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placing this instrument at the vertex of the angle to be measured; that is, at the place in the ground where the two sides of the field, or space to be measured, meet; and directing one pair of sights along the one side to a mark placed at its extremity, and the other pair of sights along the other side to a mark placed at its extremity, the angle between them is measured on the semicircle; for it is ascertained at once by the number of degrees on the arc between the two limbs or moveable arms on which the sights are placed. The form of this instrument without the staff is represented in fig. 3. In using this instrument care must be Fig 3. taken that the marks set up at the extremities of the two sides are visible through the sights at the same instant; otherwise the angle will not be correctly ascertained. The sights in this instrument may be advantageously replaced by telescopes mounted on the centre, where very great accuracy is required. Also, in the use both of the graphometer and the surveying-cross it is necessary that the staff which supports them be placed vertically, and the instruments themselves horizontally; these positions are ascertained by the use of the plumb-line and level.
An instrument preferable to the graphometer is constructed of the entire circle completely graduated, and receiving different names according to the manner in which it is mounted and arranged. If it be furnished with two telescopes placed across its centre, one fixed and the other moveable, or with one fixed to a circle which is moveable over a fixed circle on the same centre, it is called a repeating circle. With this instrument, properly adjusted, angles can be measured, and the measurement repeated two, three, four, and even ten times. By this means errors of observation and graduation, and in reading off the angles, can be so compensated as to obtain the greatest possible approximation to accuracy. For as ten times an angle is thus obtained with as great an approximation to truth as the angle itself, the tenth part of this angle is likely to have an error of only the tenth part of that which would arise from the observation of the single angle. The invention of the repeating circle is due to the French mathematician Borda, who employed it in the Trigonometrical survey instituted for the measurement of an arc of the meridian between Barcelona and Dunkirk, in 1792. The principle of the repetition of angles in the construction of the reflecting circle had been previously proposed by the astronomer Tobias Mayer, of Gottingen. A sketch of this instrument is represented Fig. 4. in fig. 4; it is capable of being used with great facility, and is sure to correct errors of graduation by the repetition of the measurement of angles; but it possesses some disadvantages which render it of less value in the ordinary practice of surveying, than some other instruments. Angles taken by this instrument require to be reduced to the plane of the horizon, and involve a calculation for this purpose which may be avoided by the use of the Theodolite. It possesses also certain other defects, notwithstanding its simplicity and portability which have rendered its use unadvisable in practice.
Reserving the description of the Theodolite for another lesson, on account of its importance, we proceed to explain the nature of a useful and simple instrument for surveying, called the Plane-Table. This instrument was invented towards the end of the 16th century, by Praetorius, a German mathematician, and is used for drawing at once a plan of the ground to be measured, upon paper. It is usually made of a square or rectangular form, and is supported on a three-legged stand, which is made to move every way by means of a ball and socket, or other moveable joint. The table has a moveable frame which is used to hold the paper fast on which the plan is to be drawn; and the sides of the frame facing the paper are divided into equal parts every way, for the convenience of drawing parallel or perpendicular lines. It is furnished with a magnetic needle and compass, to point out the directions of the lines drawn on the plan, and to be a check on the sights; and an index with sights, or a telescope to determine their directions, and to draw them on the paper at the same time. These sights, or
this telescope, and one edge of the index, called the graduated or fiducial edge, are in the same plane. On the edge of the frame are also marked, degrees and minutes.
To use this instrument, which is represented in fig. 5, you take a sheet of paper sufficient to cover it, and wet it to make it expand; then spread it flat on the table, pressing down the frame on Fig. 5. the edges to stretch it, and keep it fixed in its position; so that when the paper becomes dry, it will by contracting again, stretch itself smooth and flat, from any cramps and unevenness; as on this paper is to be drawn the plan or form of the ground to be measured. You then begin at any suitable spot on this ground, and having properly adjusted and fixed the table, by fastening the legs of the stand in the earth, mark a point on a convenient part of the paper to represent that spot on the ground. You then fix in that point, one leg of the compasses, or a fine steel pin, and apply to it the fiducial edge of the index, moving it round until through the sights you observe some suitable object, as the corner of a field, &c.; from the station point, you then draw a line with the point of the compasses along the fiducial edge of the index-a process which is called setting or taking the object. Next, set another object or corner, and draw its line; do the same by another, and so on, till as many objects are taken as may be deemed necessary. Then measure with the chain from the station in a straight line towards the objects, taking offsets to corners or crooks in the fences or hedges, and laying down their measurements on their respective lines in the table. Then, at any other convenient spot to which a measurement has been taken, fix the table in the same manner as before, and set the same objects again as they appear from this new station. Continue this operation until all the necessary work is finished, measuring only such lines as are known to be indispensable for the calculation, and determining as many as possible by the intersection of the lines of direction, drawn from the different stations in order to complete the plan. This being done, the area of the field may be determined by the rules given in our last lesson, and the plan of the whole exhibited, as nearly as possible, just as it appears on the ground. In fig. 6 is represented a sketch of an index furnished with its sights, and its fiducial edge; and in fig. 7 one of an index mounted with a telescope. The latter index affords a morc exact and a more extended line of sight than the former. Fig. 6.
We shall conclude this lesson by giving an account of the cir cumferentor, or common theodolite, used by surveyors for the purpose of taking horizontal angles. It is founded on the property which the magnetic needle possesses, when suspended freely, of taking always the same direction in the same place, at least within a given small period. This instrument consists of a brass circle and index in one piece, commonly about seven inches in diameter, with an index about fourteen inches long, and one inch and a half broad. On the circle is a card or compass divided into 360 degrees; of which the meridian line (that is, from north to south) answers to the middle of the breadth of the index. There is soldered on the circumference a brass ring, on which screws another ring with a flat glass in it, so as to form a sort of box for the needle, which is suspended on a pin in the centre of the circle. There are also two sights to screw on, and slide up and down the index; as also a ball and socket screwed on the under side of the circle, to receive the head of the three-legged staff on which it is placed when in operation. This is the simplest form of the circumferentor; but improved instruments of this kind are made in London, which answer in some measure the
LESSONS IN ENGLISH-No. IV.
As in English nouns, there are at the most only two cases, so are we without an objective or accusative case. Yet sentences in English, as in Latin, have their object. That object must be recognised. Let it be called the object of the proposition, for so it is; in any given instance let it be termed the object of the verb, for it is the object of the verb.
Here you must carefully distinguish between a case and a relation. A case denotes a change in a noun corresponding to the change in its relation. This you will see in these two propositions:
Deus fecit mundum God made the world. (2) Mundus factus est a Deo
The world was made by God.
Now without knowing Latin you may clearly understand what case means, and learn that in English we have no objective case. The Deus of number 1, becomes Deo in number 2; but in both, the English word God remains the same, though in the former, is in what is commonly called the nominative, and in the latter in what is commonly called the ablative case. Look also at mundus and mundum, you see that the nominative mundus is, in the objective or accusative case, changed into mundum. Here you clearly have two cases, but the English word world represents both. Consequently if world is in the nominative it is not also in the objective case, for there is no alteration of form what. ever. Yet in the latter case there is a change of relation; for while in number 1, world is the object; in number 2, it is the subject of the proposition. The English then does not conform to the Latin custom of expressing diversity of relations in nouns by diversity of form, or does so only in a limited degree. In fact the tendency of the English language has long been to drop the terminations and inflexions which it borrowed from its Anglo-Saxon parent. The tendency has for ages continued to become more and more strong. It is a tendency which deserves encouragement, for in proportion as it is effectual, it gives freedom and power to the language, and makes the acquisition of it easy, and the diffusion of it rapid.
I have intimated that propositions have each an object as well as a subject. Such is generally the case, and such is the case more widely than may at first appear. In our standard phrase, Alfred reads, no object is expressed. And the statement may be made without any clear reference to an object. Verbs in which there is no reference, or no clear and obvious reference to an object, are called intransitive verbs,—that is, verbs the action of which does not (instransitive-in, not; trans, across; eo, I go) pass over to an object. Alfred sleeps, Alfred runs, Alfred rides, supply other instances of intransitive verbs; because in each case the action remains with the subject. But these and most other intransitive verbs may become transitive by having an object placed after them;
INTRANSITIVE. TRANSITIVE. INTRANSITIVE. TRANSITIVE.
Object. Alfred sleeps. Alfred runs. Alfred sleeps a deep sleep. Alfred runs a long way. Alfred rides. Alfred sings. Alfred rides a fine horse. Alfred sings a fine song. If, however, propositions in general have an object, then we must add an object to our grammatical formula; thus :
The grammatical formula is thus made complete. The verb reads is, as we have seen, equivalent in grammar (or logic) to the form is good; where the former is the copula, and the latter the attribute; so that an attribute with its copula is equivalent to the verb and its object, in forming the predicate of a proposition..
The proposition which, as it stands, has all the essential parts of a proposition, may receive additions in order to express modifications of the meaning. Introduce and, then it runs,
Alfred reads writing and manuscript.
This particle and is termed a conjunction. Conjunctions (Latin, cum, with, and jungo, I join) join together words and sentences. And, in this case, unites manuscript with writing. Before writing, insert a; then the proposition stands thus :Alfred reads a writing.
A is called an article (properly in Latin a little joint). A is called the indefinite article, inasmuch as it leaves it indefinite what object is meant, merely intimating that it is not many objects but only one object that is intended. A, indeed, is only a variety of our word one, ane. Being so, its original form was en. The n is now dropt before a consonant for the sake of euphony (Greek eu, well, and phoné, a sound;-meaning agreeable sound).
Contrasted with the indefinite article a, is another form which bears the name of the definite article; that is, the. The is a reduced form of these. Consequently the refers to an object previously mentioned or known; as,
Alfred soon reads TO ME the obscure writing and manuscript. Me is a pronoun, as we found he to be. Me, you see, holds the place of a noun. Me is the objective case corresponding to the nominative case I. Our pronouns, as you here see, have some diversities of case, for in them you find varying forms corresponding to varieties of meaning. The other word just added,-namely, to, is called a preposition. The word preposition signifies, according to its Latin element, that which is put before; a preposition, then, is a word put before a noun; and it is put before a noun, in order to modify its signification, or mark the relation in which the noun stands to another word, or to other words; e. g.— he gave the book to he took the book from he read the book with he bought the book of
where to, from, with, and of are prepositions.
In the ordinary list of the parts of speech stands the participle. This word, of Latin origin, denotes the partaker (from pars, a part, and capio, I take). The participle is so denominated because it partakes of the qualities of the verb and the adjective. Thus shining is a participle from the verb to shine. It may also be employed as an adjective. Thus,
PARTICIPLE. The sun shining disperses the clouds.
The right of the participle to be accounted a separate part of speech has been contested not without reason. Perhaps less valid is the claim of the interjection. An interjection (inter, between; and jacio, I cast) is a sound of surprise, or sorrow, thrown out under the impulse of strong and sudden emotion, as O! Oh! Ah. and is with little propriety placed among the forms of articulate speech. Let us introduce a participle into our model.
The form is thus seen to comprise nine parts of speech. If the interjection, or exclamation, is to be reckoned a part of speech it may be prefixed in the shape of Yes! Here, then, we find a condensed view of all the parts of speech, and in the remarks by which the view has been prefaced and prepared, lies the kernel of the entire English Grammar. If you have gone with me understandingly thus far, you will have no difficulty in following me to the end, for having developed these general facts and principles, I have now only to take up each part of speech in succession, and in connexion with it, enter into such particulars as may appear desirable with a view to my object.
Before I close the chapter, however, I will add a few general remarks respecting the actual classification, which bears the name of the nine (or ten) parts of speech. The aim of the classifi. cation is to arrange under separate heads all the words of the English (or any other) language. Now a good classification has two qualities; first, it is exhaustive; secondly, it is distinctive. It is exhaustive, that is, it comprises and places under some suitable head, all the facts. It is distinctive,—that is, it makes such clear and sharp distinctions as to place the several facts each under its own head, without confounding similar facts together, or putting under one head, facts which may as properly stand under another head. The classification under review is neither exhaustive nor distinctive. It is not exhaustive, for it leaves out the infinitive mood which has as good a right to be called a part of speech as the participle. It is not distinctive, for the term adjective makes no distinction where a distinction exists, and the term participle makes a distinction where no distinction is required. Indeed the classification is wholly unscientific, being based not on a principle, but on vague and general views. Something less objectionable may be offered in the following words.
brave Nelson, defying danger,
brave Nelson, defying danger and death,
Other explanatory words or phrases might be added. Thus to the
brave Nelson fought and conquered the enemy,
2. Propositions with an object.
The universe proclaims its author.
Qualifying words may be added at will, as
3. Propositions with a subject and object qualified.
A diligent scholar learns all his lessons.
I subjoin some fragments to be made into complete sentences :
Propositions lacking subjects.
leads a blind man.
aids his sick mother.
Speech corresponds to the realities which it represents. Those realities are thoughts and things. Now, thoughts and things may be reduced to three classes:-1, Objects; 2, qualities of objects; 3, actions. Consequently the essential parts of speech are the noun, the adjective, and the verb. But objects and their qualities are the same things differently viewed. We may therefore strike out qualities. Thus we have two classes left, namely, the noun and the verb. Verbs, however, are the names of action, as nouns are the names of being. Hence language resolves itself into names. We may, then, declare that speech is made up of names. These names may be expanded and divided into 1, names of being, or neglect their duty. nouns; 2, names of action, or verbs; and 3, names of qualities, or adjectives. Under the last head, or names of qualities, may stand other parts of speech, for the adverb names the quality of the action of the verb, and the article names the extent in which the noun is to be taken. The term particles has not inappropriately been applied to adverbs and conjunctions, for, to a considerable degree they appear to be parts (particles, that is, little parts) or fragments of once existing nouns and verbs. If, however, our analysis of language into names of being and names of action, is correct, then the sentence which, as given above, contains all the nine parts of speech, may be reduced to two; as,
3. Propositions lacking verbs. the eldest sister the younger ones. the father his incorrigible son. noisy boys the neighbourhood.
- public order.
a grateful daughter tender mother.
our human infirmities. the providence of God - our lot on earth.
It may here be necessary, by anticipation, to inform the totally
SINGULAR: a boy loves; the house stands; the duck swims.
The rule might be put in another form, as, when the noun has an
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J. M. H-The term "rock" is, in Geology, applied to all the mineral masses which compose the crust of the earth, whether they be clay or sand, soft or hard,-e g., any soft clay is a rock. A book lying on the table has all its leaves horizontal and parallel; but if it be partly opened, and put to rest on the table with its back upwards, the leaves will dip, some to the right and the others to the left. The two downward strokes in the letter A dip in different directions. Fossil wood and vegetables are not reckoned "beings" in the science of Paleontology. FRENCH.-J. W. (York), and R. MELLORS (Nottingham): The French grammarians say, We have only one article in French, which is, le for the masculine singular, la for the feminine singular, and les for the plural of both genders; as, LE mérite, LA vertu, LES talents ont droit à nos hommages;" that is, merit, virtue, talents, have a right to our respect. They also say, "Gender is the property which substantives possess of representing the distinction of the sexes. There are consequently two genders, the masculine for the names of male beings, as man, lion; and the feminine for the names of female beings, as woman, lioness. Substantives representing inanimate beings ought to have no gender; yet custom has assigned to them, but arbitrarily, both genders. Thus, soleil, chateau, pays, have been made of the masculine gender, and lune, maison, ville, of the feminine gender."
TROIS ECOLIERS ATTENTIFS (Liverpool): The imperfect past tense j'avais is employed to signify I was having, or I used to have; it leaves the beginning, middle, and end of the action undetermined. The definite past tense j'eus, is employed to signify I had, or did have; it denotes an action completed and entirely past.-EDITH M-IE, (Oxfordshire): Du, des, de la, are used before substantives in a partitive sense, that is, to denote a part or a portion of the persons or things spoken of: thus, il a du papier, that is, quelque papier; vous avez de la fortune, that is, quelque fortune; nous possedons des amis,-that is, quelque amis. The article is omitted and de alone is used when the substantive taken in a partitive sense is preceded by an adjective; thus, donnez moi de bon pain; je bois d'excellente biere; il possede de belles maisons. But in the second part of the French lessons more specific rules will be given J. W. S. (Glasgow): The French exercises are so constructed that with a very little perseverance, it will be seen that the English exercises form a sort of key to the French, and the French to the English.-P. M. K. (Greenock): There are three kinds of negation in French: ne, ne pas, and ne point; thus, je n'ose, je n'ose pas, and je n'ose point; all signify I dare not; but ne is the feeblest negation, ne point the strongest, and ne pas the medium state. The words pas and point are omitted when there is in the sentence any expression or word having a negative meaning; as, guère, jamais, nul, nullement, aucun, rien, personne, and ni repeated; also ne.. que, signify ing only.
tion; yet these are evidently employed by the writer to remove the harshness of the double aspirate of h, for one of them is removed by the use of an.-The question of DISCIPULUS (Wandsworth) is one in Inverse Proportion; for if you have to pay £600 in 105 days, and having paid down £250 now, you are to pay £350 in a certain time, this must be greater than 105 days; therefore, say as £350: £600 :: 105 days: 180 days, answer.-LLEWELLYNN LLOYD (Norwich): 5451776000 cubic yards make a cubic mile; in a cubic yard there are 168 imperial gallons, and nearly a quarter of a gallon more; or, more accurately, this fraction is about four-fifteenths of a gallon.
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dicular height of the triangle is the centre or point directly over which the fourth tree must stand, we say that if a circle be described about an equilateral triangle, he will find this point the centre of the circle. -A SCHOOL ASSISTANT (Reigate) has proposed a good plan of study for himself, Botany, Natural History, and German-a good interchange. Ornithology shall find its place and time. A CONSTANT READER shall have drawing-W. L. (Somerset-place) should get an admission ticket to the British Museum, where he might read all day, and be sure to ** ¿PORTFOLIOS for enclosing 26 numbers of THE POPULAR EDUCAfind Horne Tooke's Diversions of Purley." The study of two lan-TOR, price 18. 6d., may be procured at our office. These Portfolios are guages such as the Italian and Spanish might facilitate each other, but so constructed as to form, upon the completion of each volume, a neat we think a language and a science are better companions.-The plan of Case for binding the same, which will be done at a trifling expense by T. B. K. (Macclesfield) would defeat the purpose of making good scholars; any bookbinder. answering questions would then become mere school routine.-LUCIAS is perhaps rather hypercritical; the a and the an escaped our observa
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LESSONS IN ANCIENT HISTORY.-No. VII.
THE sun of Egypt was now fast setting. Ptolemy Epiphanes,
tion he ascribed to his brother, and he took the field against him. Philometor came off victorious, but treated Physcon with the utmost leniency, reinstated him in his dominions, and added to his territorial possession.
Philometor having thus asserted his right to the island of Cyprus, invested one Archias with the office of governor. He proved a traitor. He agreed with Demetrius, king of Syria, to give up the island to him for five hundred talents. His treason was discovered, and to escape the punishment due to his crime he put an end to his life. Philometor now sought to avenge himself on Demetrius, and set up in the person of Alexander Balas, a pretender to the crown of Syria. But though Philo
the whole kingdom, except Pelusium, to Philometor. The two brothers agreed to reign jointly, and to make common cause against the common enemy. But no sooner did they feel themselves secure against foreign power than they quarrelled. Their differences came to such a height that Philometor was a second time driven from the throne. He appealed to the Roman senate, who divided the Egyptian dominions between the two brothers. Though the treaty was confirmed with oaths and accompanying sacrifices, it was not kept inviolate. Physcon was dissatisfied, and tried every possible expedient to wrest the island of Cyprus from his brother. His unjust procedure awakened the opposition of his own subjects, who laid in wait for his life. This opposi
metor faithfully maintained the pretensions of the usurper, and even gave him his own daughter in marriage, Balas dared soon afterwards to enter into a conspiracy against his benefactor. This roused the wrath of Philometor so much that he marched against Balas. In an engagement which followed, he came off victorious; the wounds, however, which he received caused his death after a reign of thirty-six years.
By the death of his brother, and his marriage with Cleopatra, his brother's widow, Physcon came to the throne of Egypt. On the day of his marriage with Cleopatra, he caused her infant This was followed by cruelties towards his subjects. He put to son, his own nephew, and heir to the throne, to be murdered. death all who showed the least pity for the death of the young 14