planes passing through the centre of the sun; the sun itself being placed in one of the foci of the ellipse.

2. That the radius vector, or straight line drawn from the centre of the sun to the centre of the planet, passes over equal areas in equal times in every part of the orbit; that is, whether the planet be in its aphelion, or farthest from the sun, in its perihelion, or nearest to the sun, or at its mean distance from the sun.

3. That the squares of the periodic times of the planets-that is, of the times of a complete revolution in their orbits-are proportional to the cubes of their mean distances from the sun; in other words, that the square of the periodic time of one planet is to the square of the periodic time of another planet, as the cube of the mean distance of the former from the sun is to the cube of the mean distance of the latter from it.

hangeth the earth upon nothing" (Job xxvi. 7). This passage is singularly true in regard to the first sentence as well as to the second, for the axis of the earth is inclined to the plane of its orbit, at an angle of 66 degrees 32 minutes, that is, rather more than two-thirds of a right angle; so that literally and truly "the north is stretched over the empty place," and not over the body of the earth itself, in either of its motions, whether axial or orbitual. This inclination is preserved during the whole of its motion in its orbit, and is the cause of the variation of the seasons; the preservation of the inclination of this axis has been not inaptly called the parallelism of the earth's axis.

E

C

A

Before explaining the effect of this parallelism and inclination of the earth's axis in producing the seasons, it will be proper to explain what is meant by tangential impulse. In Fig. 2, let A C B represent the orbit of the earth, which is nearly circular; let D represent the place of the sun, and A the place of the earth at the moment when it began its revolution in its orbit. At B this moment the force of the sun's attraction would begin to act on the earth in the direction A D, and had this alone been allowed to operate, would have drawn it rapidly towards the sun in a straight line, until it had come finally in contact with the sun itself; but at the same moment an original impulse was, or is supposed to have been given to the earth in the direc

Fig. 2.

the axis.

We think we hear some of our readers exclaiming, notwithstanding the elevated position in which we have supposed them be placed, "What! Will you tell us that the sun is the cause flight and heat on the earth's surface, and yet you assert that be earth is nearer to the sun in winter than in summer? How this be?" Paradoxical as this may seem, it is nevertheless e and the reason we shall now give. As you are supposed be looking from a great distance, and to be able to discern the motions of the planets, if you look narrowly at the earth, will perceive that besides its orbitual or annual motion round un, it has a revolving or diurnal motion on its own axis. aris here is meant that imaginary straight line passing rough the globe of the earth, on which its rotation is supposed take place, and which is aptly represented in artificial globes the strong wire passing from one side to the other, at the ats called the poles (that is, pivots), which are the extremities The revolving motion on its own axis may be likened to the aning of a top, a motion which continues while the top is en forward in any direction from one place to another. In the analogy would be so far complete independently of the Bes of the motion, if the top, while it is spinning or revolving were on its own axis, were made to run regularly round in ral ring on the ground, under the lash of the whip. Thus, earth has two motions; one on its own axis, performed once twenty-four hours; and one in its orbit, performed once 7365 days 6 hours. We have stated these periods in round abers, in order that they may be easily remembered; but exact period of the earth's daily revolution on its axis is hours, 56 minutes, 4 seconds, and 9 hundredth parts of a end; and the exact period of the earth's annual revolution in brbit is 365 days, 5 hours, 48 minutes, 49 seconds. The analogy of the motions of the top, however, to the moof the earth, as thus described, is incomplete in respect of position of their axes. The axis of the spinning top is in ral upright or perpendicular to the ground, which may be led the plane of its orbit, that is, of the oval ring in which it pposed to move; but the axis of the earth in its daily motion ot perpendicular to the plane of its orbit, or the ellipse in which annual motion is performed. In speaking of the plane of the h's orbit our analogy fails, for there is nothing to represent ground on which the motion of the spinning top takes place. mere attraction of the sun, coupled with the effect of an origiimpulse in the direction of a tangent to its orbit, is sufficient preserve the earth in its orbitual motion in empty space. Hence amblimity and truth of the ancient passage in the book of b: "He stretcheth out the north over the empty place, and

the circle at the point A; so that the earth, which under the action of the former force would in a certain time have been found at some point in A D, and under that of the latter force would, in the same time, have been found at the point F in a E, would, by the combined action of both forces, be found near the point c in the curvilinear orbit a C B. This original impulse, the effect of which remains to this day unaltered by the action of attraction (seeing it has met with no resistance in empty space, and has been so balanced against the force of attraction as to retain the earth in its orbit), is called the tangential impulse or force, which was imparted to it when it began its orbitual revolution. Young, in his "Night Thoughts," alluding to this tenet of the Newtonian philosophy, asks

"Who rounded in his palm those spacious orbs ?
Who bowled them flaming through the dark profound ?"

Night IX.

Let us now consider the effect of the inclination of the earth's axis to the plane of its orbit. In Fig. 1 we have supposed the sun to be at the focus F', while the earth is at the point a in mid-winter. Now, at this point, you would see from your sup. posed elevated position, that the northern half of the earth's axis is inclined to the major axis A B at an angle of 113 degrees 28 minutes, the supplement of its angle of inclination to the plane of the orbit; so that the North Pole, with the space on the earth's surface around it to a considerable extent, is prevented from receiving the rays of the sun, and consequently the heat of those rays; while the South Pole, with the space around it to the same extent, is made to receive these rays and to enjoy their heat. Hence, while it is winter in the northern or arctic regions of the earth, it is summer in the southern or antarctic regions. While the earth is still in this position, the rays of the sun fall more obliquely upon the illuminated portions of the northern hemisphere than they do upon the southern hemisphere, and thus have less power to produce heat than if they fell perpendicularly; just as a person sitting at the side of a fire-place with a good fire in it, feels less heat than a person who sits exactly in the front of it.

On the other hand, if you consider the earth from your elevated position, when it is at the point B in mid-summer, the reverse of all this takes place. The northern half of the earth's axis is inclined to the major axis (or line of apsides, as it is sometimes called; that is, the line of junction of the two opposite points A and B) at an angle of 66 degrees 32 minutes, which is its angle of inclination to the plane of its orbit; so that the North Pole, with the space on the earth's surface around it, above-mentioned, is made to receive the sun's rays, and consequently their heat; while the South Pole, with the similar space around it, is prevented from receiving those rays and enjoying their heat. Hence, while it is summer in the northern or arctic regions, it is winter in the southern or antarctic regions. While the earth remains in this position, the rays of the sun fall more directly upon the northern hemisphere than they do upon the

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,
Winter and summer in alternate round;
And night and day in close succession rise,
While each is regulated by the skies.
Supreme o'er all, at first, Jehovah stood,
And, with creative voice, pronounced it good."

LESSONS IN ARITHMETIC.—XXIV. 1. FROM the tables given in Lessons XXI., XXII., XXIII. (Vəl 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 38. 6d. could be indicated as here written, or by 522 pence, or again, by 43 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. 7 d. to farthings.

Since there are 20 shillings in a pound, in 5 pounds there are 5 × 20, or 100 shillings; and therefore, in £5 2s., 100 + 2, æ 102 shillings. Since there are 12 pence in a shilling, in 10 shillings there are 102 x 12, or 1224 pence; and therefore, £5 28. 7d., 1224 +7, or 1231 pence. Since there are farthings in a penny, in 1231 pence there are 1231 × 4 4924 farthings; and therefore, in £5 2s. 72d. there are + 3, or 4927 farthings.

The process may be thus arranged :— £5 2s. 73d.

20

100+ 2 = 102s.

12

12247 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. 12 divided by 12 gives a quotient 102, and a remainder 7; hena 1231 pence are 102 shillings and 7 pence. 102 divided by 2 gives a quotient of 5, and a remainder 2; hence 102 shilling are 5 pounds and 2 shillings. Therefore 4927 farthings 1231 pence, which is 102s. 73d., which is £5 2s. 7 d. 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 a other kind.

Hence we get the following

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

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

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

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

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

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,
Winter and summer in alternate round;
And night and day in close succession rise,
While each is regulated by the skies.
Supreme o'er all, at first, Jehovah stood,
And, with creative voice, pronounced it good."

LESSONS IN ARITHMETIC.-XXIV. 1. FROM the tables given in Lessons XXI., XXII., XXIII. (Vol I., pp. 366, 379, 304), 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 43 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. 7d. 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 2s., 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 4924 farthings; and therefore, in £5 2s. 73d. there are 4924 + 3, or 4927 farthings.

The process may be thus arranged :— £5 28. 74d.

20

100 + 2 = 102s.

12

1224+7= 1231d.

4924 +34927 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 102s. 73d., which is £5 2s. 7 d. The operation may be thus arranged :

4) 4927

12) 1231... 3f.

20) 102...7d. £5 28. 73d.

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 quantities 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 per formed 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.

7. 415739 farthings to pounds, and to yards. shillings, etc.

8. 67256 farthings toguineas, etc. 9. £36 4s. to sixpences and to groats.

10. £75 12s. 6d. to threepences. 11. 29 lbs. 7 oz. 3 dwts. to grains. 12. 37 lbs. 6 oz. to pennyweights. 13. 175 lbs. 4 oz. 5 dwts. 7 grs. to grains.

14. 12256 grs. to pennyweights, ounces, etc.

15. 42672 dwts, to ounces and pounds.

16. 15 cwt, 3 qrs. 21 lbs.to pounds. 17. 17 tons 12 cwt. 2 qrs. to ounces.

18. 52 tons 3 cwt. 1 qr. 25 lbs. to pounds.

55, 5023480 seconds to days, etc. 56. A solar year to seconds. 57. 30 Julian years to seconds. 58. The time from 9 o'clock a.m. Jan. 2, to 11 p.m. March 1, 1868, to seconds.

59. 110 days 20 minutes to seconds.

60. 27 degrees to seconds. 61. 7654314 seconds to degrees, etc.

62. 1,000,000,000 minutes to right angles, degrees, etc.

63. 1728 sq. rods 23 sq. yds. 5 sq. ft. to square feet.

64. 100 acres 37 sq. rods to square feet and to square inches.

65. 832590 sq. rods to square inches.

66. 25363896 sq. feet to acres, etc.

67. 150 cubic feet to cubic inches. 68. 97 cubic yards 15 cubic feet to cubic inches.

69. 49 cubic yds. 23 cubic ft. to cubic inches.

70, 84673 cubic inches to cubic feet.

71. 39216 cubic feet to cubic yards.

72. 65 loads of rough timber to cubic inches.

83. How many acres in a field 50 rods long by 45 wide?

84. How many sq. yds. in a ceiling 35 feet long by 28 wide?

85. How many acres in a field 420 rods long and 170 wide? 86. Find the area of a field 80 rods square.

87. How many yards of carpeting, yard wide, will cover a room 18 feet square?

88. How many yards of painting will cover the four walls of a room 18 feet long, 15 feet wide, and 9 feet high ?

89. Find the area of a pitched roof whose rafters are 20 feet and ridge-pole 25 feet long.

90. How many cubic feet in a box 5 feet long, 4 wide, and 3 deep?

91. How many cubic inches in a block 65 inches long, 42 wide, and 36 thick ?

92. In 10752 cubic feet how many imperial bushels ?

93. In 1155 cubic feet 33 inches how many imperial gallons?

94. How many bushels in a bin 5 feet long, 5 wide, and 4 deep? 95. How many cubic feet in a 100 bushel bin?

73. 4532100 cubic inches to tons ing of hewn timber.

74. 700 lbs. of silver to pounds,

etc., avoirdupois.

96. How many yards of carpetyard wide will cover a room

25 feet long and 18 feet wide ?

97. How many cubic inches in a mass of earth 40 yards long, 5

75. 840 lbs. 6 oz. 10 dwts. to yards wide, and 3 yards deep? pounds, etc., avoirdupois.

76. 1000 lbs. Troy to pounds, etc., avoirdupois.

98. Reduce 93756 cubic yards to inches.

99. How many pieces of paper

77. 1500 lbs. Troy to pounds, 12 yards long, and 2 feet 3 inches etc., avoirdupois. wide, will it take to cover a room 78. 48 lbs, avoirdupois to pounds, 20 feet long, 16 feet wide, and 13 etc., Troy. feet high, allowing for 3 doorways, each measuring 8 feet by 3 feet 9 inches r

79. 100 lbs. 10 oz. avoirdupois to pounds, etc., Troy.

80. 5656 carats to pounds, etc., avoirdupois.

81. How many sq. yds. in a room 4 yards long and 3 wide?

82. How many sq. ft. in a floor

to inches.

40. 12256 pints to barrels of gallons.

....

30

41. 475262 quarterns to gallons. 42. 50 tuns of 250 gallons each to pints.

43. 45 pipes of 120 gallons each

19. 140 tons 17 cwt. 3 qrs. 27 lbs. to pints. to drams.

20. 16256 oz. to hundredweights,

etc.

44. 25264 pints to barrels of 30 gallons each.

45. 136256 quarts to hogsheads

of 63 gallons each.

46. 45 hogsheads 10 gallons to pints. 47. 15 bushels 1 peck to quarts. 48. 763 bushels 3 pecks to quarts." 49. 56 quarters 5 bushels to pints. 50. 45672 quarts to bushels, etc. 51. 260200 pints to quarts, pecks, etc.

52. 25 days 6 hours to minutes,

and also to seconds.

53. 365 days 6 hours to seconds. 54. 847125 minutes to weeks, etc., and to days, etc.

100. The moon is about 240,000 miles from the earth: if it were possible to go there in a balloon, how many days would it take to accomplish the journey, moving at the rate of 123 miles per hour?

LESSONS IN DRAWING.-XIV. WINTER, as we have said before, is the best time for studying the ramifications of trees; close observation at that period of the year is very necessary, and much profitable information may bė gained. A country walk, if only to the extent of a mile, will afford abundant material for observation; the mind may then be exercised in comparing one tree with another, for by comparison only will their characteristic differences be made apparent, and facts will be revealed which the mind can store up for future use. To employ the pencil only in noting down the forms and growth of trees would be of little service, unless the mind is doing more than the pencil can perform. There are innumerable peculiarities and points of difference which distinguish trees, and enable us to recognise them independently of their foliage, and close observation will make that easy which at first sight might seem to be difficult; for although we advise the pupil to make good use of his pencil whenever he is engaged in studying trees divested of their leaves, yet we must at the same time remind him that it will be more to his advantage to reflect without drawing than to draw without reflecting.

From the observations we have made, it will be understood that we fully intend the pupil should take Nature for his guide, yet we can assist him in this part of his study by introducing some examples, which he must copy as well as compare. Copying will not only be a practical benefit, but also a means for establishing in his own mind the facts and principles we have endea voured to make clear to him. Let him compare the outline of the oak (Fig. 98) in the last lesson with the lime (Fig. 100). His attention must also be given to the bark, which in some trees