Abbildungen der Seite


Quelqu'un a-t-il honte ? 31. Non, Monsieur, personne n'a honte. 32. | through the gramme, which is the weight of 1 cubic centi. Votre frère a-t-il raison ou tort? 33. Mon frère a raison, et le vôtre mètre of pure water, taken at the maximum density of water, a tort. 34. Votre soeur n'a ni son chapeau de satin, ni son chapeau de

a temperature of 4o Centigrade, and weighed at Paris. velours. 35. Le boulanger a-t-il la commode d'acajou ? 36. Il ne l'a pas, il a le sofa d'acajou. 37. Le ferblantier a-t-il mon assiette ? 38.

THERMOMETRY. Il n'a pas votre assiette, il a la mienne,

Heat is—"that which produces in us the sensation of warmth." EXERCISE 15 (Vol. I., page 59).

Temperature is—" that energy with which one body seeks to 1. Have you the carpenter's hammers ? 2. We have the black impart its heat to another." smith's hammers. 3. Have the blacksmiths two wooden hammers ? Thus the temperature of a body is no indication of the real 4. They have two iron hammers. 5. Have the generals the silk hats quantity of heat in the body. Equal weights of mercury and of the child ? 6. They have the child's jewels and playthings. 7. Have water may have the same temperature, and yet the water will the children the birds of your wood ? 8. They have not the birds of contain really thirty times more heat or caloric than the metal. my wood, but they have the horses of my general. 9. Has the black- Thermometers are measurers of " temperature,” not of heat. smith a pair of woollen stockings? 10. The blacksmith has two pairs High temperatures are measured by pyrometers; extremely low of woollen stockings. 11. Sir, are you not cold? 12. No, Sir, I am temperatures by alcohol thermometers; while mercurial therwarm. 13. Have you coffee or chocolate ? 14. I have neither coffee mometers are used for the intermediate ordinary temperatures. nor chocolate. 15. Have you not the cabbages of my large garden ? 16. I have the vegetables of your small garden.

These instruments depend for their action upon the

17. What is the matter with your son ? 18. My son has nothing. 19. Have you two fact that all bodies, with the rise and fall of their pieces of bread ? 20. The miller has a piece of bread and two barrels temperatures, expand and contract.

In pyrometers of flour. 21. Has the grocer coffee, tea, chocolate, and pepper? 22. He (Fig. 1), a small bar of platinum, s, which can only be has tea and coffee, and your merchant's chocolate and pepper. 23. Who melted by the intense heat of the flame of the oxy. has money? 24. I have no money, but I have paper. 25. Have you hydrogen blowpipe, is placed in a hole, b b, drilled good paper ? 26. I have bad paper.

in a piece of graphite, o, a form of carbon which is capable of supporting any heat. The bar projects

above the hole, and is bound to the graphitoa LESSONS IN CHEMISTRY.-III. - piece of which has been sliced away to expose the THE French weights and measures, which are on the decimal hole-by a platinum strap, a. The position of the system, are universally adopted in chemistry, on account of their top of the bar is carefully noted. It is now introsimplicity.

duced into the furnace whose temperature is required. MEASURES OF LENGTH.

The bar expands, and when it is removed, the strap English Inches.

prevents it from resuming its former position. Thus Millimètre

the expansion of the platinum is found, and from Centimètre


experiment we have learnt that for every 100° Cent. Decimètre

3.93707 METRE


platinum expands n'st of its length, and therefore we Fig. 1. Decamètre


can calculate the heat of the furnace. Hectomètre

3937 07900

Mercury is chiefly used for thermometers for five reasons :Kilometre


1. It is easily got pure, for mercury can be distilled like Myriomètre



2. It does not stick to the glass. MEASURES OF CAPACITY.

3. It has a long range, freezing at — 40° Cent., and boiling Millilitre


at 350o Cent. Centilitre


4. It expands uniformly—that is, it increases as much in bulk Decilitre 6.102705

if heated from 50° to 60°, as it LITRE (a cubic decimètre) 61.027051 - 1.76

will from 150° to 160°. Decalitre

610 270515 Hectolitre. 6102.705151

5. Having a low "capacity far Kilolitre 61027.051519

heat,” its temperature soon Myriolitre. 610270-515194

changes; it is, therefore, Fery

English Grains.




1. Take a glass tube with a chGRAMME 15.452

pillary bore (fine, " like a hair"), Decagramme 154.323

2S represerted at a in Fig. 2; Hectogramme 1543.234

make about half an inch of mer Kilogramme

15432 318 Myriogramme 154323.488

cury run down it, and measure it A kilogramme = 2.2046 lbs, avoirdupois.

at different points in its descent.

If it retain its length, the bore In verifying the following results by arithmetical calculation,

is uniform. the student will impress on his mind this system of weights and

2. Blow the bulb, B, not with measures :-

the mouth, lest moisture be intro1 inch 2-539954 centimètres.

duced, but by connecting the tube, 1 foot = 3·0479449 decimètres. 1 yard = 0.9143834 mètre.

by an india-rubber pipe, with a 1 mile 1'6093149 kilomètre.

bag of the same material, and 1 cubic inch 16.3861 cubic centimètres.

then pressing the bag while the 1 cubic foot 28.31531 cubic decimètres.

end of the tube is held in a gas 1 gallon 4.54345 litres.


as hereafter to be described 1 grain 0.06480 gramme.

3. Fasten a funnel of paper, 1 Troy oz. 31.103496 grammes.

to the top of the tube, and put 1 lb. avoir. 0:45359 kilogramme.

Fig. 2.

into it some purified mercury; 1 cwt. 50-80237 kilogrammes.

now heat the bulb, and the air The whole of the above system is founded on the “ mètre,” expanding will bubble through it.

Upon removing the lamp, which measuro distance along a meridian from the equator to the pole. But bulb. Repeating this process a few times, the bulb and tubo

was originally intended to be more of the the air will contract, and the mercury will be forced into the since the “ mètre” was thus fixed, an error

has been discovered will be filled. The lamp flame is again applied to the bulb, and in the measurement of the earth, and now a "standard" mètre while the mercury is oozing out, the tube is hermetically sealed, is kept in Paris.

by bringing a blowpipe flame to play upon its open end. The measures of weight are connected with those of length 4. Thermometers are graduated according to three scales.

In Cubic Inches.


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- 200

Fahrenheit's Scale, which is best known in England, divides the The reason of the following rules will be at once evident :space between the two fixed points—the freezing and boiling To transfer Fahrenheit degrees to the other scales, subtract points of water—into 180°. Fahrenheit fixed as his zero (0°) 32o, in order that the number of degrees from the freezing the temperature which had been observed at Dantzic in 1709, point may be ascertained. These multiplied by 8 will give the and which he found could always be reproduced by mixing salt equivalent number of Centigrade, and by the required Reaumur and snow together. He therefore, though erroneously, con- degrees. cluded that this was nature's zero—the absolute zero. He com- To reduce Centigrade and Reaumur degrees to the Fahrenheit puted that his instrument contained at 0°, 11,124 parts of scale, multiply by and respectively, and add 32o. mercury, and at the freezing point 11,156 parts; hence he If the temperature be below the zero in any of the scales, divided the space between zero and the freezing point of water a minus (-) is placed before the number, thus : — 5o Fahreninto 32 parts (11,156 – 11,124 = 32). From this point to heit means 37° below freezing. boiling point contained 180 of these degrees, therefore 212° In verifying the following, the student will become expert in indicates the boiling point of water.

these conversions :It was Fahrenheit who first used mercury for purposes of


Reau. thermometry,


68° The Centigrade Scale was introduced by the Swedish philo


56° sopher, Celsius, who was a professor at Upsal. In it the freezing


410.7 point is the zero, and the boiling


13° point 100°. This scale is the one

39° - 390.4 - 31.5. generally in use in the scientific world.

Reaumur's Scale was proposed by In a good thermometer, the mercury ought to run to the end a French philosopher of that name of the tube with a “click” when it is inverted, proving the in 1731. His thermometers were absence of air, and completely fill the tube; and when placed constructed with alcohol of such a in melting ice, the mercury ought to stand at 0°. It frequently strength, that 1,000 parts at the happens that the mercury stands above the freezing point. This freezing point of water became 1,080 error is called “the displacement of zero," and is caused by the at its boiling point. Hence the in- curious fact that sometimes the bulb does not perfectly contract terval between the two fixed points for two or three years after it was blown; so that for the best was divided into 80°.

instruments the bulbs are kept for more than that time unfilled. It is evident that these scales are If the bulb be made of thick glass, it is less likely to change. quite arbitrary, and that we have It is plain that in a thermometer we are not given the only two fixed points. It is neces- absolute expansion of the mercury, but the difference between sary, therefore, to determine these the expansion of the mercury and that of the glass. Mercury before the instrument can be gra- expands about seven times more than glass. duated. TO FIND THE FREEZING POINT OF


Fig. 3.

Water does not always freeze at

the same temperature. If water be It is easier to work than to ait. The Italians say, "Il mondo gradually reduced in temperature, and be kept perfectly still, 3 è, di chi ha pazienza,” or, the world is his who has patience ; or 4 degrees below 0° Cent. may be reached before the ice will and of all difficult exercises in the science of morals the applibegin to form ; but ice invariably melts at a fixed temperature. cation of this principle is perhaps the most so.

Not only may Therefore immerse the thermometer in melting ice, and mark the men overshoot their mark by too much eagerness, but they may point to which the mercury falls.

neglect that personal fitness by which they may best succeed.

It is self-evident that he who rows against a strong tide, TO FIX THE BOILING POINT.

exhausting thereby his strength and energy in the tussle with Place the thermometer in a vessel such as is represented in its forces, is not so wise as he who husbands his strength, and Fig. 3, in which water is boiling, and the steam generated patiently waits the turn of the tide. Patience, however, does passes round the walls, cc, of the

E. R c. not imply idleness, for in most matters of earthly duty we may partition to make its escape at b.

best employ our energies in preparation before we enter upon Thus the compartment p in which the

the strife. It is wiser far for the student to complete his instrument is placed, being enclosed


100° 80° long curriculum at college, than for him to rush into the disby steam, cannot be affected by the

charge of duties for which he is only half prepared ; and in temperature of the air.

the long run the measure of a man's preparation is the measure A is a bent tube of glass, open at

of his duration—that is to say, he has less exhaustible forces each end, in which is a little mercury.

than the man who has stocked his vessel with too small stores So long as the exit of the steam from

for a long life-voyage! How many lives have miscarried in their B is not impeded, the steam will be of

highest ends for want of patience! There are not many like a uniform temperature. If the steam

Columbus, ready to hold out to the last; nor, like Palissy, could not escape at B, it would be in

steadily bent, through long seasons of misfortune, on the attain. dicated by A, for if the pressure of the

ment of his end. As a rule, men like quick investments and

0° steam increase, the mercury will not

quick returns, both in mental and material things; but those are remain level. The point at which the

both wiser and nobler who with patient persistency are ready mercury in the thermometer stands, is

to wait for the issue which, though long delayed, may be well marked as the "boiling point.”.

worth having when it comes. Patience shonld characterise our The tube is then mounted on a piece

dealings with each other. Much petulance, irritability, and of board, upon which is marked the

Fig. 4. seale. If Fahrenheit's (Fig. 4 a), the

anger come from want of patience. Especially should we

remember, in our dealings with the ignorant, that it becomes us space between the two fixed points is divided into 180 equal to bear with the faults of native temperament and the mistakes parts, which are produced above and below 320 and 212° (which of untrained judgment. Hastiness irritates others and harms indicate the freezing and boiling points), as far as is required. ourselves, for no man can be said to be master of himself who For Centigrade (Fig. 4 b), the division is into 1000, the freezing permits a spirit of impatience to make him nervous and pettish. point being 0° ; for Reaumur (Fig. 4 c), into 80°. Fig. 4 com

Patience, however, suggests the value of prior preparation. pares at a glance these scales.

It may be true enough that the occasion will come for future TO CONVERT DEGREES OF ONE SCALE INTO ANOTHER. success, but then we must have fitted ourselves for the occaSince 180° Fahr. 100° Cent. 80° Reau,

sion, or it will be like a high tide rising to fill the creek, Therefore 1° Fahr. = 1° Cent. = 30 Reau.

and finding us without a vessel ready to launch. Of the many




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characters in history that are teaching us this folly of neglect, therefore add 1 penny, or 4 farthings, to the 1 forthing of the foremost there stands Echelred the Unready, who did not lack upper quantity, and 1 penny to the 9 pence of the lower opportunities for success, but was simply unprepared for them. quantity. Then 3 farthings subtracted frona 5

£ s. d. far. The Persians have a saying, “A stone that is fit for the farthings leave 2 farthings. Again, 10 pence 25 9 7 1 wall is not left in the way;" but then the stone must be fit, cannot be subtracted from 7 pence. We therefore 14 17 9 3 and those who are to find their place of honour in the fabric add 1 shilling, or 12 pence, to the 7 pence of the of society must not mind the toil and pains of being pre- upper quantity, ani i shilling to the 17 shillings 10 11 9 2 pared for their place, assured that they will not be left neglected of the lower quantity. Then 10 pence subtracted by the wayside. In all civilised states it is not that there are from 19 pence leave 9 pence. Again, 18 stillings cannot be too many ready for superior posts, but that there are few well subtracted from 9 shillings. We therefore and 1 pound, or 20 prepared when the morning of opportunity comes. The young shillings, to the 9 shillings of the upper quantity, and 1 pound student of German or French, as he ponders the lessons in the to the 14 pounds of the lower quantity. Then 18 shillings POPULAR EDUCATOR, may see no direct connection between subtracted from 29 shillings leave 11 shillings; and 15 pounds these studies and his future advancement; but it may so happen subtracted from 25 pounds leave 10 pounds. that an opening will occur in some future day in which even mer.

£ s. d. far,

We have, in fact, subtracted the less of the cantile partnership or commercial success may depend upon his

25 29 19 5

annexed two quantities from the greater, and they acquaintance with these or other Continental tongues. Patience, 15 18 10 are obtained by adding (as it will be found by then, does not imply idleness, but steady plodding in the path

examination we have done) £1 1s. 1d. to each of of preparation while waiting for the dawn of opportunity's day. 10 11 9 the quantities originally given. Differences of constitutional temperament will doubtless affect

Hence we get the following the exercise of this virtue, but all men may be schooled to its 6. Rule for Compound Subtraction. exercise in matters of common life. Some persons are impatient Write the less quantity under the greater, so that the same of contradiction-some impatient of precedence—some impatient denominations stand beneath each other. Beginning with the of attention, even in matters of dress or diet. Impatience is lowest denomination, subtract the number in each denomination selfishness in a hurry, and needs check and control in its very of the lower line from that above it, and set down the remainder earliest manifestations. “ Teach them to wait,” is counsel as below. When a number in the lower line is greater than that appropriate to the young as “ Teach them to work." No virtue of the same denomination in the upper, add one of the next has a stronger influence in its operation over other minds than highest denomination to the number in the upper line. Subtract that of patience ; we learn not only to respect but to imitate. as before, and carry one to the next denomination in the lower Steady and patient endurance in an hour of danger not only line, as in simple subtraction. honours us, but saves the lives of others; whereas hot and 7. ADDITIONAL EXAMPLE. heady conduct, in its foolish rashness, is ruinous often to the Subtract 75 gals. 3 qts. 1 pt. from 82 gals. 2 qts. interests of those with whom we may be associated.

gals. qts, pts.

Here, there being no pints in the upper Many of the scientific successes of later days have been

line to subtract the 1 pint of the lower line marvels of patience—not only the bridging of straits, which

from, we add 1 quart-i.e., 2 pints—to the more properly may be considered as belonging to perseverance,

upper line, and the same quantity to the quarts but the steady and slow induction of facts which have taken

1 Ang. of the lower line. Then 1 pint subtracted place previous to the adoption of any new principle of action.

from 2 pints leaves 1 pint. 4 quarts cannot Patience is always a characteristic of power. Strong minds be subtracted from 2 quarts. We therefore add 1 gallon—, can afford to wait. It is the sign of weakness to be subject to 4 quarts—to the 2 quarts of the upper line, and 1 gallon to the panic in the presence of some unexpected difficulties, or to be 75 gallons of the lower. Then 4 quarts sub

gals. qts. pts. determinately pushing on some enterprise, regardless of the tracted from 6 quarts leave 2 quarts; and 76 wisdom of the course pursued.

gallons subtracted from 82 gallons leave 6 The student of military campaigns will see that success has gallons. The operation we have really peroftener resulted from patient endurance than from brilliant formed is the subtraction of the less of the charges; and that the statesmen who have carried the most subjoined quantities from the greater, and they decisive measures have been men also who did not try to hurry are obtained from the original two quantities by the addition their party into action, but calmly adopted the appropriate of 1 gal. 1 qt. to each. method, and waited the appropriate time. Patience is of

EXERCISE 44. essential importance to all the other virtues of character. Indeed, it is so necessary to their health and culture, that

Find the difference of without it they shoot up into hasty and weedy growth. Those

1. £48 179. 6 d. and £37 14s. 94. characters blossom best that have had time to let the roots of

2. £1,000 and (£500 6s. 7.d. + £495 78. 6d.) principle strike deep down into the soil.

3. 16 cwt. 3 qrs. 15 lbs. and 8 cwt. 2 qrs, 8 lbs, 6 oz.

4. 85 tons 16 cwt. 39 lbs. and 61 tons 14 cwt. 68 lbs. Apart, however, altogether from issues of success, patient

5. 69 m. 41 r. 12 ft. and 89 m. 10 r. 14 ft. endurance is noble and beautiful ; and as life is a state in which 6. 17 leagues 2 m. 3 fur. 4 r. 4 ft. and 19 leagues 1 m. 2 fur. 15 r. we must all look for checks and hindrances to our most che- 7. 85 bush. 2 pks. 4 qts, and 49 bush. 3 pks. 6 qts. rished purposes, we shall be ill prepared to act well our part in 8. 115 qrs. 3 bush. 1 pk. and 95 grs. 4 bush. 3 pks. the common arena of life unless we cultivate a patient spirit. In 9. 85 yds. 1 qr. 2 nls, and 29 yds. 2 qrs. 3 nls. any system, therefore, of moral science which is to be adapted 10. 100 yds, and 55 yds. 2 qrs. 1 nl. not only to man's mental and moral constitution, but to his

11. 140 acres 17 rods and 54 acres 1 rood 18 rods. earthly condition, there must be a place found for the principle

12, 465 acres 48 rods and 230 acres 1 rood 30 p. of an earnest and intelligent patience.

13. 446 cubic ft. 75 in. and 785 cubic ft. 69 in.
14. 30° 55' 15" and 55° 58' 30''.
15. 71° 10' and 36° 6' 30".

16. 160 yrs. 11 mo. 2 wks. 5 d. 16 h. 30 min. 40 sec. and 106 yrs. 8 na LESSONS IN ARITHMETIC.—XXVI. 3 wks. 6 d. 13 h. 45 min. 34 sec. COMPOUND SUBTRACTION.

17. How many days from February 22, 1845, to May 21, 1847?

18. How many days from August 25, 1840, to February 6, 182? 5. The process of finding the difference of any two compound

COMPOUND MULTIPLICATION. quantities of the same kind is called Compound Subtraction. This is performed upon the same principle as simple subtrac

8. Multiply £5 28.7d. by 6. tion-namely, that the difference between any two quantities is

We may perform the operation as follows: not altered by adding the same quantity to ex h. EXAMPLE.-From £25 9s. 7 d. subtract £

0 0 4 178. 9 d.

3 farthings 6 is 18 farthings, or Write the less quantity under the greater, with the corre

7 pence x 6 is 42 pence,

2 shillings X 6 is 12 shillings, or sponding denominations under each other, and express, for

5 pounds * 6 is 30 pounds, clearness, the farthings in a separate column. Three farthings cannot be subtracted from 1 farthing. We

The sum of all these is £30 15 101



2 1



1 Aos.


£ s. d.

or 0 36

0 12 0 or 30 0 0


This is the required result, because, in multiplying any quan

LESSONS IN GEOGRAPHY.-XVI. tity by a number, if we multiply separately the parts of which the quantity is composed, and then add the products together, Having explained, in a previous Lesson (see Vol. II., page 4), the resuit is the same as would be obtained by multiplying the the nature of the seasons arising from the annual motion of the whole quantity by that number. The above operation would, in earth in its orbit or path round the sun, and the parallelism of practice, be thus arranged :

its axis, or the invariable inclination of that axis to the plane of 2s. 7d.

its orbit, we shall render this subject more strikingly evident by .

means of the accompanying diagram of the seasons. Here the

sun is considered to be fixed at the point F in Fig. 4 (page 80), £30 15s. 104d.

which is considered to be the focus of the elliptical or oval orbit Hence we see the truth of the following

in which the earth moves, and which is so near to the centre of 9. Rule for Compound Multiplication.

the curve that it may be, on this small scale of figure, reckoned Multiply each denomination separately, beginning with the the same with that centre; and you know that the centre is lowest, and divide each product by that number which it takes the point where the major axis, between summer and winter, of the denomination multiplied to make one of the next higher. intersects or crosses the minor axis, between spring and autumn. Set down the remainder, and carry the quotient to the next If you are curious enough to know how far the focus, F, is from product, as in addition of compound numbers.

the real centre of the orbit, we shall tell you; it is about oneObs.--Any multiplier is of necessity an abstract number. sixtieth part of the half of the major axis, or of the mean disTwo concrete quantities cannot be multiplied together. Multi- tance between the earth and the sun, from the real centre. Let plication implies the repetition of some quantity a certain

us see if we can express this distance in some known measure. number of times; and we see, therefore, that to talk of multiply. The mean distance of the earth from the sun, or the length of ing one concrete quantity by another is nonsense.

the mean semi-diameter of the earth's orbit, is about 23,109 In the case of geometrical magnitudes--in finding the area of times the length of the mean terrestrial radius, or of the mean a rectangle, for instance—we do not multiply the feet in one side distance from the centre of the globe of the earth to its surface. by those in the other, but we multiply the number of feet in one

The earth's mean radius is 3,956British miles, its mean diaside by the number of feet in the other, and from geometrical meter being 7,913 miles. Therefore multiplying 3,956] miles by considerations we are able to show that this process will give us 23,109, we have the mean distance of the earth from the sun, the number of square feet which the rectangle contains. The that is, half the major axis of its orbit, about 91,431,000 in very idea of multiplication implies that the multiplier must be round numbers. This makes the mean diameter of the earth's an abstract number. It is of the nature of twice, thrice, etc. orbit about 182,862,000 miles, and its approximate circum(Vide Obs. of Art. 7, Lesson XXII., Vol. I., page 380.)

ference about 574,709,000 miles. The linear eccentricity of the

earth's orbit being .0168, or about one-sirtieth of its semi-axis 10. ADDITIONAL EXAMPLE IN COMPOUND MULTIPLICATION. major, or mean distance of 91,431,000 miles, we have 1,523,850 Multiply 12 lbs. 3 oz. 16 dwts. by 56.

miles for the distance between the centre of the orbit and the In a case like this, where the multiplier exceeds 12, it is centre of the sun, or the focus of that orbit. Consequently, often more convenient to separate it into factors, and to mul- the earth is about double this distance, or 3,047,700 miles nearer tiply the compound quantity successively by them (Lesson VI., to the sun in winter than in summer. Art. 2, Vol. I., page 95). Now 56 = 7 X 8.

In Fig. 4, the earth is represented in four different positions lbs. oz, dwts.

(momentary positions) in its orbit; namely, at mid-summer, mid

spring, mid-winter, and mid-autumn. In all these positions, 7

as well as all round in its various positions in the orbit, the parallelism of its axis, N s, is preserved. This axis is inclined to the plane cf the orbit, as we have before observed, at an anglo of 66° 32'; hence it makes an angle of 23° 28' with the perpen

dicular to the plane of its orbit; for the perpendicular, repre16 Answer.

sented by the dotted line passing through the centre, o, makes EXERCISE 45.

an angle of 90° with the plane of the orbit; and subtracting Work the following examples in compound multiplication :

66° 32' from 90° gives the remainder 23° 28', which is the angle 1. £35 6s. 78, by 7.

between the axis, N s, and the perpendicular, or dotted line. By 2. £1 6s. 8. d. by 18.

reason of this parallelism of the axis N s, it so happens that at 3. 1 ton 27 } lbs. by 15.

mid-spring, or March 20th, the half of the globe is illuminated 4. 16 tons 3 cwt. 10} lbs. by 25 and 84.

from pole to pole, that is, from the northern extremity of the 5. 17 dwts. 4. grs. by 96.

axis n, to the southern extremity of the axis s, and the days 6. 15 gals. 2 qts. 1 pt. by 63 and 126.

and nights are then exactly equal all over the earth; that is, 7. 175 miles 7 fur. 18 rods by 81, 196, and 96.

there are twelve hours of light and twelve hours of dark& 40 leagues 2 m. 5 fur. 15 r. by 50, 200, and 385.

ness to every spot on the earth's surface for this day. Hence 9. 149 bush. 12 qts. by 60, 70, 80, and 90.

this day is called the equinoc (equal night) of spring, or the 10. 25 qrs. 7 bush. 3 pks. 5 qts. by 110 and 1008.

vernal equinox. Again, at mid-summer, or June 21st, the half 11. 150 acres 65 rods by 52, 400, and 3000. 12. 70 yrs. 6 mo. 3 wks. 5 d. by 17, 29, and 36.

of the globe is illuminated from the circumference of a small 13. 265 cubic ft. 10 in. by 93, 496, and 5008.

circle of the globe at the distance of 23° 28' from the north 14. 75° 40' 21" by 210, 300, and 528.

pole, n, to the circumference of a small circle at the distance of 15. £213 58. 6. d. by 819 and by 918.

23° 28' from the south pole, s; anu the day is twenty-four hours 16. 5 tons 15 cwt. 17 lbs. 3 oz. by 7, by 637, and 763.

long at all places of the earth contained in the space between 17. 213 78. 9fd. by 1086012 and by 1260108.

the small circle and the north polo; that is, there are twenty(For the last three questions refer to Lesson VII., Arts. 15, 16, four hours of light and no darkness at all to every spot within

this space on this day; but the night is twenty-four hours long

at all places of the earth contained in the space between the KEY TO EXERCISE 43, LESSON XXVI. (Vol. II., page 37). small circle and the south pole, that is, there are twenty-four

9. 109 leagues 2 miles, 15. 2 oz. 3 drachm 12 hours of darkness and no light at a'l to every spot within this 6 fur. 1 foot. 1 grains.

space on this day. As at this point the earth begins to return 10. 468 acres 1 rood 6p. 16. 1203 cubic yards 6 to a position similar to that at tho vernal equinox, and the sun

11. 43 sq. yds. 5 sq. ft. 5. £37613 23. 6a.

seems to be stationary as to its appearance and effects on the 125 sq. iu. 17. 9 square miles 86 earth's surface for two or three days before and after this day, 8 cwt. 5 12. 240 gallons.

acres 1 rd. 35 p.

it is called the summer solstice (sun-standinc), or the tropic 13. 115 weeks 15 hours ' 18. 22 Fr. e. 4 qr. 2 nl. 7. 45 tons 4 cwt. 45 25 minutes. 19. il cong. 70 16 13 (turning) of summer. Next, at mid-autumn, or Sept. 23rd, the Iba. 2 oz. 14. 71 years 5 months 5 f3 6 11.

half of the globe is again illuminated from polo to pole, and the 107 lbs. 7 oz. 8 dwts. 1 week 4 days 11 20. 22 loads 1 quarter samo appearances take place as at the equinox of the fpring, 11 grains. hours 7 min.

3 bushels 2 pecks. that is, the days and nights are then exactly equal all over the









Vol. I, page 111.)

1. 213 39. 40. 2. 2102 36, 5d. 3. 293 Os. 2,7:. 4 21315 23.0d.

feet 1059 inches.

89 tons



earth, or there are twelve hours of light and twelve hours of would pass through c, the centre of the sphere. Every circle, darkness to every spot on the earth's surface for this day. whose plane thus passes through the centre of the sphere, is Hence this day is called the equinox of autumn, or the autumnal called a great circle of the sphere. It is further evident that equinox. Lastly, at mid-winter, or Dec. 21st, the half of the every point, such as M, on the surface of the sphere, will describe globe is illuminated from the circumference of a small circle of a circle smaller than the circle o in proportion to its distance the globe at the distance of 23° 28' from the south pole, s, to from the point E on either side, or to its vicinity to either of the the circumference of a small circle at the distance of 23° 28' points P P; and that if the sphere were cut by a plane or flat from the north pole, n, and the day is twenty-four hours long surface, like an orange by a knife, through such a circle as u s, at all places of the earth contained in the space between the it would not pass though c, the centre of the sphere. Every small circle and the south pole ; that is, there are twenty-four circle whose plane does not pass through the centre of the hours of light and no darkness at all to every spot within sphere, is called a small circle of the sphere. Accordingly, the this space

circles Ms and on this day;

TN are called but the night


small circles of is twenty-four

the sphere; and hours long at

if the points all places of the

Mand T be earth contained


equally distant in the space

from the point between the

E, these circles small circleand

will be equal in the north polo;

size, and their that is, there SUMMER.


planes will are twenty

cut the axis four hours JUNE 21.

in two points of darkness


Q equally disand no light

tant from the at all to every

centre,c. The spot within

plane of a great this space on

circle, such this day.

as El, cuts In looking

the globe or at the dia

sphere into the gram, you see


equal hemiat the equinox

spheres; but of spring, or


a small circle the whole of

ents it into the the illuminated half of the globe, because from the represen- | unequal parts, or segments (cuttings) of a sphere. For some pur. tation of its position it is turned in front both to the sun at F, poses, the circumference of a circle, large or small, is divided and to you the spectator ; at the summer solstice, or June 21st, into 360 equal parts, in order to enable us to measure distances yon see only half of the illuminated half of the globe, because along the circumference; each of these equal parts being it is turned in front to the sun at F, but only sideways to you called a degree; for other purposes, the circle is divided into the spectator, you being outside of the orbit; at the autumnal two equal parts called semicircles, and these are also divided equinox, or Sept. 23rd, you see none of the illuminated half into degrees, each containing 180 degrees, and both 360 of the globe, because it is turned in front to the sun at F, but degrees as before ; and for other purposes still, the circle is at the back to you, the spectator, you being

divided into four equal parts called quadoutside the orbit and as it were behind the


rants, each containing 90 degrees, and the globe; and at the winter solstice, or Dec.

whole containing 360 degrees as before. 21st, you again soo half of the illuminated

Each degree is divided into 60 equal half of the globe, because it is turned in front to the sun at F, but only sideways to

parts called minutes, and these minutes MC


(minute parts) are employed to express you, the spectator, for the same reason as before. But were you placed in the middle

any part or fraction of a degree which may

be found over and above a certain number of the orbit at the point F, you would,

Q of degrees in any distance

. Again, each by turning round and round to the different


minute is divided into 60 equal parts called points of it we have been describing, see the

seconds, and these seconds (second minute whole of the illuminated half of the globe at


parts) are employed to express any part each point; and were you placed outside of

or fraction of a minute which may be found the orbit in the directions of the major and T


over and above a certain number of degrees minor axes, and made to look at the globe in these directions only, you would see none of

and minutes in any distance; and so on,

to thirds, fourths, etc. This division of the the illuminnted half of the globe, but only

degree is called the sexagesimal (by sixtieth) the dark side in each position.


division of the degree; the division of We must now explain the nature of some

FIG. 5.

the quadrant of a circle into 90 degrees is of the more important circles

on the sphere or globe of the earth. If in Fig. 5, which we suppose to be a re- 1 of the quadrant. The French, in some of their scientific works,

called the nonagesimal (by ninetieths) division presentation of the globe of the earth, P p denotes the axis—that adopt à different division of the circle and its parts. They is, tho diameter of the sphere, passing through the centre, c, on divide the circle into 400 equal parts, calling them degrees; and which the sphere or globe revolves like a wheel on an axle—then of course, the quadrant into 100 degrees ; also the degree into it is evident that every point on its surface will, in the course of 100 parts called minutes ; and so on : this is called the center its revolution or whirling on its axis, describe a circle. Thus the simal (by hundredths) division of the quadrant. Any number of points, ar, n, and r on the surface, will describe the circles u s, degrees is marked by a small circle placed on the right of the 10, and r n rospoctively; and it is evident that the point e, number in a small character, and above the line ; thus 270 equnlly distant from the two points P p, the extremities or poles denotes 27 degrees. Any number of minutes is marked by ore of the axis will describe the largest circle of all in the course of dash from right to left, on the right of the number; of seconds, the rovolntion ; and that if the sphere were cut by a plane or flat by two dashes, and so on; thus 10 denotes 10 minutes, 10"

wurface, like an orange by a knife, through the circle E q, it denotes 10 seconds, etc. ho oris, W. revolution : 80 faco, like an a

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