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100 + 2 = 102s.

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southern hemisphere, and thus have more power to produce heat LESSONS IN ARITHMETIC.-XXIV. than if they fell obliquely, according to the illustration given above. Now, as we in this country are inhabitants of the 1. From the tables given in Lessons XXI., XXII., XXIII. (VoL northern hemisphere, and of that part which is within the circle I., pp. 366, 379, 394), it is evident that any compound quantity of illumination all the year round, we experience the vicissitudes could be expressed in a variety of ways, according as we use of the seasons just described as belonging to it, and we are con- one or other of the various units, or denominations, as they sequently colder in winter than in summer, although the earth are called, which are employed. Thus the compound quantity be actually noarer the sun in winter than in summer.

£2 3s. 6d. could be indicated as here written, or by 522 pence, But we must explain more fully what we mean by the circle or again, by 431 shillings, etc. The process of expressing * of illumination. It is plain that the rays of light falling from compound quantity given in any one denomination in another, the sun upon the opaque or dark body of the earth in straight is called reducing the quantity to a given denomination. The lines, can never illuminate more than one-half of its surface at a process is termed time; as may be seen by the very simple experiment of making

REDUCTION. 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

2. EXAMPLE 1.-Reduce £5 2s. 77d. to farthings. evident that the illuminated half, and consequently the circle of Since there are 20 shillings in a pound, in 5 pounds there are illumination which is the boundary of that half, is perpetually 5 X 20, or 100 shillings; and therefore, in £5*28., 100 + 2, changing, so that almost all parts of the globe receive light for 102 shillings. Since there are 12 ponce in a shilling, in 10 several hours in succession, and that they are also enveloped in shillings there are 102 X 12, or 1224 pence; and therefore, in darkness for several hours in the same manner. If the axis of £5 28.7d., 1224 + 7, or 1231 pence. Since there ani the earth, instead of being inclined at a certain angle to the farthings in a penny, in 1231 pence there are 1231 x 47 plane of its orbit, which we shall hereafter call the Ecliptic, 4924 farthings; and therefore, in £5 28. 77d. there are 8% were at right angles to that plane, and preserved its parallelism, + 3, or 4927 farthings. then the circle of illumination would continually extend from The process may be thus arranged :polo to pole, and all places on the earth's surface would enjoy

£5 28.730. 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 plano, and preserved its parallelism, this would happen

12 only twice a year; and each hemisphere would at opposite periods be in total darkness for a whole day, while the

1224 + 7 = 1231d. variations between these extremes would be both inconvenient and injurious. In the former case the seasons would be all the

4924 + 3 = 4927 farthings. same, that is, there would be perpetual sameness of season all the year round; in the latter case, the seasons, instead of being EXAMPLE 2.-In 4927 farthings how many pounds, shilling four only, would be innumerable, that is, there would be per- pence, and farthings are there ? petual change.

4927 divided by 4 gives a quotient 1231, and a remainders Here, then, creative wisdom shines unexpectedly forth. The hence 4927 farthings are 1231 pence and 3 farthings. 19 inclination of the earth’s axis is such as to produce the four divided by 12 gives a quotient 102, and a remainder 7; bend seasons in a remarkable manner, and to permit sufficient time 1231 penco are 102 shillings and 7 pence. 102 divided by for the earth to bring her fruits to perfection, as well to let her gives a quotient of 5, and a remainder 2; hence 102 shilling lie fallow for a period that she may renew her fruitfulness. are 5 pounds and 2 shillings. Therefore 4927 farthings

In Fig. 1, when the earth is supposed to be at the point c, she 12314 pence, which is 1025. 77d., which is £5 2s. 74d. is at her mean distance from the sun at the vernal equinox, which The operation may be thus arranged :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

4) 4927 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,

12) 1231...34. nearly coincides with the centre o, the rays of light proceeding

20 ) 102 ...7d. from the sun nearly in the straight line o c, fall upon that axis nearly perpendicularly, and illuminate the globe from pole to

£5 28. 70. pole, so that the circle of illumination passes through the poles, and the days and nights are equal all over the globe, each con- In dividing by 20, note the remark (Lesson VII., Art. 7). sisting of 12 hours, while the earth is in this position. In the The same method would apply to compound quantities of opposito position at d, the earth is again at her mean distance other kind. from the sun at the autumnal equinox, which is the second time Hence we get the following of the year when day and night are equal, which happens on or Rule for the Reduction of Compound Quantities. about the 22nd of September. At this point the circumstances (1.) To reduce quantities in given denominations to equirai of the globe and the circle of illumination are exactly the same quantities of lower denominations. As we have just described. At these four points, A, C, B, and D, Multiply the quantity of the highest denomination by in the orbit of the earth, are found the middle points of the four number which it takes of the next lower denomination to seasons of the year, viz., at a, mid-winter; at c, mid-spring; at one of the higher; and to the product add the number of B mid-summer ; and at D, mid-autumn. At the point

A, or mid- tities of that lower denomination, if there are any. Proceed winter, which is on or about the 21st of December, we have the like manner with the quantity thus obtained, and those of shortest day in the northern hemisphere and the longest day in successive denomination, antil the required denomination the southern hemisphere; and at the point B, or mid-summer, arrived at. which is on or about the 22nd of June, we have the longest day (2.) To reduce quantities of given denominations to come in the northern hemisphere and the shortest in the southern lent quantities of higher denominations. hemisphere.

Divide the number of quantities of the given denomination “Thus is primeval prophecy fulfilled :

that number which it takes of quantities of this denomises While earth continues, and the ground is tilled ;

to make one of the next higher. Proceed in the same mua Spring time shall come, when seeds put in the soil

with this and each successivo denomination, until the requis Shall yield in harvest full reward for toil ;

denomination is arrived at. The last quotient, with the ser Heat follow cold, and fructify the ground, Winter and summer in alternate round;

remainders, will be the answer required. And night and day in close succession rise,

Obs. It is manifest that the correctness of an operation While ench is regulated by the skies.

formed in accordance with either of the foregoing rules suas Supreme o'er all, at first, Jehovah stood,

tested by reversing the operation—that is, by reducing And, with creative voice, pronounced it good.”

result to the original denomination.

E

planes passing through the centre of the sun; the sun itself hangeth the earth upon nothing” (Job xxvi. 7). This passage being placed in one of the foci the ellipse.

is singularly true in regard to the first sentence as well as to the 2. That the radius vector, or straight line drawn from the second, for the axis of the earth is inclined to the plane of its centre of the sun to the centre of the planet, passes over equal orbit, at an angle of 66 degrees 32 minutes, that is, rather areas in equal times in every part of the orbit; that is, whether more than two-thirds of a right angle; so that literally and truly the planet be in its aphelion, or farthest from the sun, in its "the north is stretched over the empty place," and not over the perihelion, or nearest to the sun, or at its mean distance from body of the earth itself, in either of its motions, whether axial the sun.

or orbitual. This inclination is preserved during the whole of its 3. That the squares of the periodic times of the planets—that motion in its orbit, and is the cause of the variation of the is, of the times of a complete revolution in their orbits--are pro- seasons ; the preservation of the inclination of this axis has been portional to the cubes of their mean distances from the sun ; in not inaptly called the parallelism of the earth’s axis. other words, that the square of the periodic time of one planet is Before explaining the effect of this parallelism and inclination to the square of the periodic time of another planet, as the cube of the earth's axis in producing the seasons, it will be proper to of the mean distance of the former from the sun is to the cube of explain what is meant by tangential impulse. In Fig. 2, let AC B the mean distance of the latter from it.

represent the orbit of the earth, which is nearly Into the full explanation of these laws we cannot enter until circular ; let D represent the place of the sun,

F Fre treat of astronomy; in the meantime it is necessary to give and a the place of the earth at the moment some explanation of the law which we have marked first, though when it began its revolution in its orbit. At Bí it is generally accounted the second, in order to clear up some this moment the force of the sun's attraction points connected with phenomena relating to the earth, and the would begin to act on the earth in the direction circles drawn on the globe, which is the only true representation A D, and had this alone been allowed to ope

Fig. 2. of the earth's surface. Supposing, then, the ellipse in Fig. 1 to rate, would have drawn it rapidly towards the represent the earth's annual orbit round the sun, and the focus sun in a straight line, until it had come finally in contact with 7 the place of the sun's centre; then the point A will represent the sun itself; but at the same moment an original impulso the position of the earth's centre at mid-winter, when it is was, or is supposed to have been given to the earth in the direcnearest the sun, or in its perihelion ; B will represent its posi- tion A E, which is that of a tangent, or straight line touching tion at mid-summer when it is farthest from the sun, or in its the circle at the point A; so that the earth, which under the sphelion; c will represent its position at the spring or vernal action of the former force would in a certain time have been equinox, when it is at its mean distance from the sun; and d its found at some point in A D, and under that of the latter forco position at the harvest or autumnal equinox, when it is also at would, in the same time, have been found at the point F in A E, its mean distance from the sun.

would, by the combined action of both forces, be found near the We think we hear some of our readers exclaiming, notwith- point c in the curvilinear orbit A C B. This original impulse, standing the elevated position in which we have supposed them the effect of which remains to this day unaltered by the action of to be placed, “What? Will you tell us that the sun is the cause attraction (seeing it has met with no resistance in empty space, of light and heat on the earth's surface, and yet you assert that and has been so balanced against the force of attraction as to the enrth is nearer to the sun in winter than in summer? How retain the earth in its orbit), is called the tangential impulse or can this be ?" Paradoxical as this may seem, it is nevertheless force, which was imparted to it when it began its orbitual revo. true; and the reason we shall now give. As you are supposed lution. Young, in his “Night Thoughts," alluding to this tenet to be looking from a great distance, and to be able to discern of the Newtonian philosophy, asks all the motions of the planets, if you look narrowly at the earth, “ Who rounded in his palm those spacious orbs ? you will perceive that besides its orbitual or annual motion round Who bowled them flaming through the dark profound ?" the sun, it has a revolving or diurnal motion on its own axis.

Night IX. By aris here is meant that imaginary straight line passing Let us now consider the effect of the inclination of the earth's through the globe of the earth, on which its rotation is supposed axis to the plane of its orbit. In Fig. 1 we have supposed the to take place, and which is aptly represented in artificial globes sun to be at the focus F', while the earth is at the point A in by the strong wire passing from one side to the other, at the mid-winter. Now, at this point, you would see from your suppoints called the poles (that is, pivots), which are the extremities posed elevated position, that the northern half of the earth's of the axis.

axis is inclined to the major axis A B at an angle of 113 degrees This revolving motion on its own axis may be likened to the 28 minutes, the supplement of its angle of inclination to the spinning of a top, a motion which continues while the top is plane of the orbit; so that the North Pole, with the space on driven forward in any direction from one place to another. In the earth's surface around it to a considerable extent, is prefact, the analogy would be so far complete independently of the vented from receiving the rays of the sun, and consequently the causes of the motion, if the top, while it is spinning or revolving heat of those rays; while the South Pole, with the space aronnd as it were on its own axis, were made to run regularly round in it to the same extent, is made to receive these rays and to enjoy an oval ring on the ground, under the lash of the whip. Thus, their heat. Hence, while it is winter in the northern or arctic the earth has two motions ; one on its own axis, performed once regions of the earth, it is summer in the southern or antarctic every twenty-four hours; and one in its orbit, performed once regions. While the earth is still in this position, the rays of every 365 days 6 hours. We have stated these periods in round the sun fall more obliquely upon the illuminated portions of the numbers, in order that they may be easily remembered; but northern hemisphere than they do upon the southern hemisphere, the exact period of the earth's daily revolution on its axis is and thus have less power to produce heat than if they fell per23 hours, 56 minutos, 4 seconds, and 9 hundredth parts of a pendicularly; just as a person sitting at the side of a fire-place recond; and the exact period of the earth's annual revolution in with a good fire in it, feels less heat than a person who sits its orbit is 365 days, 5 hours, 48 minutes, 49 seconds.

exactly in the front of it. The analogy of the motions of the top, however, to the mo- On the other hand, if you consider the earth from your tions of the earth, as thus described, is incomplete in respect of elevated position, when it is at the point B in mid-summer, the the position of their axes. The axis of the spinning top is in reverse of all this takes place. The northern half of the earth's general upright or perpendicular to the ground, which may be axis is inclined to the major axis (or line of apsides, as it is called the plane of its orbit, that is, of the oval ring in which it sometimes called ; that is, the line of junction of the two oppois supposed to move; but the axis of the earth in its daily motion site points A and B) at an angle of 66 degrees 32 minutes, which is not perpendicular to the plane of its orbit, or the ellipse in which is its angle of inclination to the plane of its orbit; so that the its annnal motion is performed. In speaking of the plane of the North Pole, with the space on the earth's surface around it, carth's orbit our analogy fails, for there is nothing to represent above-mentioned, is made to receive the sun's rays, and consethe ground on which the motion of the spinning top takes place. quently their heat; while the South Pole, with the similar space The mere attraction of the sun, conpled with the effect of an origi. around it, is prevented from receiving those rays and enjoying nal impnlse in the direction of a tangent to its orbit, is sufficient their heat. Hence, while it is summer in the northern or arctic to preserve the earth in its orbitual motion in empty space. Hence regions, it is winter in the southern or antarctic regions. While the sublimity and trath of the ancient passage in the book of the earth remains in this position, the rays of the sun fall more Job: " He stretcheth out the north over the empty place, and directly upon the northern hemisphere than they do apon the

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southern hemisphere, and thus have more power to produce heat LESSONS IN ARITHMETIC.-XXIV. than if they fell obliquely, according to the illustration given above. Now, as we in this country are inhabitants of the 1. From the tables given in Lessons XXI., XXII., XXIII. (VoL northern hemisphere, and of that part which is within the circle I., pp. 366, 379, 394), it is evident that any compound quantity of illumination all the year round, we experience the vicissitudes could be expressed in a variety of ways, according as we use of the seasons just described as belonging to it, and we are con- one or other of the various units, or denominations, as they sequently colder in winter than in summer, although the earth are called, which are employed. Thus the compound quantity be actually nearer the sun in winter than in summer.

£2 3s. 6d. could be indicated as here written, or by 522 pence, But we must explain more fully what we mean by the circle or again, by 431 shillings, etc. The process of expressing a of iUumination. It is plain that the rays of light falling from compound quantity given in any one denomination in another, the gun upon the opaque or dark body of the earth in straight is called reducing the quantity to a given denomination. The lines, can nover illuminate more than one-half of its surface at a process is termed time; as may be seen by the very simple experiment of making

REDUCTION. 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

2. EXAMPLE 1.-Reduce £5 23. 77d. to farthings. evident that the illuminated half, and consequently the circle of Since there are 20 shillings in a pound, in 5 pounds there are illumination which is the boundary of that half, is perpetually 5 X 20, or 100 shillings; and therefore, in £5 2s., 100 + 2, or changing, so that almost all parts of the globe receive light for 102 shillings. Since there are 12 ponce in a shilling, in 102 several hours in succession, and that they are also enveloped in shillings there are 102 X 12, or 1224 pence; and therefore, in darkness for several hours in the same manner. If the axis of £5 28.7d., 1224 + 7, or 1231 pence. Since there are 4 the earth, instead of being inclined at a certain angle to the farthings in a penny, in 1231 pence there are 1231 x 4, or plane of its orbit, which we shall hereafter call the Ecliptic, 4924 farthings; and therefore, in £5 28. 77d. there are 4924 were at right angles to that plane, and preserved its parallelism, + 3, or 4927 farthings. then the circle of illumination would continually extend from The process may be thus arranged :polo to pole, and all places on the earth's surface would enjoy

£5 28.74d. light for 12 hours in succession, and would be enveloped in

20 darkness for exactly the same period the whole year round. On the other hand, if the axis of the earth were coincident

100 + 2 = 1028. 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

1224 + 7 = 1231d. variations between these extremes would be both inconvenient and injurious. In the former case the seasons would be all the

4924 + 3 = 4927 farthings. same, that is, there would be perpetual sameness of season all the year round; in the latter case, the seasons, instead of being EXAMPLE 2.-In 4927 farthings how many pounds, shillings, four only, would be innumerable, that is, there would be per- pence, and farthings are there ? petual change.

4927 divided by 4 gives a quotient 1231, and a remainder 3; Hero, thon, creative wisdom shines unexpectedly forth. The hence 4927 farthings are 1231 pence and 3 farthings. 1231 inclination of the earth's axis is such as to produce the four divided by 12 gives a quotient 102, and a remainder 7; hence seasons in a remarkable manner, and to permit sufficient time 1231 pence are 102 shillings and 7 pence. 102 divided by 20 for the earth to bring her fruits to perfection, as well to let her gives a quotient of 5, and a remainder 2; hence 102 shillings lie fallow for a period that she may renew her fruitfulness. are 5 pounds and 2 shillings. Therefore 4927 farthings are

In Fig. 1, when the earth is supposed to be at the point c, she 1231pence, which is 102s. 77d., which is £5 28. 7 d. is at her mean distance from the sun at the vernal equinox, which The operation may be thus arranged :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

4) 4927 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,

12) 1231 ... 38. nearly coincides with the centre o, the rays of light proceeding

20 ) 102...722 from the sun nearly in the straight line o c, fall upon that axis nearly perpendicularly, and illuminate the globe from pole to

£5 28. 7d. pole, so that the circle of illumination passes through the poles, and the days and nights are equal all over the globe, each con- In dividing by 20, note the remark (Lesson VII., Art. 7). sisting of 12 hours, while the earth is in this position. In the The same method would apply to compound quantities of any opposite position at D, the earth is again at her mean distance other kind. from the sun at the autumnal equinos, which is the second time Hence we get the following of the year when day and night are equal, which happens on or Rule for the Reduction of Compound Quantities. about the 22nd of September. At this point the circumstances (1.) To reduce quantities in given denominations to equivalent of the globe and the circle of illumination are exactly the same quantities of lower denominations. as we have just described. At these four points, A, C, B, and D, Multiply the quantity of the highest denomination by that in the orbit of the earth, are found the middle points of the four number which it takes of the next lower denomination to make Seasons of the year, viz., at A, mid-winter; at c, mid-spring; at one of the higher; and to the product add the number of quan B, mid-summor ; and at D, mid-autumn. At the point A, or mid- tities of that lower denomination, if there are any. Proceed in winter, which is on or about the 21st of December, we have the like manner with the quantity thus obtained, and those of each shortest day in the northern hemisphere and the longest day in successive denomination, until the required denomination is the southern hemisphere; and at the point B, or mid-summer, arrived at. which is on or about the 22nd of June, we have the longest day (2.) To reduce quantities of given denominations to equiva: in the northern hemisphere and the shortest in the southern lent quantities of higher denominations. hemisphere.

Divide the number of quantities of the given denomination by “ Thus is primeval prophecy fulfilled :

that number which it takes of quantities of this denomination While earth continues, and the ground is tilled ;

to make one of the next higher. Proceed in the same manner Spring time shall come, when seeds put in the soil

with this and each successive denomination, until the required Shall yield in harvest full reward for toil ;

denomination is arrived at. The last quotient, with the several Heat follow cold, and fructify the ground, Winter and summer in alternate round;

remainders, will be the answer required. And night and day in close succession rise,

Obs.It is manifest that the correctness of an operation perWhile ench is regulated by the skies.

formed in accordance with either of the foregoing rules may be Supreme o'er all, at first, Jehovah stood,

tested by reversing the operation that is, by reducing the And, with creative voice, pronounced it good."

result to the original denomination.

4

196

EXAMPLE 3.-Reduce 52 tons 3 cwt. 1 qr. 25 lbs. to pounds. 55. 5623180 seconds to days, eto, 83. How many acres in a feld

56. A solar year to seconds. 50 rods long by 45 wide ? 52 tons

57. 30 Julian years to seconds. 84. How many sq.yds. in a ceil20

58. The time from 9 o'clock ing 35 feet long by 28 wide ?

a,m. Jan. 2, to 11 p.m. March 1, 85. How many acres in a field 1040 + 3 = 1013 cwt.

1868, to seconds.

420 rods long and 170 wide? 59. 110 days 20 minutes to se- 86. Find the area of a field 80 conds.

rods square. 4172 + 1 = 4173 qrs.

60. 27} degrees to seconds.

87. How many yards of carpet28

61. 7654314 seconds to degrees, ing, yard wide, will cover a room eto.

18 feet square ? 33384

62. 1,000,000,000 minutes to right 88. How many yards of painting 8346

angles, degrees, etc.

will cover the four walls of a room

63. 1728 sq. rods 23 sq. yds, 5 18 feet long, 15 feet wide, and 9 116844 + 25 = 116869 pounds.

sq. ft. to square feet.

feet bigh ? Proof of Correctness.

64. 100 acres 37 sq. rods to 89. Find the area of a pitched 28 ) 116869 ( 4173 qrs.

square feet and to square inches. roof whose rafters are 20 feet and 112

65. 832590 sq. rods to square ridge-pole 25 feet long. inches.

90. How many cubic feet in a

66. 25363896 sq. feet to acres, box 5 feet long, 4 wide, and 3 deep? 48

etc.

91. How many cubic inches in a 28

67. 150 cubic feet to cubic inches. block 65 inches long, 42 wide, and 206

68. 97 cubic yards 15 cubic feet 36 thick ? to cubic inches.

92. In 10752 cubic feet how 69, 49 cubic yds. 23 cubic ft. to many imperial bushels ? cubic inches.

93. In 1155 cubic feet 33 inches 109

70. 84673 cubic inches to cubic how many imperial gallons ? 84

feet.

94. How many bushels in a bin 25 pounds.

71. 39216 cubic feet to cubic 5 feet long, 5 wide, and 4 deep ? yards.

95. How many cubic feet in a 4) 4173

72. 65 loads of rough timber to 100 bushel bin ? cubic inches.

96. How many yards of carpet20 ) 1043...1

73. 4532100 cubic inches to tons ing yard wide will cover a room qr.

of hewn timber.

25 feet long and 18 feet wide ?

74. 700 lbs. of silver to pounds, 52 tons 3 cwt. 1 qr. 25 lbs.

97. How many cubic inches in a etc., avoirdupois.

mass of earth 40 yards long, 5 Hence the process has been correctly performed.

75. 840 lbs. 6oz. 10 dwts. to | yards wide, and 3 yards deep? EXERCISE 42.

pounds, etc., avoirdupois.

98. Reduce 93756 cubic yards to

76. 1000 lbs. Troy to pounds, inches. 1. Work the following examples in Reduction, bringing each etc., avoirdupois.

99. How many pieces of paper quantity, whether simple or compound, to the denomination or

77. 1500 lbs. Troy to pounds, 12 yards long, and 2 feet 3 inches denominations required.

etc., avoirdupois.

wide, will it take to cover a room 1 £7 10s. 6d. to pence.

28. 45 leagues to feet and inches. 78. 48 lbs, avoirdupois to pounds, 20 feet long, 16 feet wide, and 13 2, £71 138. 6 d. to farthings. 29. 3,000 miles to perches and etc., Troy.

feet high, allowing for 3 doorways, 3. £90 78. 8d. to farthings. to yards.

79. 100 lbs. 10 oz. avoirdupois to each measuring 8 feet by 3 feet 9 4. £295 189. 3 d. to farthings. 30. 290375 feet to furlongs and pounds, etc., Troy.

inches 5. 98 guineas 178. 94d. to farth- miles.

80. 5656 carats to pounds, etc., 100. The moon is about 240,000 ings. 31. 1875343 inches to miles, and avoirdupois.

miles from the earth: if it were 6. 24651 farthings to pounds, also to leagues,

181. How many sq. yds. in a room possible to go there in a balloon, shillings, etc. 32. 15 m. 5 fur. 31 r, to rods 4 yards long and 3 wide ?

how many days would it take to 7. 415739 farthings to pounds, and to yards.

82. How many sq. ft. in a floor accomplish the journey, moving at shillings, etc.

33. 1081080 inches to yards, fur- | 20 feet long by 18 feet wide ? the rate of 127 miles per hour ? 8. 67256 farthings toguineas, etc. longs, and miles.

9. £36 4s. to sixpences and to 34. The earth's circumference Toats, (25,000 miles) to feet.

LESSONS IN DRAWING.–XIV. 10. £75 128. 6d. to threepences. 35. 160 yards to nails and quar. 11. 29 lbs. 7 oz. 3 dwts. to grains. ters.

WINTER, as we have said before, is the best time for studying 12. 37 Ibs. 6 oz. to pennyweights. 36. 1,000 English ells to quarters the ramifications of trees; close observation at that period of 13. 175 lbs. 4 oz, 5 dwts. 7 grs. and yards.

the year is very necessary, and much profitable information may to grains.

37. 102345 nails to yards, etc. be gained. A country walk, if only to the extent of a mile, will 14. 12256 grs. to pennyweights, 38. 223267 nails to French ells.

afford abundant material for observation; the mind may then be Onnces, etc.

39. 634 yds. 3 qrs, to nails and exercised in comparing one tree with another, for by comparison 15. 42672 dwts. to ounces and to inches. pounds.

40. 12256 pints to barrels of 30 | only will their characteristic differences be made apparent, and 16. 15 cwt. 3 qrs, 21 lbs.to pounds. gallons.

facts will be revealed which the mind can store up for future use. 17. 17 tons 12 cwt. 2 qrs, to 41. 475262 quarterns to gallons. To employ the pencil only in noting down the forms and growth ounces.

42. 50 tuns of 250 gallons each of trees would be of little service, unless the mind is doing more 18. 52 tons 3 cwt. 1 qr. 25 lbs. to pints.

than the pencil can perform. There are innumerable peculiarities to pounds.

43. 45 pipes of 120 gallons each and points of difference which distinguish trees, and enable us to 19. 140 tons 17 cwt. 3 qrs. 27 lbs. to pints.

recognise them independently of their foliage, and close observato drams.

44. 25264 pints to barrels of 30 tion will make that easy which at first sight might seem to be 20. 16256 oz. to hundredweights, gallons each.

difficult;

for although we advise the pupil to make good use of etc.

45, 136256 quarts to hogsheads his pencil whenever he is engaged in studying trees divested of 21. 267235 lbs, to stones, quar- of 63 gallons each. ters, hundredweights, etc.

46. 45 hogsheads 10 gallons to their leaves, yet we must at the same time remind him that it 22. 563728 drums to tons, pints.

will be more to his advantage to reflect without drawing than to pounds, etc.

47. 15 bushels 1 peck to quarts. draw without reflecting. 23. 95 lbs. (apothecaries' weight) 48. 763 bushels 3 pecks toquarts: From the observations we have made, it will be understood to drams.

49. 56 quarters5 bushels to pints. that we fully intend the pupil should take Nature for his guide, 24. 130 lbs. 7 oz. to scruples 50. 45672 quarts to bushels, etc. yet we can assist him in this part of his study by introducing and to grains.

51. 260200 pints to quarts, pecks, 25, 6237 drams (apothecaries'

some examples, which he must copy as well as compare. Copying etc.

will not only be a practical benefit, but also a means for estaFeight) to pounds, etc.

52. 25 days 6 hours to minutes, blishing in his own mind the facts and principles we have endea 26. 25463 scruples to ounces, and also to seconds. pounds, etc.

53. 365 days 6 hours to seconds. voured to make clear to him. Let him compare the outline of 27. 27 miles to yards, to feet, 54. 847125 minutes to weeks, the oak (Fig. 98) in the last lesson with the lime (Fig. 100). His and to inches. etc., and to days, etc.

attention must also be given to the bark, which in some trees

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the oak and willow, for example—is hard and rough, while in the in the light, will have their own especial forms in mass to beech and birch it is smooth. The straight parts of the branches characterise them, and it is those forms in masses which we of some trees are short, from their slow growth, while others that must copy. But lest our pupil should suppose from these increase more rapidly shoot forth their stems in one direction to remarks upon generalising foliage that we intend him to stop a greater extent. The smaller twigs and shoots of some, like here, and to represent nothing more than the breadth of light and the birch, are very slender, numerous, and drooping; the horse- shade, we must remind him of what has been said above respect chestnut has fewer shoots, but they are thicker, and growing the details in light; we must remember also that, however apwards. Much more might be added to our consideration of broadly and definitely the light may fall upon a tree, since it is this important subject, but we think enough has been said to not a flat surface like a wall, there will be hundreds of minor point out the way, trusting our pupils will perfectly comprehend shadows and semi-tones scattered all over the extent of light, and our intention by these remarks, and be prepared to accompany there is as much individuality amongst these as in the whole us in the consideration of foliage.

mass, and their characteristics in detail are not less striking and In our last lesson we mentioned that, in drawing foliage, the significant because they are small : in short, they are reduced mode of treatment must in a very great measure be influenced repetitions of the general masses of light, and must be treated by the light and shade. We propose now to proceed with this with the same feeling if we wish to make a faithful represen. interesting part

tation.

Here of our subject,

again is the and show what

point of differ. is meant by the

ence between a term massing

first-rate and an in the foliage.

inferior artist, There are some

mentioned who think that

& former les it is necessary to

namely, have for each

the ability he kind of treesome

possesses to re. distinct and es

present the mi. pecial touch,clas.

nor shades and sifying them as

semi-tones, both “the oak touch,"

in regard to their “the elm touch,"

number and ex. “the beech

pression, and his touch," and nu

capability for merous others,

doing this will regardless of the

determine his fact that as the

rank as an artist. casts its

Sir Joshua Rey light upon a tree

nolds mentions it brings out the

a landscape shape and indi.

painter who was vidual character

remarkable for of its branches

his patience in 80 definitely that

what he consieven at a con.

dered high siderable dis.

finish,"

and tance, when it

thought that the would be impos

greatest excel sible to recognise

lence to be at the leaves, we

tained consisted pronounce

in the represen. the tree to be an

tation of every oak, or elm, or

leaf on a tree. whatever else it

“ This picture," may be, simply

says Sir Joshta, from the manner

I never saw; in which, as an

but I am very artist would say,

sure that an ar. “the sun lights

tist who regards it up.” The Fig. 100.

only the general most important

character of the consideration in

species, the order drawing a tree is

of the branches, to devote much attention to the light, and the parts that are made and the masses of the foliage, will in a few minutes produce a out in light. There are two reasons why the lights are considered more true resemblance of trees than this painter in as many to have such special importance (this principle belongs not to months." We must dwell for a few moments upon the printrees only, but to every other object that claims the attention of ciples here inculcated, and explain by what means a painter the painter): the first is, because the details are more recognisable obtains the enviable power of making a faithful resemblance in the light than in the shade, and require particular care to with comparatively slight labour: it is because he adopts the represent them faithfully, for without the details in light there excellent practice of making separate studies of details, such as would be very little to show for our pains, as the shadows to a branches, trunks, stems, weeds, and foregrounds—in short, great extent absorb or obscure not only the colour but also the everything that may be deemed worthy of note. It is this form; the other reason is, that the eye naturally rests upon the method of copying parts of objects with close accuracy that lights and all the brighter parts first-afterwards, when we make gives him the power of representing them generally and yet a further and closer examination, we see the parts in shadow. I faithfully, with the natural effect which they bear to one another Nor must we enter into laborious and painful detail, as in the as a whole. An eminent English landscape painter, whose practice of mere leaf-painting. As we have said before, we do manner was as remarkable for its freedom of execution as it not look at leaves singly, but at foliage collectively; therefore was for the truthfulness of its results, once remarked to us those branches of a tree, let its kind be what it may, which are "The secret of my success is in having bestowed much time

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