a tort. Quelqu'un a-t-il honte ? 31. Non, Monsieur, personne n'a honte. 32. Votre frère a-t-il raison ou tort? 33. Mon frère a raison, et le vôtre 34. Votre sœur n'a ni son chapeau de satin, ni son chapeau de 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. Il n'a pas votre assiette, il a la mienne. EXERCISE 15 (Vol. I., page 59). 1. Have you the carpenter's hammers? 2. We have the blacksmith's hammers. 3. Have the blacksmiths two wooden hammers ? 4. They have two iron hammers. 5. Have the generals the silk hats of the child? 6. They have the child's jewels and playthings. 7. Have the children the birds of your wood? 8. They have not the birds of my wood, but they have the horses of my general. 9. Has the blacksmith a pair of woollen stockings ? 10. The blacksmith has two pairs of woollen stockings. 11. Sir, are you not cold? 12. No, Sir, I am warm. 13. Have you coffee or chocolate? 14. I have neither coffee through the gramme, which is the weight of 1 cubic centimètre of pure water, taken at the maximum density of water, a temperature of 4° Centigrade, and weighed at Paris. THERMOMETRY. Heat is "that which produces in us the sensation of warmth." Temperature is-" that energy with which one body seeks to impart its heat to another." Thus the temperature of a body is no indication of the real quantity of heat in the body. Equal weights of mercury and water may have the same temperature, and yet the water will contain really thirty times more heat or caloric than the metal. Thermometers are measurers of "temperature," not of heat. High temperatures are measured by pyrometers; extremely low temperatures by alcohol thermometers; while mercurial ther nor chocolate. 15. Have you not the cabbages of my large garden?mometers are used for the intermediate ordinary temperatures. 16. I have the vegetables of your small garden. 17. What is the matter with your son? 18. My son has nothing. 19. Have you two pieces of bread? 20. The miller has a piece of bread and two barrels of flour. 21. Has the grocer coffee, tea, chocolate, and pepper? 22. He has tea and coffee, and your merchant's chocolate and pepper. 23. Who has money? 24. I have no money, but I have paper. 25. Have you good paper? 26. I have bad paper. 1.6093149 kilomètre. 16.3861 cubic centimètres. 28 31531 cubic decimètres. 4.54345 litres. 0.06480 gramme. 31.103496 grammes. 0.45359 kilogramme. 50 80237 kilogrammes. These instruments depend for their action upon the fact that all bodies, with the rise and fall of their temperatures, expand and contract. In pyrometers (Fig. 1), a small bar of platinum, s, which can only be melted by the intense heat of the flame of the oxyhydrogen blowpipe, is placed in a hole, b b, drilled 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 graphite-a piece of which has been sliced away to expose the hole-by a platinum strap, a. The position of the top of the bar is carefully noted. It is now introduced into the furnace whose temperature is required. The bar expands, and when it is removed, the strap prevents it from resuming its former position. Thus the expansion of the platinum is found, and from experiment we have learnt that for every 100° Cent. platinum expands of its length, and therefore we Fig. 1. can calculate the heat of the furnace. Mercury is chiefly used for thermometers for five reasons:1. It is easily got pure, for mercury can be distilled like water. 2. It does not stick to the glass. 3. It has a long range, freezing at at 350° Cent. 40° Cent., and boiling 4. It expands uniformly-that is, it increases as much in bulk if heated from 50° to 60°, as it will from 150° to 160°. Fig. 2. 5. Having a low "capacity for heat," its temperature soon changes; it is, therefore, very sensitive. TO MAKE A MERCURIAL THER- 1. Take a glass tube with a ca pillary bore (fine, "like a hair"), as represented at A in Fig. 2; make about half an inch of mer cury run down it, and measure it at different points in its descent. If it retain its length, the bore is uniform. 2. Blow the bulb, B, not with the mouth, lest moisture be introduced, but by connecting the tube, by an india-rubber pipe, with a bag of the same material, and then pressing the bag while the end of the tube is held in a gas flame, as hereafter to be described. 3. Fasten a funnel of paper, C, to the top of the tube, and put into it some purified mercury; 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 measure was originally intended to be of the the air will contract, and the mercury will be forced into the distance along a meridian from the equator to the pole. But bulb. Repeating this process a few times, the bulb and tube since the "mètre " was thus fixed, an error has been discovered will be filled. The lamp flame is again applied to the bulb, and while the mercury is oozing out, the tube is hermetically sealed, by bringing a blowpipe flame to play upon its open end. 4. Thermometers are graduated according to three scales. in the measurement of the earth, and now a "standard" mètre is kept in Paris. The measures of weight are connected with those of length Fahrenheit's Scale, which is best known in England, divides the space between the two fixed points-the freezing and boiling points of water-into 180°. Fahrenheit fixed as his zero (0°) the temperature which had been observed at Dantzic in 1709, and which he found could always be reproduced by mixing salt and snow together. He therefore, though erroneously, concluded that this was nature's zero-the absolute zero. He computed that his instrument contained at 0°, 11,124 parts of mercury, and at the freezing point 11,156 parts; hence he divided the space between zero and the freezing point of water into 32 parts (11,156 — 11,124 = 32). From this point to boiling point contained 180 of these degrees, therefore 212° indicates the boiling point of water. It was Fahrenheit who first used mercury for purposes of thermometry. The Centigrade Scale was introduced by the Swedish philosopher, Celsius, who was a professor at Upsal. In it the freezing ว. point is the zero, and the boiling point 100°. This scale is the one generally in use in the scientific world. Reaumur's Scale was proposed by a French philosopher of that name in 1731. His thermometers were constructed with alcohol of such a strength, that 1,000 parts at the freezing point of water became 1,080 at its boiling point. Hence the interval between the two fixed points was divided into 80°. It is evident that these scales are quite arbitrary, and that we have only two fixed points. It is necessary, therefore, to determine these before the instrument can be graduated. TO FIND THE FREEZING POINT OF Fig. 3. Water does not always freeze at the same temperature. If water be gradually reduced in temperature, and be kept perfectly still, 3 or 4 degrees below 0° Cent. may be reached before the ice will begin to form; but ice invariably melts at a fixed temperature. Therefore immerse the thermometer in melting ice, and mark the point to which the mercury falls. TO FIX THE BOILING POINT. E. R C. Place the thermometer in a vessel such as is represented in Fig. 3, in which water is boiling, and the steam generated passes round the walls, cc, of the partition to make its escape at B. Thus the compartment D in which the instrument is placed, being enclosed by steam, cannot be affected by the temperature of the air. A is a bent tube of glass, open at each end, in which is a little mercury. So long as the exit of the steam from B is not impeded, the steam will be of a uniform temperature. If the steam could not escape at B, it would be indicated by A, for if the pressure of the steam increase, the mercury will not remain level. The point at which the mercury in the thermometer stands, is marked as the "boiling point." 2/20 32 a 1000 Deiling 0° Freezing Point Fig. 4. Point The tube is then mounted on a piece of board, upon which is marked the scale. If Fahrenheit's (Fig. 4a), the *pace between the two fixed points is divided into 180 equal parts, which are produced above and below 320 and 212° (which indicate the freezing and boiling points), as far as is required. For Centigrade (Fig. 4b), the division is into 100°, the freezing point being 0°; for Reaumur (Fig. 4 c), into 80°. Fig. 4 compares at a glance these scales. TO CONVERT DEGREES OF ONE SCALE INTO ANOTHER. = The reason of the following rules will be at once evident :To transfer Fahrenheit degrees to the other scales, subtract 32°, in order that the number of degrees from the freezing point may be ascertained. These multiplied by will give the equivalent number of Centigrade, and by the required Reaumur degrees. To reduce Centigrade and Reaumur degrees to the Fahrenheit scale, multiply by and respectively, and add 32o. If the temperature be below the zero in any of the scales, a minus (-) is placed before the number, thus: -5° Fahrenheit means 37° below freezing. In verifying the following, the student will become expert in these conversions : In a good thermometer, the mercury ought to run to the end of the tube with a "click" when it is inverted, proving the absence of air, and completely fill the tube; and when placed in melting ice, the mercury ought to stand at 0°. It frequently happens that the mercury stands above the freezing point. This error is called "the displacement of zero," and is caused by the curious fact that sometimes the bulb does not perfectly contract for two or three years after it was blown; so that for the best instruments the bulbs are kept for more than that time unfilled. If the bulb be made of thick glass, it is less likely to change. It is plain that in a thermometer we are not given the absolute expansion of the mercury, but the difference between the expansion of the mercury and that of the glass. Mercury expands about seven times more than glass. ESSAYS ON LIFE AND DUTY.—VI. PATIENCE. IT is easier to work than to wait. The Italians say, Il mondo è, di chi ha pazienza," or, the world is his who has patience; and of all difficult exercises in the science of morals the application of this principle is perhaps the most so. Not only may men overshoot their mark by too much eagerness, but they may neglect that personal fitness by which they may best succeed. It is self-evident that he who rows against a strong tide, exhausting thereby his strength and energy in the tussle with its forces, is not so wise as he who husbands his strength, and patiently waits the turn of the tide. Patience, however, does not imply idleness, for in most matters of earthly duty we may best employ our energies in preparation before we enter upon the strife. It is wiser far for the student to complete his long curriculum at college, than for him to rush into the discharge of duties for which he is only half prepared; and in the long run the measure of a man's preparation is the measure of his duration-that is to say, he has less exhaustible forces than the man who has stocked his vessel with too small stores for a long life-voyage! How many lives have miscarried in their highest ends for want of patience! There are not many like Columbus, ready to hold out to the last; nor, like Palissy, steadily bent, through long seasons of misfortune, on the attainment of his end. As a rule, men like quick investments and quick returns, both in mental and material things; but those are both wiser and nobler who with patient persistency are ready to wait for the issue which, though long delayed, may be well worth having when it comes. Patience should characterise our dealings with each other. Much petulance, irritability, and anger come from want of patience. Especially should we remember, in our dealings with the ignorant, that it becomes us to bear with the faults of native temperament and the mistakes of untrained judgment. Hastiness irritates others and harms ourselves, for no man can be said to be master of himself who permits a spirit of impatience to make him nervous and pettish. Patience, however, suggests the value of prior preparation. It may be true enough that the occasion will come for future success, but then we must have fitted ourselves for the occa sion, or it will be like a high tide rising to fill the creek, and finding us without a vessel ready to launch. Of the many 14 17 9 3 therefore add 1 penny, or 4 farthings, to the 1 farthing of the £ s. d. far. 25 29 19 5 15 18 10 3 characters in history that are teaching us this folly of neglect, Many of the scientific successes of later days have been marvels of patience-not only the bridging of straits, which more properly may be considered as belonging to perseverance, but the steady and slow induction of facts which have taken place previous to the adoption of any new principle of action. Patience is always a characteristic of power. Strong minds can afford to wait. It is the sign of weakness to be subject to panic in the presence of some unexpected difficulties, or to be determinately pushing on some enterprise, regardless of the wisdom of the course pursued. The student of military campaigns will see that success has oftener resulted from patient endurance than from brilliant charges; and that the statesmen who have carried the most decisive measures have been men also who did not try to hurry their party into action, but calmly adopted the appropriate method, and waited the appropriate time. Patience is of essential importance to all the other virtues of character. Indeed, it is so necessary to their health and culture, that without it they shoot up into hasty and weedy growth. Those characters blossom best that have had time to let the roots of principle strike deep down into the soil. Apart, however, altogether from issues of success, patient endurance is noble and beautiful; and as life is a state in which we must all look for checks and hindrances to our most cherished purposes, we shall be ill prepared to act well our part in the common arena of life unless we cultivate a patient spirit. In any system, therefore, of moral science which is to be adapted not only to man's mental and moral constitution, but to his earthly condition, there must be a place found for the principle of an earnest and intelligent patience. We have, in fact, subtracted the less of the annexed two quantities from the greater, and they are obtained by adding (as it will be found by examination we have done) £1 1s. 1d. to each of the quantities originally given. Hence we get the following 6. Rule for Compound Subtraction. Write the less quantity under the greater, so that the same denominations stand beneath each other. Beginning with the lowest denomination, subtract the number in each denomination of the lower line from that above it, and set down the remainder below. When a number in the lower line is greater than that of the same denomination in the upper, add one of the next highest denomination to the number in the upper line. Subtract as before, and carry one to the next denomination in the lower line, as in simple subtraction. 7. ADDITIONAL EXAMPLE. Subtract 75 gals. 3 qts. 1 pt. from 82 gals. 2 qts. gals. qts. pts. 75 82 2 0 3 1 6 2 Here, there being no pints in the upper line to subtract the 1 pint of the lower line from, we add 1 quart―i.e., 2 pints to the upper line, and the same quantity to the quarts 1 Ans. of the lower line. Then 1 pint subtracted from 2 pints leaves 1 pint. 4 quarts cannot be subtracted from 2 quarts. We therefore add 1 gallon—ie, 4 quarts-to the 2 quarts of the upper line, and 1 gallon to the 75 gallons of the lower. Then 4 quarts subtracted from 6 quarts leave 2 quarts; and 76 gallons subtracted from 82 gallons leave 6 gallons. The operation we have really performed is the subtraction of the less of the subjoined quantities from the greater, and they are obtained from the original two quantities by the addition of 1 gal. 1 qt. to each. Find the difference of EXERCISE 44. 1. £19 17s. 6d. and £37 14s. 93d. 2. £1,000 and (£500 6s. 7}d. + £493 7s. 6d.) gals. qts. pts. 82 6 2 76 4 1 3. 16 cwt. 3 qrs. 15 lbs. and 8 cwt. 2 qrs. 8 lbs. 6 oz. 5. 69 m. 41 r. 12 ft. and 89 m. 10 r. 14 ft. 6 2 1 Ans. 6. 17 leagues 2 m. 3 fur. 4 r. 4 ft. and 19 leagues 1 m. 2 fur. 15 r. 11. 140 acres 17 rods and 54 acres 1 rood 18 rods. 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 mo 3 wks, 6 d. 13 h. 45 min. 34 sec. 17. How many days from February 22, 1845, to May 21, 1847? 8. Multiply £5 2s. 73d. by 6. This is the required result, because, in multiplying any quantity by a number, if we multiply separately the parts of which the quantity is composed, and then add the products together, the result is the same as would be obtained by multiplying the whole quantity by that number. The above operation would, in practice, be thus arranged : - £5 28. 73d. 6 £30 15s. 10 d. Hence we see the truth of the following 9. Rule for Compound Multiplication. Multiply each denomination separately, beginning with the lowest, and divide each product by that number which it takes of the denomination multiplied to make one of the next higher. Set down the remainder, and carry the quotient to the next product, as in addition of compound numbers. Obs. Any multiplier is of necessity an abstract number. Two concrete quantities cannot be multiplied together. Multiplication implies the repetition of some quantity a certain Ramber of times; and we see, therefore, that to talk of multiply. ing one concrete quantity by another is nonsense. In the case of geometrical magnitudes-in finding the area of a rectangle, for instance-we do not multiply the feet in one side by those in the other, but we multiply the number of feet in one side by the number of feet in the other, and from geometrical considerations we are able to show that this process will give us the number of square feet which the rectangle contains. The very idea of multiplication implies that the multiplier must be It is of the nature of twice, thrice, etc. (Fide Obs. of Art. 7, Lesson XXII., Vol. I., page 380.) an abstract number. 10. ADDITIONAL EXAMPLE IN COMPOUND MULTIPLICATION. Multiply 12 lbs. 3 oz. 16 dwts. by 56. In a case like this, where the multiplier exceeds 12, it is often more convenient to separate it into factors, and to multiply the compound quantity successively by them (Lesson VI., Art. 2, Vol. I., page 95). Now 56 = 7 x 8. lbs. oz. dwts. 12 3 16 7 86 2 12 8 689 8 16 Answer. EXERCISE 45. Work the following examples in compound multiplication: 1. £35 63. 7d. by 7. 2. £1 6s. 8d. by 18. 3. 1 ton 27 lbs. by 15. 4. 16 tons 3 cwt. 10 lbs. by 25 and 84. 5. 17 dwts. 44 grs. by 96. 6. 15 gals. 2 qts. 1 pt. by 63 and 126. 7. 175 miles 7 fur. 18 rods by 81, 196, and 96. 11. 150 acres 65 rods by 52, 400, and 3000. 12. 70 yrs. 6 mo. 3 wks. 5 d. by 17, 29, and 36. 13. 265 cubic ft. 10 in. by 93, 496, and 5008. 14. 75° 40′ 21" by 210, 300, and 528. 15. £213 58. 6d. by 819 and by 918. 16. 5 tons 15 cwt. 17 lbs. 3 oz. by 7, by 637, and 763. 17. £13 78. 9 d. by 1086012 and by 1260108. LESSONS IN GEOGRAPHY.-XVI. HAVING explained, in a previous Lesson (see Vol. II., page 4), the nature of the seasons arising from the annual motion of the earth in its orbit or path round the sun, and the parallelism of its axis, or the invariable inclination of that axis to the plane of 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), which is considered to be the focus of the elliptical or oval orbit in which the earth moves, and which is so near to the centre of the curve that it may be, on this small scale of figure, reckoned the same with that centre; and you know that the centre is the point where the major axis, between summer and winter, intersects or crosses the minor axis, between spring and autumn. If you are curious enough to know how far the focus, F, is from the real centre of the orbit, we shall tell you; it is about onesixtieth part of the half of the major axis, or of the mean disLet tance between the earth and the sun, from the real centre. us see if we can express this distance in some known measure. The mean distance of the earth from the sun, or the length of the mean semi-diameter of the earth's orbit, is about 23,109 times the length of the mean terrestrial radius, or of the mean distance from the centre of the globe of the earth to its surface. The earth's mean radius is 3,956 British miles, its mean diameter being 7,913 miles. Therefore multiplying 3,9563 miles by 23,109, we have the mean distance of the earth from the sun, that is, half the major axis of its orbit, about 91,431,000 in round numbers. This makes the mean diameter of the earth's orbit about 182,862,000 miles, and its approximate circumference about 574,709,000 miles. The linear eccentricity of the earth's orbit being 0168, or about one-sixtieth of its semi-axis major, or mean distance of 91,431,000 miles, we have 1,523,850 miles for the distance between the centre of the orbit and the centre of the sun, or the focus of that orbit. Consequently, the earth is about double this distance, or 3,047,700 miles nearer to the sun in winter than in summer. In Fig. 4, the earth is represented in four different positions (momentary positions) in its orbit; namely, at mid-summer, midspring, mid-winter, and mid-autumn. In all these positions, 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 of the orbit, as we have before observed, at an angle of 66° 32'; hence it makes an angle of 23° 28' with the perpendicular to the plane of its orbit; for the perpendicular, represented by the dotted line passing through the centre, o, makes an angle of 90° with the plane of the orbit; and subtracting 66° 32′ from 90° gives the remainder 23° 28', which is the angle between the axis, N S, and the perpendicular, or dotted line. By reason of this parallelism of the axis N s, it so happens that at mid-spring, or March 20th, the half of the globe is illuminated from pole to pole, that is, from the northern extremity of the axis N, to the southern extremity of the axis s, and the days and nights are then exactly equal all over the earth; that is, there are twelve hours of light and twelve hours of darkness to every spot on the earth's surface for this day. Hence this day is called the equinox (equal night) of spring, or the vernal equinox. Again, at mid-summer, or June 21st, the half of the globe is illuminated from the circumference of a small circle of the globe at the distance of 23° 28' from the north pole, N, to the circumference of a small circle at the distance of 23° 28' from the south pole, s; and the day is twenty-four hours long at all places of the earth contained in the space between the small circle and the north pole; 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 Vol. I, page 111.) KEY TO EXERCISE 43, LESSON XXVI. (Vol. II., page 37). 1. £18 3s. 44d. 2. £102 3s. 534. 3. £93 0s. 2.3d. 4. £4345 28. 0a. 5. £37613 28. Ga 6.9 tons Ibs. 8 cwt. 6 fur. 1 foot. 10. 468 acres 1 rood 6 p. 16. 1203 cubic yards 6 125 sq. in. 5 12. 240 gallons. 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 small circle and the south pole, that is, there are twenty-four hours of darkness and no light at all to every spot within this space on this day. As at this point the earth begins to return to a position similar to that at the vernal equinox, and the sun seems to be stationary as to its appearance and effects on the earth's surface for two or three days before and after this day, it is called the summer solstice (sun-standing), or the tropic (turning) of summer. Next, at mid-cutumn, or Sept. 23rd, the 19. 11 cong. 7 o 16 13 half of the globe is again illuminated from polo to pole, and the same appearances take place as at the equinox of the spring, that is, the days and nights are then exactly equal all over the 17. 9 square miles 86 acres 1 rd. 35 p. 13. 115 weeks 15 hours 18. 22 Fr. e. 4 gr. 2 ul. 25 minutes. earth, or there are twelve hours of light and twelve hours of darkness to every spot on the earth's surface for this day. Hence this day is called the equinox of autumn, or the autumnal equinox. Lastly, at mid-winter, or Dec. 21st, the half of the globe is illuminated from the circumference of a small circle of the globe at the distance of 23° 28' from the south pole, s, to the circumference of a small circle at the distance of 23° 28' from the north pole, N, and the day is twenty-four hours long at all places of the earth contained in the space between the small circle and the south pole; that is, there are twenty-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 would pass through c, the centre of the sphere. Every circle, whose plane thus passes through the centre of the sphere, is called a great circle of the sphere. It is further evident that every point, such as M, on the surface of the sphere, will describe a circle smaller than the circle E Q in proportion to its distance from the point E on either side, or to its vicinity to either of the points P P; and that if the sphere were cut by a plane or flat surface, like an orange by a knife, through such a circle as м s, it would not pass though c, the centre of the sphere. Every circle whose plane does not pass through the centre of the sphere, is called a small circle of the sphere. Accordingly, the FIG. 4.-DIAGRAM SHOWING THE CHANGES OF THE SEASONS. the illuminated half of the globe, because from the representation of its position it is turned in front both to the sun at F, and to you the spectator; at the summer solstice, or June 21st, you see only half of the illuminated half of the globe, because it is turned in front to the sun at F, but only sideways to you the spectator, you being outside of the orbit; at the autumnal equinox, or Sept. 23rd, you see none of the illuminated half of the globe, because it is turned in front to the sun at F, but at the back to you, the spectator, you being outside the orbit and as it were behind the globe; and at the winter solstice, or Dec. 21st, you again see half of the illuminated half of the globe, because it is turned in front to the sun at F, but only sideways to M you, the spectator, for the same reason as before. But were you placed in the middle of the orbit at the point F, you would, by turning round and round to the different E points of it we have been describing, see the whole of the illuminated half of the globe at each point; and were you placed outside of th orbit in the directions of the major and minor axes, and made to look at the globe in these directions only, you would see none of the illuminated half of the globe, but only the dark side in each position. T P P circles M s and TN are called small circles of the sphere; and if the points M and T be equally distant from the point E, these circles will be equal in size, and their planes will cut the aris Rin two points Qequally dis tant from the centre, c. The plane of a great circle, such as E Q, cuts the globe or sphere into tico equal hemispheres; but the plane of a small circle cuts it into fico unequal parts, or segments (cuttings) of a sphere. For some pur poses, the circumference of a circle, large or small, is divided into 360 equal parts, in order to enable us to measure distances along the circumference; each of these equal parts being called a degree; for other purposes, the circle is divided into two equal parts called semicircles, and these are also divided into degrees, each containing 180 degrees, and both 360 degrees as before; and for other purposes still, the circle is S divided into four equal parts called quadrants, each containing 90 degrees, and the whole containing 360 degrees as before. Each degree is divided into 60 equal parts called minutes, and these minutes (minute parts) are employed to express any part or fraction of a degree which may be found over and above a certain number of degrees in any distance. Again, each minute is divided into 60 equal parts called seconds, and these seconds (second minute parts) are employed to express any part or fraction of a minute which may be found over and above a certain number of degrees and minutes in any distance; and so on, to thirds, fourths, etc. This division of the degree is called the sexagesimal (by sixtieths) division of the degree; the division of the quadrant of a circle into 90 degrees is called the nonagesimal (by ninetieths) division of the quadrant. The French, in some of their scientific works, adopt a different division of the circle and its parts. They divide the circle into 400 equal parts, calling them degrees; and of course, the quadrant into 100 degrees; also the degree into 100 parts called minutes; and so on: this is called the cente simal (by hundredths) division of the quadrant. Any number of degrees is marked by a small circle placed on the right of the number in a small character, and above the line; thus 279 denotes 27 degrees. Any number of minutes is marked by one dash from right to left, on the right of the number; of seconds, by two dashes, and so on; thus 10 denotes 10 minutes, 10" denotes 10 seconds, etc. FIG. 5. We must now explain the nature of some of the more important circles on the sphere or globe of the earth. If in Fig. 5, which we suppose to be a reprosentation of the globe of the earth, P P denotes the axis-that is, the diameter of the sphere, passing through the centre, c, on which t'in sphere or globe revolves like a wheel on an axle-then it is evident that every point on its surface will, in the course of its revolution or whirling on its axis, describe a circle. Thus the points, M, F, and T on the surface, will describe the circles M S, 1: q, and r N respectively; and it is evident that the point E, mally distant from the two points P P, the extremities or poles of the n is, will describe the largest circle of all in the course of the revolution; and that if the sphere were cut by a plane or flat face, like an orange by a knife, through the circle E Q, it |