a stand, such as is shown in Fig. 10, shallow than the last, are in nests of nine for 6s. in which to hold test tubes. The stand may be bought for 1s. 9d. Distillation is carried on by turning a liquid into vapour, and condensing this vapour again into liquid. A very useful condenser is the one shown in Fig. 12, Liebig's Condenser, price 14s. and upwards. a b is a glass tube, which passes through cold water held in the larger tin tube c; instead of the retort d, a Florence flask may be used, the tube which passes through a cork fitted into a being attached to its neck. The distilled liquid falls from the pipe e into the vessel f. The water in the condenser is kept cool by continually renewing it; the cold water entering from the barrel g by the funnel i; and, as warm water always rises, the warmest escapes by the pipe h. Liquids are often purified by filtering (Fig. 13); for this funnels of glass or orcelain are used, and white blotting paper is cut into a round disc, then folded thus, a, and again into half, a b, opened, c, and placed in the funnel, d. The arrangement in this figure is simple and convenient. We advise students not to lay in a stock, but to get chemicals and apparatus as they are needed. The prices of preparations Fig. 11. will be found in catalogues, which will be forwarded by any working chemist. Of Glass Jars (Fig. 11 a), one ought to be graduated as a measure All acids must be kept in stoppered bottles, and no bottle 12 oz. an 8 oz.“measuring glass” is 1s. 8d. "Beakers" may be had should be without a label descriptive of its contents. with spouts, but if not, then a glass rod must be held at the place bottles, with ground-glass stoppers, are 6s. a dozen ; 1s. more over which the liquid is to run, as in (Fig. 9). per dozen for each additional 4 oz. Jars are required for collecting gases; those in which confec tioners keep LESSONS IN ARITHMETIC.-XXVII. COMPOUND DIVISION. necked bottles 11. The process of dividing a compound quantity may be also used by regarded in two aspects. them are very (1.) We may divide a compound quantity by an abstract cheap, and an. number ; that is, we may divide the compound number into swer every pur- a given number of equal parts, and thus find the magnitude of pose. one of these parts. Thus £14 10s. 6d. = 7 times £2 ls. 6d. cer or oilman, Therefore £14 10s. 6. divided by the abstract number 7 either for no- gives as a result £2 1s. 6d. Here we have shown that if thing or for a trifling sum. They come from Italy, filled with £14 108. 6d. be divided into 7 equal parts, the magnitude of olive oil. The glass flasks are chiefly made at Florence—hence each part is £2 1s. 60. their name, Florence flasks; they are covered with rushes, not Again, £14 10s. 6d. divided by £2 ls. 60. gives 7 as a only for their preservation, but that a flat bottom may be pro- quotient. This is the same as saying that £14 109. 6d. contains vided on which they stand. For chemical use the rushes are cut £2 1s. 6d. 7 times. off, and the flask cleaned with a little soda and warm water. Hence we see that a compound quantity divided by an abstract. a cale 2 8 3 qrs. 0 2 number gives a compound quantity, and that a compound quan. sively by them, instead of dividing at once by the whole divisor. tity divided by a compound quantity of the same kind gives an For instance, if it be required to divide 75 ewt. 2 qrs. 8 lbs. by abstract number as a quotient. 35, which = 7 X 5, we can perform the operation thus :Obs.—The last remark is the same thing as saying that the cwt, qrs. lbs. ratio (Art. 1, Lesson XXI., Vol. I., page 342) of two concrete 7) 75 quantities of the same kind must be an abstract number. It is of the nature of how many times. 5) 10 57 Furthermore, notice that if two concrete numbers are to be 0 17% + I. compared—that is, if one is to be divided by the other-they must be of the same kind. The ratio of one sum of money to Notice that the is arises from the division of the by 5. another sum can be found, or that of one weight to another Adding { and 3 we get ; so that the required answer would weight; but money cannot be compared with weight or with be written cwt. lbs. length. To talk, for instance, of the ratio of 25 shillings to 13 lbs. would simply be an absurdity. 17H 12. EXAMPLE.—Divide £87 10s. 7d. by 47. And, if necessary, the ide of a pound could be further reduced Beginning with the pounds, we find that £87 divided by to ounces, etc. 47 gives £1, with a remainder £40. Reducing these £40 to 15. When it is required to divide one compound quantity by shillings, and adding in the 10 shillings of the dividend, we another of the same kind, we must reduce each to the same got 810 shillings, which, divided by 47, gives 17 shillings, with denomination, and then divide as in ordinary simple division; a remainder 11s. Reducing these 11 shillings to pence, and for, clearly, the number of times which one compound quantity adding in the 7 pence of the dividend, we get 139 perse, which contains another does not depend upon the particular denominadivided by 47, gives 2 pence and a remainder 45 pence. tion or denominations in which they happen to be expressed. Reducing the 45 pence to farthings, and adding in the 2 far- Supposing one man to have 5 sovereigns in his pocket , and things of the dividend, we get 182 farthings, which, divided by another 1 sovereign, the former would still have 5 times as 47, gives 3 farthings, and a remainder 41, which, divided by 47, much as the latter, if they had respectively 100 and 20 shillings gives a fraction of a farthing. The answer, therefore, in . instead of the sovereigns. £1 178. 2d. 34f. 16. EXAMPLE.—Divide £35 178. 6d. by £2 11s. 3d. The operation may be thus arranged : £35 175. 6. 8610 pence. 47) £87 10 7. (£1 £2 lls. 3a. 615 pence. 47 615 ) 8610 ( 14 615 40 20 340 329 11 12 45 2460 2460 Hence 14 is the answer. EXERCISE 46.-EXAMPLES IN COMPOUND DIVISION. Divide 1. £87 10s. 7d. by 18, 27, and 39. 2. £33 by 96. 47) 132 + 7 = 139d. (24. 3, 312 lbs. 9 oz. 18 dwts. by 7, 43, 84, and 160. 4, 410 lbs. 4 oz. 5 dwts. 6 grs. by 8, 25, 39, 73, and 210. 8. 365 days 10 h. 40 min. by 15 and 48. 9, 111 yrs. 20 d. 13 h. 25 min. 10 sec, by 11, 19, 83, and 100. 141 10. 45° 17' 10" by 25, 35, and 45. Answer £i 178. 20. 314. 11. How much a day is £200 a year? 41 Remainder. How many times is 13. The principle upon the truth of which this process 12. 6s. 3}d. contained in £5? depends is the same as that mentioned in Art. 3, Lesson V. 13. £29 7s. 6d. contained in £523 15s, 3 d. ? (Vol. I., page 69), namely, that when a quantity is to be 14. 2 qrs. 13 lbs. 5 oz. contained in 4 tons 3 cwt. 2 qrs. 6 lbs.? divided, if we separate it into a number of parts, and divide Divide each part individually, the sum of all the quotients so obtained will be the required quotient. 15. 195 m. 7 fur. 30 ft. by 7 ft. 6 in. Here notice that we have, in reality, divided £87 10s. 71d. 16. 531 m. 2 fur. 10 p. by 17 m. 5 fur. 27 p. into the following parts : 17. 950 days 1 h. 11 min. 6 sec. by 4 days 8 h. 6 min. 54 sec. The Key to Exercises 44, 45 (Vol. II., page 78), will be found at the £47 + 7998. + 94d. + 182 farthings; end of Lesson XXVIII. Or, £47 + (47 x 178.) + (47 28.) + (47 x 38} farthings). The quotients of each of these separate sums, divided by 47, are respectively LESSONS IN GEOGRAPHY.—XVII. £1, 17s., 20., and 38 farthings. THE GREAT CIRCLES OF THE EARTH-THE MERIDIANHence the required quotient is THE EQUATOR. €1 178. 2d, 31}f. On the globe of the earth, or terrestrial globe, as it is called, the 14. From the above remarks we see the truth of the fol. first great circle of importanoe is the meridian ; this is a great lowing circle which passes through the two poles, P P (Fig. 6), of the scis Rule for Compound Division when the Divisor is an Abstract of the earth, and through any point, as x, on the earth's surface. Number. It is called meridian, because when the sun in our climate shines Beginning with the highest denomination, divide each sepa- on a gnomon or style (the pin of a sun-dial), and casts its shader rately and in succession. When there is a remainder, reduce it in the direction of this line on the surface of the earth, it is to the next lower denomination, adding the number of that then (meridies) mid-day or noon; and whenever any heavenly denomination contained in the dividend, and divide the sum as body appears in the plane of this circle, as determined by the before. Proceed in this manner through all the denominations. position of the style and its shadow at noon, it is said to be on Obs.-It is sometimes convenient, when the divisor is a com- the meridian, posite number, to separate it into factors, and divide succes- The meridian of the point » in Fig. 6 is, according to this P M X R E N the definition, the circle PUT PN s. But as every spot on the Navigation are the meridian and the equator. We proceed now all others in point of angles, as in Fig. 7. In this figure, the straight line A Y represents the north and A great circle which passes east, and if you go from x to A you go west. Fig. 7. through all the points The directions of the fences being thus Q on the earth's surface understood, suppose that you were told the exact distance of situated at an equal dis- the place where the golden treasure lay from the fence A x, say tance from the two poles, 20 yards; this would not be enough to enable you to find it, PP, of the earth’s axis ; because there are ever so many points in the field, all at 20 it is called the equator, yards distance from the fence A X. Now suppose you were also because when the sun's told the exact distance of the place where the golden treasure rays are vertical to this lay from the fence A Y, say 25 yards; this alone would not be line there is no shadow enough to enable you to find it, because there are ever so P to the gnomon or style many points in the field, all at 25 yards distance from the Fig. 6. at noon, and there is an fence A y. Among those latter points, however, there can be equalisation of light all only one which is at the exact distance of 20 yards from the Over the globe (on the days when this takes place), this position fence AX; so that if you were told both distances at once, you of the sun being the equaliser (equator). The equator is also could evidently, by some means or other, determine the place made the starting place for the measurement of the distances where the golden treasure lay hid. It is necessary, therefore, of places on the surface of the earth as to their position in and sufficient, to inform you of the exact distances of the place the northern or southern hemisphere; for the equator divides in the field from both fences, in order to enable you to find it. the globe into two equal parts, called the northern and southern With the information now supposed to be given, the next hemispheres or half-globes : that hemisphere in which we live question is, how should you proceed to determine the exact is called the northern hemisphere, because our Saxon ancestors place of the golden treasure. A little reflection would suggest called the point opposite to the sun at noon the north; and that the following method. In Fig. 8, measure off hemisphere in which the point opposite to the sun in the con- from the point A, along the fence a x, Y trary direction is seen, is called the southern hemisphere, because given distance of 25 yards, at which the they called the point where the sun is seen at noon the south. place is said to be situated from the fence P The distance of any place on the earth's surface in the A Y; let this distance be a M. Then, from northern or southern hemisphere from the equator is usually the point m, draw a straight line, M P, paralmeasured in degrees of the quadrant of the meridian of that lel to the fence AY; or, which is easier in this place. Thus, the meridian of the place or point m on the sur- case, draw MP a perpendicular to the fence face of the globe (Fig. 6) being the circle P MPS; the distance a x from the point m; for M P and A y being Fig. 8. of u from the equator, E Q, is measured by the number of degrees both at right angles to a X, are parallel to of the quadrant, E P, contained in the arc EM, the extent of each other. Lastly, measure off from the point m, along the opening of the angle EC M. Now the quadrant E P is divided straight line M P, the given distance of 20 yards, at which the into 90° from E to P, that is, from the equator to the north pole place is said to be situated from the fence AX; and the point at P, and the degrees are reckoned from E, which is marked 0° P will be the place in the field where the golden treasure is to (no degrees), to p, which is marked 90° (ninety degrees). Hence, if be found. be any point on the earth's surface to which the rays of the sun That this mode of determining the place of the golden are vertical on the 21st of June as shown in the diagram of the treasure is correct may be proved thus : in Fig. 9 let P be the seasons (Fig. 4, page 80) at R at mid-summer-then the distance place in question ; from p draw in perpen Y of the point m from the equator is 23° 28' N.; that is, 23 dicular to a Y, and P M perpendicular to AX; degrees 28 minutes north. The reason of this is plain ; for, if then, according to the data (things given), P from the right angle or 90° formed between the plane of the PM is a distance of 20 yards, and PN is a N earth's orbit and the perpendicular to that plane (see Fig. 4, distance of 25 yards. But by the nature of page 80), and also from the right angle or 90° formed between the construction, the figure AMP N is a rectthe plane of the earch's equator and the perpendicular to that angular (right-angled) parallelogram, and its plane in the axis of the earth, we take away the common angle opposite sides are therefore equal; whence X NOR, the inclination of the earth's axis to the plane of the A M is equal to NP, and an equal to M P. It Fig. 9. earth's orbit, which is 66° 32', we shall have 23° 28' in either follows, therefore, that the point p is found case; and this is the distance between the polar circle and the by the method shown in the preceding paragraph. In mathepole, or the inclination of the plane of the earth's equator to matical language, the distances P N and PM of the point p from the plane of the earth's orbit, and consequently the distance M E the fences A Y and a x, are called the rectangular co-ordinates (Fig. 6). The distance of any point on the earth's surface, mea- of that point; but the distances A M and MP, which are equal sured in degrees, from the equator is called its latitude (from to the former, are more usually denominated the rectangular the Latin latitudo, breadth), because the extreme distance of the co-ordinates of the P; and by these co-ordinates we can always earth from north to south was by early geographers reckoned determine the position of any point, when their exact lengths less than its extreme distance from east to west; the term longi- are given. The straight lines A X and A Y, from which the tude (from the Latin longitudo, length) being applied to distances given distances are measured, are called rectangular axes, and reckoned east or west from the first meridian. The latitude of the point a, where these axes intersect each other, is called the point m on the earth's surface is thus reckoned 23° 28' N. the origin of the rectangular axes. With the origin and the In like manner the latitude of the point r on the earth's surface, direction of the rectangular axes in our figures, the fences at or any point to which the rays of the sun are vertical on the 21st right angles), and the lengths of the rectangular co-ordinates, of December, is reckoned 23° 28' S.; that is, 23 degrees 28 minutes all given, in reference to any point on a given surface, we south. always find the true position or place of that point The two circles of the greatest importance in Geography and required. А M A M LESSONS IN DRAWING.–XVII. mode of treatment of the form, as we have already remarked; TREATMENT OF TREES AND FOLIAGE (concluded). but now it is the strength and quantity of the work we more especially allude to. If the same tree were drawn on a dull BEFORE concluding our observations upon trees and foregrounds, heavy day, there might be much more leaf character introduced we will offer a few additional remarks upon that which we have both in the lights and in the shades. There is a very common so often maintained to be of the utmost importance, and which and well-known custom when in difficulties as to the true extent of our pupils will by this time begin to realise. It is because, in light and shade ; when the pupil is in doubt as to where the light this particular instance of trees, there is some difference of treat ends and shade begins, let him half close his eyes when looking ment in making the outline, to that required by a solid object, at the object; the minor tones, or those which seem to belong to the form of which is unmistakable, that we think it unnecessary neither light nor shade, will apparently disappear, and the true to offer any excuse for this repetition. The power of drawing extent and force of both extremes become distinct, and so far is the rock upon which the whole superstructure of art is based; evident as to enable him to determine their shape and character. in other words, it is practically the foundation of all that after. Fig. 110 is the general character of a fir-tree, in which we have wards commands admi. endeavoured to show ration or praise. To how the foregoing inwhatever point of excel structions are to be oblence we may hereafter served. Fig. 109 in the attain, we shall invari. last lesson will also ably look back with Fig. 110. illustrate our meaning. satisfaction upon the Now the pupil must exertions we have used, clearly understand that and the time we have whilst we advocate a devoted to ensure our breadth of treatment on success in making a really learned and care the whole, characteristic details must not be fully-constructed out omitted; these details line; it must be the one may be expressed in only starting-point of all such a way (without who are ambitious to descending to littleness excel, though the sub of manner) as not to jects they may eventu destroy that breadth, ally choose will vary according to their indi and yet be sufficiently vidual tastes, wishes, carried out to enable us and circumstances. to say whether the tree be an oak, a poplar, & In the case of foliage it is necessary to explain fir, or one of any other what we mean by out description. We will now introline, and how it is to be duce & few practical treated when subject to hints respecting some the various changes of the uses to which the caused by sun and shade under which the tree is knowledge of drawing found. Let us suppose trees, shrubs, or wild ourselves to be standing plants may be applied, opposite a tree on a dull, especially by designers of patterns and omacloudy day. The force ment. Our country lanes of light and depth of shadow will each be less and hedgerows afford than if the sun were abundance of material shining upon it, and the to supply us with an endless variety of form half-tints will be more and culture especially apparent and varied. All applicable for the decoround the tree ration of our walls, and against the grey sky behind there will be for the enrichment of the same articles of ornament and distinctive The Corinthian and uniform character capital is said to have throughout; but let the sun break out, and then had its origin from the observe what a remark circumstance of a tile having been placed on able change takes place. The general or the top of a basket, around which grew the larger masses of light and shade will be more decided, leaves of the acanthus plant. This, whether true or not, is the neutralising tones among the half-tints will in a great highly suggestive, and tells us there are beautiful combina measure have disappeared; the shadow side of the tree will be tions to be found in nature, which the designer would do well distinctly made out against the sky, whilst the details in light to cultivate. To point out a few of them will be sufficient to will be less definite than they were before the sun shone, owing direct the way in which the lover of nature and art may select to the radiation of light from the leaves; the half-tints and examples for himself without fearing to exhaust the supply . small shadows in the light will have less strength than they had The most graceful of all the wild plants are those which cling to before-they will be of a warmer tone, and partake of the light others for support. Who has not noticed the wild convolvulus, and colour around them; the corresponding half-tints on the with its elegant elongated leaves, and its simple symmetrical shadowed side will follow the same course on the same principle flowers twined about the stem of a brier or hazel + The hop ---that is, become more general and less distinct in form. We plant, also, the black bryony, and others may be named whose therefore advise the pupil, when “massing in the foliage” of a spiral twistings round stems of various kinds produce natural tree in sunshine, to use his pencil less vigorously on the lights, combinations which no mind could suggest, or power of invention and not to be betrayed into leaf-drawing and making dark heavy could supply. The leaves alone are models for imitation. The lines. The kind of tree he may be drawing will suggest its own ancient Greeks saw this, and proved it by their frequent appli use. how many times, may cation of the vine-leaf, the oak, and the ivy. In fact, as Mr. We now take up another portion of our subject relating to Redgrave has said, " He that would be a great designer must landscape—the principles of the reflection of objects in water, as be in the hedgerows and fields at all times, sketching with by reflection only can water be represented. patient diligence the form and curvatures of leaves, fruits, and It has been frequently said that a landscape is incomplete fowers, their groupings and foreshortenings; studying them as without water; it is certainly an element which contributes a whole, and in their minutest details, together with their much additional beauty and effect to any scene, be it ever so growth and structure. Not to repeat as a mere imitator, but simple ; yet we cannot go so far as to say that it must necesto display them as ornament; to dispose them geometrically, sarily be introduced in all cases. Independently of itself, there to arrange them to suit the various fabrics or manufactures for are associations connected with water that cannot be passed over which they may be called on to design, and to give them life without notice, and which bear an important part in the whole and words, as it were, by using them as emblems of some living composition whenever it forms a portion of the picture, such as thought or poetical allusion.” shipping, barges, boats, fishermen, and picturesque bridges. Why It is the application of the graceful forms of the vegetable is it that, in our choice of a walk, we generally prefer a stroll kingdom that constitutes the most important part of the study near some stream? We attribute it to the variety of scenery of the designer and decorator: the power of drawing, important afforded by the winding river, and the numberless points of inteas it is , is only the means; the adaptation is the end sought for. rest that catch the eye as' we ramble along its banks. The life Here it is, we can say with truth, that it requires the mind of and motion connected with water have no limit; and besides, we an artist to accomplish it, to be imbued with an originality of cannot forget, when it is clear and calm, its capability of reflecting thought, that can make the simplest object do duty for worthy every object near it in full perfection, and increasing our admirapurposes. tion by the It very fre. fidelity quently with which it reverses occurs, in art univer form, and sally, that reflects by contrast colour, or applica light and tion we dis Fig. 111. shade, thus cover excel making a lences not double before ob picture. served: re There are specting several the use of phenomena this idea, resulting from theap pearances we ask, of reflec. have we tions upon trod on the the surface decaying of water leaf in our which unpathway, doubtedly without require having had more at the atten. tention tion in the than is least di. generally rected to it devoted to as capable such sub of suggest jects by ing either an original aim at reform or a presenting fresh them. A arrangement of colour? However insignificant and valueless an course of study is necessary which some would suppose to be object the fallen leaf may seem to be, it is capable of teaching beyond the limits pursued by artists generally, but which we us a lesson of great practical ity. It has been supposed contend is indispensable; for every on who undertakes or by some that the shape of the vase owes its origin to a leaf ; hopes to paint Nature as she is, must go deeply into her mysit may be so or not, but it is sufficient for us to know its teries, and endeavour as far as possible to understand them, and capability of suggesting it, and it leads us to where the designer not abide by a mere superficial following of outward appearances. may apply if any new form is required. Such resources, when Why is it that the sculptor and the historical painter seek the regulated by a disciplined and scientific taste, must produce advantages to be gained in the dissecting-room? Because they something as beautiful as it is original. In search for hints for feel that a knowledge of anatomy is of the utmost importance to decorative purposes it is not absolutely necessary to confine our them when engaged upon the human form. Similarly the landchoice to the floral varieties of a conservatory or greenhouse, scape painter wisely looks about for aid when difficulties arise, however valuable they may be for the purpose; the green lanes which have their remedy often beyond the limits of his own legitiand hedgerows can boast of gems of form amongst nettles and mate art; and he will meet with an abundant source of difficulty wild flowers, from which articles of ornament and utility may with regard to reflections. There are incidents so puzzling con. borrow their simple elegance either to decorate a palace or nected with these, that unless he possesses a little geometrical perform some humble service in a cottager's dwelling. Nature knowledge, he cannot avoid falling into endless mistakes. We everywhere offers hints that are useful as well as beautiful, and must again have recourse to geometrical perspective, which the designer need never sigh for a model. As an illustration of will not only assist us in our explanations, but will set at rest the way in which plants may be adapted to ornament and many doubts which might arise in the minds of our pupils with design, we have introduced one for a candlestick in Fig. 111, regard to facts that seem to be impossibilities, unless we employed the socket of which is a lily; the extinguisher inserted in this conclusive help in rendering them intelligible. Sir Joshua, the side is a dead blossom of the same plant, emblematic of Reynolds said, “ The rules of art are not fetters to genius ; they are fetters only to men of no genius.” many who its use. |