southern hemisphere, and thus have more power to produce heat than if they fell obliquely, according to the illustration given above. Now, as we in this country are inhabitants of the northern hemisphere, and of that part which is within the circle of illumination all the year round, we experience the vicissitudes of the seasons just described as belonging to it, and we are consequently colder in winter than in summer, although the earth be actually nearer the sun in winter than in summer.

But we must explain more fully what we mean by the circle of illumination. It is plain that the rays of light falling from the sun upon the opaque or dark body of the earth in straight lines, can never illuminate more than one-half of its surface at a time; as may be seen by the very simple experiment of making the light of a candle fall upon a ball at a distance from it. Now, as the earth revolves on its axis once every 24 hours, it is evident that the illuminated half, and consequently the circle of illumination which is the boundary of that half, is perpetually changing, so that almost all parts of the globe receive light for several hours in succession, and that they are also enveloped in darkness for several hours in the same manner. If the axis of the earth, instead of being inclined at a certain angle to the plane of its orbit, which we shall hereafter call the Ecliptic, were at right angles to that plane, and preserved its parallelism, then the circle of illumination would continually extend from pole to pole, and all places on the earth's surface would enjoy light for 12 hours in succession, and would be enveloped in darkness for exactly the same period the whole year round.

On the other hand, if the axis of the earth were coincident with the plane, and preserved its parallelism, this would happen only twice a year; and each hemisphere would at opposite periods be in total darkness for a whole day, while the variations between these extremes would be both inconvenient and injurious. In the former case the seasons would be all the same, that is, there would be perpetual sameness of season all the year round; in the latter case, the seasons, instead of being four only, would be innumerable, that is, there would be perpetual change.

Here, then, creative wisdom shines unexpectedly forth. The inclination of the earth's axis is such as to produce the four seasons in a remarkable manner, and to permit sufficient time for the earth to bring her fruits to perfection, as well to let her lie fallow for a period that she may renew her fruitfulness.

In Fig. 1, when the earth is supposed to be at the point c, she is at her mean distance from the sun at the vernal equinox, which is the first time of the year when day and night are equal, which happens on or about the 21st of March. Now, at this point the inclination of the earth's axis to the minor axis of the ellipse is a right angle, and as the focus F', in the case of the earth, nearly coincides with the centre o, the rays of light proceeding from the sun nearly in the straight line o c, fall upon that axis nearly perpendicularly, and illuminate the globe from pole to pole, so that the circle of illumination passes through the poles, and the days and nights are equal all over the globe, each consisting of 12 hours, while the earth is in this position. In the opposite position at D, the earth is again at her mean distance from the sun at the autumnal equinox, which is the second time of the year when day and night are equal, which happens on or about the 22nd of September. At this point the circumstances of the globe and the circle of illumination are exactly the same as we have just described. At these four points, A, C, B, and D, in the orbit of the earth, are found the middle points of the four seasons of the year, viz., at A, mid-winter; at c, mid-spring; at B, mid-summer; and at D, mid-autumn. At the point A, or midwinter, which is on or about the 21st of December, we have the shortest day in the northern hemisphere and the longest day in the southern hemisphere; and at the point B, or mid-summer, which is on or about the 22nd of June, we have the longest day in the northern hemisphere and the shortest in the southern hemisphere.

"Thus is primeval prophecy fulfilled:

While earth continues, and the ground is tilled;
Spring time shall come, when seeds put in the soil
Shall yield in harvest full reward for toil;

Heat follow cold, and fructify the ground,

fer and summer in alternate round;
nd day in close succession rise,

is regulated by the skies.

r all, at first, Jehovah stood,

ceative voice, pronounced it good."

LESSONS IN ARITHMETIC.-XXIV.

1. FROM the tables given in Lessons XXI., XXII., XXIII. (Vol. ' I., pp. 366, 379, 394), it is evident that any compound quantity could be expressed in a variety of ways, according as we use one or other of the various units, or denominations, as they are called, which are employed. Thus the compound quantity £2 3s. 6d. could be indicated as here written, or by 522 pence, or again, by 431 shillings, etc. The process of expressing a compound quantity given in any one denomination in another, is called reducing the quantity to a given denomination. The process is termed

REDUCTION.

2. EXAMPLE 1.-Reduce £5 2s. 73d. to farthings.

Since there are 20 shillings in a pound, in 5 pounds there are 5 X 20, or 100 shillings; and therefore, in £5 28., 100 + 2, or 102 shillings. Since there are 12 pence in a shilling, in 102 shillings there are 102 x 12, or 1224 pence; and therefore, in £5 2s. 7d., 1224 +7, or 1231 pence. Since there are 4 farthings in a penny, in 1231 pence there are 1231 × 4, or 4921 farthings; and therefore, in £5 2s. 73d. there are 4924 +3, or 4927 farthings.

The process may be thus arranged:£5 28. 73d.

20

100+ 2 = 102s.

12

1221 + 7 = 1231d.

4924 + 3 = 4927 farthings.

EXAMPLE 2.-In 4927 farthings how many pounds, shillings, pence, and farthings are there?

4927 divided by 4 gives a quotient 1231, and a remainder 3; hence 4927 farthings are 1231 pence and 3 farthings. 1231 divided by 12 gives a quotient 102, and a remainder 7; hence 1231 pence are 102 shillings and 7 pence. 102 divided by 20 gives a quotient of 5, and a remainder 2; hence 102 shillings are 5 pounds and 2 shillings. Therefore 4927 farthings are 1231 pence, which is 1028. 73d., which is £5 2s. 7ąd. The operation may be thus arranged:

4) 4927

12) 1231... 3f.

20) 102...7d.

£5 28. 7 d.

In dividing by 20, note the remark (Lesson VII., Art. 7). The same method would apply to compound quantities of any other kind.

Hence we get the following

Rule for the Reduction of Compound Quantities. (1.) To reduce quantities in given denominations to equivalent quantities of lower denominations.

Multiply the quantity of the highest denomination by that number which it takes of the next lower denomination to make one of the higher; and to the product add the number of quan tities of that lower denomination, if there are any. Proceed in like manner with the quantity thus obtained, and those of each successive denomination, until the required denomination is arrived at.

(2.) To reduce quantities of given denominations to equiva lent quantities of higher denominations.

Divide the number of quantities of the given denomination by that number which it takes of quantities of this denomination to make one of the next higher. Proceed in the same manner with this and each successive denomination, until the required denomination is arrived at. The last quotient, with the several remainders, will be the answer required.

Obs. It is manifest that the correctness of an operation performed in accordance with either of the foregoing rules may be tested by reversing the operation-that is, by reducing the result to the original denomination.

the oak and willow, for example is hard and rough, while in the beech and birch it is smooth. The straight parts of the branches of some trees are short, from their slow growth, while others that increase more rapidly shoot forth their stems in one direction to a greater extent. The smaller twigs and shoots of some, like the birch, are very slender, numerous, and drooping; the horsechestnut has fewer shoots, but they are thicker, and grow upwards. Much more might be added to our consideration of this important subject, but we think enough has been said to point out the way, trusting our pupils will perfectly comprehend our intention by these remarks, and be prepared to accompany us in the consideration of foliage.

In our last lesson we mentioned that, in drawing foliage, the mode of treatment must in a very great measure be influenced by the light and shade. We propose now to proceed with this interesting part

of our subject, and show what is meant by the term " "massing

in the foliage." There are some who think that it is necessary to have for each kind of tree some distinct and especial touch,classifying them as "the oak touch," "the elm touch," "the beech touch," and numerous others, regardless of the fact that as the sun casts its light upon a tree it brings out the shape and individual character of its branches so definitely that even at a considerable dis.

tance, when it would be impossible to recognise the leaves, we can pronounce the tree to be an oak, or elm, or whatever else it may be, simply from the manner in which, as an artist would say, "the sun lights it up." The most important consideration in drawing a tree is

to devote much attention to the light, and the parts that are made out in light. There are two reasons why the lights are considered to have such special importance (this principle belongs not to trees only, but to every other object that claims the attention of the painter): the first is, because the details are more recognisable in the light than in the shade, and require particular care to represent them faithfully, for without the details in light there would be very little to show for our pains, as the shadows to a great extent absorb or obscure not only the colour but also the form; the other reason is, that the cyo naturally rests upon the and all the brighter parts first-afterwards, when we make and closer examination, we see the parts in shadow. wo enter into laborious and painful detail, as in the f mere leaf-painting. As we have said before, we do at leaves singly, but at foliage collectively; therefore aches of a tree, let its kind be what it may, which are

in the light, will have their own especial forms in mass to characterise them, and it is those forms in masses which we must copy. But lest our pupil should suppose from these remarks upon generalising foliage that we intend him to stop here, and to represent nothing more than the breadth of light and shade, we must remind him of what has been said above respecting the details in light; we must remember also that, however broadly and definitely the light may fall upon a tree, since it is not a flat surface like a wall, there will be hundreds of minor shadows and semi-tones scattered all over the extent of light, and there is as much individuality amongst these as in the whole mass, and their characteristics in detail are not less striking and significant because they are small in short, they are reduced repetitions of the general masses of light, and must be treated with the same feeling if we wish to make a faithful represen

tation. Here again is the point of difference between a first-rate and an inferior artist, mentioned in a former lesson- namely, the ability he possesses to represent the minor shades and semi-tones, both in regard to their number and expression, and his capability for doing this will determine rank as an artist. Sir Joshua Reynolds mentions

his

a landscape painter who was remarkable for his patience in what he considered "high finish," and thought that the greatest excellence to be attained consisted in the represen tation of every leaf on a tree. "This picture," says Sir Joshua, "I never saw; but I am very sure that an artist who regards only the general character of the species, the order of the branches,

and the masses of the foliage, will in a few minutes produce a more true resemblance of trees than this painter in as many months." We must dwell for a few moments upon the principles here inculcated, and explain by what means a painter obtains the enviable power of making a faithful resemblance with comparatively slight labour: it is because he adopts the excellent practice of making separate studies of details, such as branches, trunks, stems, weeds, and foregrounds-in short, everything that may be deemed worthy of note. It is this method of copying parts of objects with close accuracy that gives him the power of representing them generally and yet faithfully, with the natural effect which they bear to one another as a whole. An eminent English landscape painter, whose manner was as remarkable for its freedom of execution as it was for the truthfulness of its results, once remarked to us:"The secret of my success is in having bestowed much time

upon the close examination of the anatomy of trees; how their branches spring from the trunks; the forms of their leaves, and the manner in which they grow or cluster in masses from the stems." When such labour and painstaking as this is the rule, we need not wonder at a successful result.

Having said thus much upon the theoretical part of our subject, we will now turn to the practical. We advise our pupils to make a drawing of Fig. 101, leaves of the lime tree, with an HB pencil. He must first make the arrangement of the whole of the stems, and then proceed with the leaves, beginning where the two stems join, arranging every leaf in succession, without passing over any, to the end, then faint the arrangement, and draw carefully every particular: it will be much better at first to make an enlarged drawing, say double the size; do the same also with Fig. 102. Fig. 103, the cluster of leaves, will require more time and attention, which must be especially bestowed on

be a rule under all circumstances; therefore after the outline has been carefully made, he must tone down, that is, draw even and close lines over the part in shade up to the outline of the leaves, and further, to make the tint even, he may cross the lines with others similar to the flat tint (Fig. 82, Lesson XII.). He must be careful to go nearly up to the edges of the leaves, as they will come out very forcibly against the dark ground; an H в pencil will make this tint sufficiently dark, as all blackness must be

avoided. Here again we must introduce another caution respect ing the treatment of shadows amongst foliage-namely, never make the interior shadows too dark; a moderate, clear, and yet decisive tone will be enough, because there must be in all cases, but especially with regard to trees, sufficient opportunities left for marking in more forcibly any form which may be remarked in the shadows, observing that the making out details in shadows cannot be carried to the extent of making out details in the lights. Trees, as we have previously said, are not flat like walls, but their branches and leaves project and recede indefinitely, and consequently those leaves which come out nearer to the light will require a different tone to those which are in shadow; the pupil's own observation must be his guide in this matter as to which leaves must receive the minor tones and the depth of tint to be laid upon them. In Fig. 103 the light falls upon the right side, where less shading is required, but the whole of the leaves to the left, away from the light, must be toned down, though not to the extent of the deep shadow in the middle and interior of the branch. Fig. 100 we recommend should be copied double the size, and according to our old principle of

marking in. We were once asked by a pupil, "When shall I leave off marking in ?" We replied, never; it is not desirable that you should ever leave off the practice, because all who do mark in find that they make progress in drawing, and that it saves time, and produces a more satisfactory result. A young mechanic whom we know, who had very much improved his power of drawing from attending a night class at a Mechanics' Institute, offered himself as a candidate for a situation as draughtsman at a manufactory where drawing was essential. Having obtained it, one of his employers, after a few days, when he had become familiar with his work, brought him three or four subjects to draw for working purposes, telling him at the same time that they would, no doubt, occupy him four days at least: at the same hour on the following day he returned the whole finished. His master was agreeably surprised, and also much pleased with the excellence of the work, and asked him

how he had done it so well and so quickly. He replied: "I

am very particular in arranging my drawing first,

and

always make

marks to in

dicate the course of the outline; the consequence is I have very little rubbing out and alteration, and that

has enabled me to finish the drawing so quickly." Therefore, in copying Fig. 100, note every angle, and the distances between each angle, and do the same respecting the positions of the branches as they grow from the trunk, the direction and inclination of the branches, and their extent, and you cannot fail to make a satisfactory drawing.

The illustrations that accompany the present lesson are representations of the stem, branches, blossom, and leaves of the Tilia Europea,

the European or common lime tree, which is the most valuable of the different varieties of this useful tree. It grows most extensively in the middle and northern parts of Europe, and is very common in England. Its large size, handsome appearance, and profusion of sweet flowers, make it a very general favourite throughout this country and most parts of the Continent, where it is extensively planted in parks and other places of public recreation. Its wood is well adapted for carving, being white, close-grained, and smooth. The carvings at Windsor Castle, those of Trinity College, Cambridge, and those at Chatsworth, are of limewood, as, indeed, are most of the other fine specimens of this branch of art in England. The fibres of the bark, which is tough, form the material of an extensive manufacture of cordage and matting in Russia and Sweden. Many specimens of this tree exist which are remarkable for their great age and size. At Neustadt, in Würtemberg, there is a prodigious lime tree, which adds its name to that of the town, this being called Neustadt an der Linden (Neustadt at the lime tree). The age of this enormous tree is said, probably with some exaggeration, to be one thousand years.

EXERCISE 92.

1. How much is my house worth? 2. It is worth about twenty thousand francs. 3. Is that horse worth as much as this one? 4. This horse is worth two hundred dollars, and that one three hundred. 5. Is it worth the while to write to your brother? 6. It is not worth the while. 7. Is it worth the while to go out when one does not wish to walk? 8. It is not (n'en) worth the while. 9. Does it suit you to write to 10. It does not suit me to write to my brother to-morrow? him. 11. Does it become you to reproach me with my neglect? 12. It becomes me to blame you when you deserve it. 13. What is that man worth? 14. I cannot tell you exactly, about fifty thousand francs. 15. Is that cloth good? 16. No, Sir, it is good for nothing. 17. Is your gun worth as much as mine? 18. Yes, Sir, it is worth more. 19. Will you go to my father's? 20. No, Sir, I have something else to do. 21. Is it better to go to market early than late? 22. It is better to go early. 23. How much may your horse be worth? 24. It is not worth much, it is very old. 25. Is your watch better than mine? 26. It is not worth much, it does not go. 27. Is that book worth two francs? 28. It is worth one, at most. 29. Have you asked your sister what that book is worth? 30. I have not. [Sect. XXIV. 1, 2; XLV. 4.] 31. What must I do? 32. You must speak to your father. 33. Must he have money? 34. He must have some. 35. Has he not sold his horse? 36. He has sold it, but it was

SECTION XLIX.-REGIMEN RELATING TO SOME VERBS. 1. When the verbs prendre [4, ir., see § 62], to take; voler,

when one has nothing to say.

De combien votre oncle est-il riche? Il est riche de deux cent mille francs.

thousand francs.

How much is your uncle worth?

to pay, are followed by one regimen only, or by several regimens in the same relation, these regimens, if nouns, must not be separated from the verb by a preposition; if pronouns, they take the form of the direct regimen, le, la, les.

1. Vous sied-il de nous reprocher notre négligence? 2. me sied de vous faire des reproches quand vous le méritez. 3. Vous convient-il d'aller trouver mon frère? 4. Il ne me convient pas d'aller le trouver, j'ai autre chose à faire. 5. Combien ce champ peut-il valoir? 6. Il peut valoir une vingtaine [§ 27 (2) de mille francs. 7. Valez-vous mieux que votre frère ? 8. Mon frère vant beaucoup mieux que moi. 9. Ce couteau ne vaut-il pas plus que le vôtre ? 10. Le mien est meilleur, il vaut davantage. 11. Combien votre montre vautelle ? 12. Elle ne vaut pas grand'chose, elle ne va pas bien. 13. De combien le négociant est-il riche? 14. Je ne puis vous le dire au juste, il est riche d'une centaine de mille francs. 15. Ne vaut-il pas mieux rester ici que d'aller au marché? 16. Il vaut mieux aller au marché. 17. Votre chaîne d'or vaut elle plus que la mienne? 18. Elle vaut tout autant. 19. Elle ne vaut pas grand chose, elle est cassée. 20. Cela vaut-il cinquante francs ? 21. Cela vaut tout au plus deux francs. 22. Avez-vous demandé au marchand ce que cela vaut ? 23. Je ne le lui pas demandé. 24. Il m'assure que cela vaut une centaine de francs.

Je le lui ai payé, etc.,

I have paid the bookseller for the book.

I have paid him for it.

3. Demander is used also in the sense of to inquire for, to ask for. J'ai demandé ce monsieur,

I asked for that gentleman.