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this position the head, legs, and tail are completely protected; and the animal may be tossed about and even roughly handled without being forced to unfold itself; indeed, the more severely it is assailed the more firmly does it contract itself, and the more pertinacious is its defence. During this armed state most dogs stand off and bark, not daring to seize it; and if they once attempt to make ita prey, their mouths are so pricked with its bristles that it is with difficulty they can be prevailed upon to repeat the attack. But, listen to a word on behalf of the hedgehog from the pen of one who often pleaded forcibly for inferior creatures, Mrs. Charlotte Smith:“Wherefore should man, or thoughtless boy, Thy quiet, harmless life destroy, Innoxious urchin? For thy food, Is but the beetle and the fly, And all thy harmless luxury The swarming insects of the wood. Should man, to whom his God has given Reason, the brightest ray of heaven, Delight to hurt, in senseless mirth, Inferior animals? And dare To use his power in waging war Against his brethren of the earth? Poor creature! to the woods resort, Lest, lingering here, inhuman sport Should render vain thy thorny case; And whelming water, deep and cold, Make thee thy spiny ball unfold, And show thy simple negro face!” “O but,” says the thoughtless, as an excuse for his brutality, “hedgehogs drain the udders of cows.” Their advocate replies, “Had you looked at the mouth of one of these creatures the sight would have been sufficient to refute the charge which ignorance has long been accustomed to advance. It is true that the hedgehog often creeps close to the cattle, as they slumber in the meadow, attracted by the warmth of the cow, or by the insects which swarm round it; and if the udders of the cows should drip, it may sip the milk; but to say it injures the cow is just as true as to declare that the cow preys on hedgehogs!” There is another charge: “Hedgehogs rob orchards, and carry away the apples and other fruits sticking to their spines, in order that they may hoard them up for the winter.” Now the fact is that they make no winter store; and if they do take some fruit, they often render man a service. The well-known naturalist, Mr. White, of Selborne, says, “They abound in my gardens and fields. The manner in which they eat the roots of the plantain in my grass-walk is very curious; with their upper mandible, which is much longer than their lower, they bore under the plant, and so eat off the roots upwards, leaving the tuft of leaves unnoticed. In this respect they are serviceable, as they destroy a very troublesome weed, but they deface the walks in some measure by digging round holes.” Some years ago, a full-grown hedgehog was put into a small yard, in which was a border of shrubs. In the course of a few days he formed, beneath a small holly-tree, a hole in the earth sufficiently large to receive his body. After a while, a small shed was built for him in the corner of the yard, and filled with straw, but the animal would not quit his former situation, until it was covered with a stone. He then took possession of the shed, and every morning carried leaves from a distant part of the border, to stop its mouth. His principal food was raw meat and mice. Of the latter, he would eat six at a time, but never more; and although these were thrown to him dead, he bit them all in the neck, before
Tuire common lieugelloG.
he began to eat any. He would also eat snails with their shells, but would leave anything for milk, which he would lap extremely slow: If the person who usually fed him neglected this duty, he would follow him along the yard; and if the door were open, he would go after him into the house. If meat were put near the mouth of his shed in the day-time, he would sometimes pull it in, and eat it. As the weather became colder, he carried more leaves into his shed; and sometimes he would not come out for two or three days successively. In this state he lived for about six months, at the end of which he died, some thought for want of food, but most probably, from the severity of the weather.
There is no doubt that the food of the hedgehog is much more various than was at one time supposed. Itis quite certain that it preys upon the eggs of pheasants, partridges, and all kinds of domestic poultry, to a considerable extent; and in other ways it seems to gratify its carnivorous propensities; of a snake, it was seen, on one occasion, to make an easy prey. Dr. Buckland laid a hedgehog on the body of a snake, with that part of the ball where the head and tail meet downwards, and touching it. The snake proceeded to crawl; the hedgehog started, and opened slightly, and seeing what was under it, gave the snake a hard bite, and instantly rolled itself up again. It soon opened a second time, repeated the bite, and then closed as if for defence; it opened carefully a third time, and then inflicted a third bite, by which the back of the snake was broken. This done, the hedgehog stood by the snake's side, and passed the whole body of the snake successively through its jaw's, cracking it, and breaking the bones at intervals of half an inch or more; by which operation the snake was rendered entirely motionless. The hedgehog then placed itself at the top of the snake's tail, and began to eat upwards, as a man would eat a radish, without intermission, but slowly, till half the snake was devoured, when the hedgehog ceased from mere repletion. During the following night, the anterior half of the snake was also entirely eaten up.
When taken young, the hedgehog may be completely tamed and rendered familiar, allowing itself to be handled, and associating, on the most amicable terms, with the dog or the cat. The landlord of the Angel Inn, at Felton, Northumberland, kept a hedgehog some years ago, which answered to the name of Tom. It was very docile, ran familiarly about the house, and would even do the work of a turnspit dog.
The hedgehog is spread over every part of Europe, except the cold countries, such as Lapland and Norway. On some parts of the continent its flesh is still eaten, as it used to be in England, when roasted, or baked in a pie; it was reckoned in season in the month of August.
pressiveness, delicacy, and music; yet it must, in these high qualities, yield to the German, which, in its turn, is surpassed by the Greek, the nearest approach to perfection to which human language ever attained, except probably the Sanscrit, or sacred language of the Brahmins. As one result of its excellence, the Greek has adapted itself with equal care and precision to the constantly growing demands of science. On its native soil, and while yet spoken in its purity, the Greek tongue had gained the power of expressing the widest generalisations, and the nicest distinctions of thought. Its resources for setting forth the truths of physical science were, in classical times, but very partially put to the test. In the pages of Cicero, however, we learn how much indebted Rome was to the Greek for terms of art and of moral and intellectual disquisition. At the true birth of science, after the revival of letters, the Greek, being cultivated anew, afforded a most appropriate vehicle for the communication and interchange of the new truths which continued to break upon the world in great profusion; and now, by the creation of several sciences wholly unknown of old, such as chemistry, botany, physiology, conchology, magnetism, &c., our scientific vocabulary, with all its multiplicity, its precision, and conciseness, is found to consist, for the most part, of elements supplied by the Greek language. You have an instance in the first word of the ensuing list, akouo, which is the parent of acoustics, or the science of heariny. The corresponding science of sight has also in optics taken a Greek term. Hence you may infer how important is an exact study of these Greek stems. In some sense, indeed, the learning of a science is the learning of the signification of its vocabulary, or list of words; assuredly he that is familiar with the elementary roots of the Greek, will, in proceeding to study science, find him. self in possession of a most powerful auxiliary.
Greek words. Stems. English words. Akoud, I hear acot. acoustics anthos, a flower antho anthology logos, a word, a dis
course, a science logo logomachy maché, a fight mach naumachy naus, a ship orate nautical
The word logos plays a very important part in the world of ancient Greek thought. It is the term by which the word of John's Gospel is expressed in the original. Logos denotes either intelligence, the unuttered thought; or speech, the uttered thought. From these radical meanings flow the numerous applications of the term. In science, the service which logos renders is very great. In the preceding list, two out of the five examples contain the term. Used in a somewhat remote sense indeed, logos, as signifying science, enters into the very designation of many of the sciences. Thus we say theology, philology, astrology, demonology, pneumatology, anemology, ouranology, nosology, phrenology, &c.
i. naus, you have a word common to the Teutonic and the Celtic elements of language, for the naus of the Greeks is the navis of the Latins. Meaning ship, it appears not only in nautical (nauta, Lat. a sailor), but in navigate (ago, Lat. I drive, guide), navigation, &c. The student, by combining naus, a ship, with mache (maké), fight, learns that naumachy denotes a sea-fight.
“Anthology signifies properly a collection of flowers, and in particular a collection of flowers or gems of poetry. There is in the Greek anthology a remarkable mention here of sneezing in an epigram upon one Proclus.”—Brown, “Wulgar Errors.”
“The contentions of the Eastern and Western churches about this subject, are but a mere logomachy, or strife about words."—Bishop Bramhall.
Greek words. Stems. English words Anthrôpos, a man anthrop misanthropy Misos, hatred miso misogamist Gamos, marriage gam bigamy
Bi (bis) signifies twice, so that bigamy is the state of being twice married.
"No bigami, that is, none that had been twice married, or such as married widows, were capable of the benefit of clergy, because such could not receive orders.”—Burnet, “History of the Reformation.”
"Bigamy, acrording to the canonists (the doctors of the ancient ecclesiastical law), consisted in marrying two virgins successively, one after another, or once marrying a widow,”— Blackstone, “Commentaries.”
Bigamy, as punished by the English law, is the crime of having two wives at the same time.
Greek words. Stems. English words.
remember, when I was young, some difficulty in ascertaining, and when ascertained in remembering, the exact difference between the barometer and the thermometer. My little Greek came to my aid, and showing me that the former was a measure of weight, and the latter a measure of heat, gave me definite and clear ideas which I have never forgotten. Biblion enters into combination with several words. With graphe, biblion, forming bibliography, originates a term which signifies the science of books. With the aid of latria (Gr. worship) we have bibliolatry, a word sanctioned by Coleridge, which may be Englished by book-worship or word-worship. Bibliomania, or book-madness, is made up of biblion, a book, and mania, the Greek for madness. United to poleo, I sell, it forms bibliopolist, a bookseller; and with thera, the Greek for a repository, it gives rise to the French bibliotheque, a repository for books; that is, a library. Let it also be distinctly mentioned that the Greek biblion is the source whence we get the name of the book of books, namely, the Bible. Language is in one view a record of human errors. The fact is illustrated in the names of some of what are still, by courtesy, called sciences, such as astrology, phrenology, &c. It is also exemplified in particular words, as, e.g., choleric, coming from cholé, bile. The term choleric shows that of old, men regarded the bile as the source of anger and passion.
“When choler overflows, then dreams are bred
Accordingly, dejection or habitual sadness was termed melancholy,
The sphere of my brother's influence is larger than my own. Autopsy, signifying self-inspection, is made up of autos, self, and opsis, sight. The kaleidoscope is an optical toy exhibiting a variety of beautiful forms and colours. The kaleidoscope is said to have been invented by Sir David Brewster. Chiromancy is the pretended science of foretelling the destiny by the lines of the palm of the hand. Chrysolite, or gold-stone, is a name given to the topaz, look at Buenos Ayres, in South America, on the same map, you will find that it lies to the left of the first meridian in the southern half of the western hemisphere, between two meridians which cross the equator, the one being that which is, or should oe, marked at the point of intersection 50°, and the other that which is, or should be, marked at the point of intersection 60°; this enables you to guess, by the vicinity of Buenos Ayres to the latter meridian, that its longitude is about 58° west; now the actual longitude is 58° 25' W. On the first meridian, the degrees of latitude are not marked; but they are marked, in the map of the world, on the circle which surrounds each hemisphere. On this circle, the points of its intersection with the equator are marked 0, to show that latitude begins to be reckoned from these points. Each of the four quadrants (or, fourth parts) of these circles is marked with degrees from 0° to 90° reckoned from the equator to the poles. In the map referred to, these degrees are marked only at the distance of every 10 degrees, on account of its smallness; in larger maps, they are marked at less distances; and the best are those in which they are marked at the distance of every single degree; but these, of course, must be of very great size. In the same map, circles are made to pass through the corresponding points on the upper or northern quadrants of the outer or surrounding circle of each hemisphere, and of the upper or northern half .# the middle straight line extending from pole to pole, at the distance of every 10 degrees; these upper quadrants, and this upper half, actually denoting the northern portions of meridians passing respectively through the points of the equator marked longitude 20° W., longitude 160°E., and longitude 70° E. These circles, which on the globe are parallel to the equator, are, from the nature of the projection employed in this map, not actually parallel to that line or to each other, being drawn from different centres; but they are still called arallels of latitude, and are used to enable us to determine the atitude of any place on the map. Similar parallels of latitude are drawn through the corresponding points on the lower or southern quadrants of the outer or surrounding circle of each hemisphere, in the same manner, and for the same purpose. For example: if you look at Pekin, in China, on this map, you will see that it lies between the equator and the north pole in the eastern hemisphere, and close to the parallel of latitude marked 40° at each side of the map; this enables you to guess that the latitude of Pekin is nearly 40° north; now the actual latitude is 39°54' N. Again, if you look at Buenos Ayres, in South America, on the same map, you will find that it lies between the equator and the south pole in the western hemisphere, and nearly in the middle between the parallels of latitude marked 30° and 408 at each side of the map; this enables you to guess that the latitude of Buenos Ayres is nearly 35° south; now the actual latitude is 34° 36' S. Having thus shown how to find separately the latitude and longitude of any place on the surface of the globe by means of the circles and lines drawn in the ...? of the world, it is easy for the student to combine these, and thus to determine the actual position of any place on the surface of the globe. Thus, we have found that the city of Pekin, in China, is situated in lat. 39°54' N., and long. 116° 26' E.; and that the city of Buenos Ayres is situated in lat. 34° 36'S, and long. 58° 25' W. ExERCISEs. Find from the map of the world, the latitudes and longitudes— that is, the geographical positions—of the following places to the nearest degree :-Tehraun, or Teheran, in Persia. Delhi, in India. Canton, in China. Sydney; in Australia. Cape of Good Hope, Africa. Cape Horn, South America. Assumpcion, South America. Chuquisa, South America. Mexico, North America. Washin ton, #: h America. Bhering's Straits, North America. Tobolsk, in usela.
ANSWERS TO CORRESPONDENTS,
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A. H. E. will be able to judge for himself, by the extracts we have made from the L. U. Calendar, whether he can go up to the University of London for Matriculation. Thanks for his suggestions.—X. Y. Z. (Dudley) will find an answer to his inquiry in the same extracts.-Newcastle: Cassell's History of England, price 3s.6d.-E.D. (Pontypool): The rule for the octagon is not correct, on the supposition that it is regular.—J. W. C. (Glasgow): We would hardly advise any addition to, or cessation from, lais studies. The dictionary he mentions (Young's) may do for a little. The maps should be pasted in their proper places according to directions & be
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Music.—WILLIAM HAMILTox (Glasgow): We are obliged by his politeness in sending us a set of his new “Penny Series of Glees and Choruses," and a list of his publications. It is a noble collection of cheap music for the Ho: R. (Ravenfield): Every member of your class can obtain a modulator for a penny by purchasing the number of the Educator in which it is printed. A large one for class purposes is published by Ward and Co., for one shilling and fourpence.—Stoukhoidae and WHITLây: Can any one answer the following questions for our correspondents? Will there be any difference in the sound of a pianoforte (flat, table-shaped) if the top has been split, but well fastened together again, with iron bands, and glued? Give a rule to get the length of organ pipes having certain different diameters, but sounding the same note? A description of Barker's pneumatic valve * The relative length of pipes between the octaves would be in the same proportion as the string of the monochord.—T. S.C. (Chudleigh): When pianofortes and organs are tuned, in every key, perfectly, according to the proper divisions of the monochord, then there will be nothing of what tuners call “wolf.” . Such instruments would, at present, be very expensive because of the number of pipes or strings required. But might not some of the money now lavished on ornament be better spent in of correct tune?—T. BAINEs (Bury): We do intend to introduce all the clefs, as he expects.-John Stocking: What is the best deal for the belly of a violin? Does it make any difference whether the back is in one or two pieces? Can any friend answer him 2–A PERs ever ING SINGER: Be content to listen while your voice is breaking.—A Musical REFokMER: We shall be hair, to see, and will promise to re-examine, the last-edition of the “Sequential System."—T. HART should not ask us questions which he can answer for himself bycareful perusal of our Lessons, neither should he “suppose" without areason.-PETER SIMPLE's questions we cannot answer.
erabatumi. No. 31, p. 71, col. 1, last line, before four insert more than.
THE ALTAR of THE Household; or, Domestic Worship. Part I. will be published on the 1st of January, 1853, price ls. This work will contain a Series of Services for the Family, adapted for every morning and evening throughout the year, viz., o: of §. F. and Thanksgivings, suitably adapted to each other, to which will be added short praetical comments to explain the subjects read, or enforce the duties enjoined. This work will be edited by the Rev. Dr. Harris, Principal of New College, assisted by a band of eminent divines in London and the country. THE SELF AND CLAss ExAMINER IN Euclid, containing the Enunciations of all the Propositions and Corollaries in Cassell's Edition, for the use of o, Schools, and Private Students, will be published in a few days, price 3d. CASSELL's ELEMENTs of ARITHMEric, ls. paper cover; 1s. 6d. neatly bound in cloth. THE ANswers To ALL THE QUESTIons IN CAssell's ARITHMEric, for the use of Private Students, and of Teachers and Professors who use this work in their classes, is preparing for publication.
THE UNCLE TOM'S CABIN ALMANACK ; or, The Aboltrioxirst MEMENTo, FoR 1853.-The most complete work on the question of slavery that has hitherto been published. Everybody who has read “Uncle Tom's Cabin” should possess themselves of a copy of this book, which more than verifies all the statements in Mrs. Stowe's thrilling narrative. This work is splendidly Illustrated by George Cruikshank, Esq.; J. Gilbert, Esq.; W. Harvey, Esq.; H. K. Browne, Esq.(“Phiz"); and other eminent artists; and contains upwards of 70 pages super-royal:8vo., replete with the most stirring incidents—Lives of Escaped Negroes: the Workings of the Fugitive slav; Law; Anecdotes, Narratives, and Historical and Descriptive Accounts of American Slavery. The sale already is very large, nearly 20,000 copies having been disposed of in a fortnight. Illustrated Exhibiton ALMANAck, Thirty splendid Engravings, 6d. PopULAR EDUCAtoR ALMANAck, Notices and Essays on Education, 2d. TEMPERANCE ALMANAck, Tale by the Authoress of Uncle Tom, &c., 2d. Protestant DissENTERs' ALMANACK, with new Historical Notices, &c. 5d.
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IN order to assist our pupils in obtaining some elementary notions relating to form, to colour, and to light and shade, as well as to natural perspective in Drawing, we shall suppose, as a first lesson, that you take up some object, such as a elosed book, and that you place it before you in various positions, in order to observe the effect which is produced upon the eye in each of these positions. Three things will particularly attract your attention, when you look at the book in any given position: first, its Fonx; then, its colour; and next, its chIARo-scuRo, or LIGHT AND shADE. When you have caretully considered and understood the appearance of the book in these particulars, you will be able to make a Drawing of it. If you have never been accustomed to use a pencil, or make a sketch of any object before, your first attempt may not please yourself, or, indeed, any one else; but a first attempt must be made; a second may be more successful; and a third, the most successful of all. It is frequently asserted that the art of Drawing, like that of writing poetry, is a natural gift; and that unless you possess this, you never can excel. It may be true that, to rise to the highest eminence in any science or art, requires a peculiar bent of the mind; but to acquire a useful practical knowledge of the art of Drawing, it is by no means necessary that every one should be a genius. With regard to the sister arts—poetry and painting—it may be truly said, in regard to their elements, at leas, that every man is endowed with some ability for their acquisition and their application. Every one, for instance, is poetical when he speaks on a subject with which he is well acquainted, or in which he is deeply interested; and, in like manner, every one is an artist, who is ready to make a sketch or a Drawing of any object, which he wishes to explain to another, when he finds that language fails to convey his ideas. The art of Drawing, therefore, may be attained to a sufficient extent for practical purposes by every one who exerts the necessary attention and assiduity. The artisan, the tradesman, or the connoisseur, may, by the use of a few well-directed strokes of the pencil, convey an idea of his plans, operations, and views in relation to artistic productions, of which the most laboured and elegant composition, consisting of many hundred words, would fail to convey the slightest impression to the mind of the hearer or the reader. But to return to our example already suggested. Let the pupil take up the book before mentioned, and hold it in a horizontal position on the palm of the right hand—that is, flat, as it would lie on a table; then raise it in this position to the height or level of the chin, with one end towards you, and at the distance of about twelve inches from the face; then, if the front or fore-edge of the book be turned to the right, it will present the appearance represented in fig. 1.
of the book be turned to the left, it will appear as represented in fig. 2. And, if the hand be held in the same position, but the farther end of the book be turned to the right, it will exhibit the appearance represented in fig. 3.
In these different positions, you see how remarkably the appearance changes, and still it is the same book. One thing, however, cannot escape your observation, and it is this: that the two ends of the book, especially in the view represented in fig. 1, appear to be of different lengths, although they be in reality of the same length, that end which is farthest from you appearing to be the smaller. Now this is according to a law of nature, the law of perspective, by which all bodies at great distances appear less than the same bodies at small distances, and that in proportion to the greatness of the distance. Every one must have noticed the regular appearance and gradation of the effects of this law, when looking down an avenue, where the trees, at the farther end appear almost to approach each other, although you know that they are exactly at the same distance as those at the near end, see fig. 4; or, when looking alongside of a wall of uniform height, and of a considerable length, the top and the bottom of the wall seem to approach each other in the distance.
There are positions in which you may look at the book and.
not perceive any difference in the apparent lengths of the two ends, viz., when you look down at it from a point directly over the middle of the side, or when you look up at it from a point directly under the same; also, when you hold the side of the book facing you, and look at it from any convenient distance. Generally speaking, however, the appearance of the book, and of the dimensions of its different parts, will vary with its position; so that, as the position changes, the appearance changes. A complete knowledge of the laws which regulate these appearances, will enable you to give a true representation of them on paper or canvass; and these laws are known under the name of the principles of perspective. It is plain, from what we have said, that these principles are not arbitrary, and that they are not mere matters of choice or of human invention. The are discoverable in all the appearances of nature; and, indeed, until the principles of perspective were well understood, natural appearances were not well understood; and, consequently, the art of drawing was not well understood. It is true that there have been men who possessed great natural powers of observation,-men who could draw well before perspective was fully understood, and among these there have been some
Report the following anecdote :-
“A friend of mine,” says Dr. Bailly, “a man of understanding and veracity, related to me these two facts, of which he was an eyewitness. He had an intelligent ape, with which he amused himself by giving it walnuts, of which the animal was extremely fond. One day he placed them at such a distance from the age that the animal, restrained by his chain, could not reach them. After many useless efforts to indulge himself in his favourite delicacy, the ape happened to see a servant pass by with a napkin under his arm; he immediately seized hold of it, whisked it out beyond his arm to bring the nuts within his reach, and so he obtained possession of them. His mode of breaking the walnut was a fresh proof of the animal's inventive powers; he placed the walnut upon the ground, let a great stone fall upon it, and so got at its contents. ne day the ground on which he had placed the walnut was so much softer that, usual, that, instead of breaking the walnut, the ape only drove it into the earth. What does the animal do? He takes up a tile, places the walnut upon it, and then lets the stone fall while the walnut is in this position.”—Sydney Smith.
LESSONS IN GEOGRAPHY.-No. XV.
Tire two circles of the greatest importance in Geography and Navigation are the meridian and the equator; these were explained in our last Lesson. We proceed now to show their use. Suppose that a golden treasure was hid in a field, and that two of its boundaries consisted of one fence lying north and south, or such that at noon its shadow coincided with itself, that is, lay in the same direction; and another fence lying east and west, or such that it intersected or crossed the former fence at right angles, as in the margin, fig. 4. In this figure, the straight line AY represents the north and south fence, and the straight line A x the east and west fence; .P that is, if you go from A to Y you go north, and if you go from Y to A you go south; but if you go from a to x you go east, and if you go from x to Ayou go west. The directions A X of the fences being thus understood, suppose that you were told the exact distance of the place where the golden treasure lay, from the fence Ax say 20 yards, this would not be enough to enable you to find it, because there are ever so
many points in the field, all at 20 yards distance from the fence Ax. Now suppose you were also told the exact distance of the place where the golden treasure lay from the fence a y, say 25 yards, this alone would not be enough to enable you to find it, because there are ever so many points in the field, all at 25 yards distance from the fence Ax. Among these latter points, however, there can be only one which is at the exact distance of 20 yards from the fence Ax; so that if you were told both distances at once you could evidently, by some means or other, determine the place where the golden treasure lay hid. It is necessary, therefore, and it is sufficient, to inform you of the exact distances of the place in the field from both fences, in order to enable you to find it.
With the information now supposed to be given, the next question is how should you proceed to determine the exact place of the golden treasure. A little reflection would suggest the following method. In fig. 5, measure off from the point A, along the fence Ax, the given distance of 25 yards, at which the place is said to be situated from the fence A Y; let this distance be a M. Then, from P the point M, draw a straight line (MP) parallel to the fence A Y ; or, which is easier in this case, draw M P a perpendicular to the fence Ax from the point M: for M P and A Y being A M. X. both at right angles to A x, are parallel to each other. Lastly, measure off from the point M, along the straight line M P, the given distance of 20 yards, at which the place is said to be situated from the fence Ax; and the point p will be the place in the field where the golden treasure is to be found.
That this mode of determining the place of the golden treasure is correct may be proved thus: in fig 6, let P be the place in question; from P draw P N perpendicular to A Y, and P M perpendicular to A x ; then according to thqata (things given) P M is Y a distance of 20 yards, and P N is a distance of 25 yards. But by the nature of the construc- N P
A Al X
tion, the figure A M P N is a rectangular (rightangled) parallelogram, and its opposite sides are therefore equal; whence A M is equal to N p, and A N equal to M. P. It follows, therefore, that the point P is found by the method shown in the preceding paragraph. In mathematical phraseology (mode of speech), the distances P N and P M of the poin. P from the fences A Y and Ax, are called the rectangular co-ordinato of that point; but the distances A M and M P, which are equal to the former, are more usually denominated the recta gular co-ordinates of the P; and by these co-ordinates we can always determine the position of any point, when their exact lengths are given. The straight lines Ax and A Y, from which the given distances are m asured, are called rectangular are, and the point A, where these axes intersect each other, is called the origin of the rectangular axes. With the origin and the direc. tion of the rectangular axes so our figures, the fences at right angles), and the lengths of the rectangular co-ordinates, all given, in reference to any point on a given surface, we can . find the true position or place of that point when required. In the preceding view of the determination of the position of a given point, we have not considered all the possible positions of a point P round the point A, the origin of the co-ordinate axes. If these axes were produced in the preceding figures so as to assume the appearance represented in fig. 7, them, with the same given distances or rectangular co-ordinates, there might be four different positions of the point p with reference to the rectangular axes xx" Fig. 7. and Y Y', or the north and south straight line Y
Y.Y', and the east and west straight line xx'. P. P. To prevent confusion, therefore, and to fix the exact position of the point in question, it so X might be agreed upon that every distance mea- X A sured from the origin A, along the portion of P.” P” the axis a x, should be called east, and every Y”
distance measured from the origin A along the .
portion of the axis a x' should be called west; in like manno that every distance measured upwards from the axis xx'should be called north, and every distance measured downwards from