each other, as in fig. 19; in this case, they for four right angles, as A B C, ABD, DBE, and E B C. Right anges may have their legs placed in all possible positions with regara to the horizon, as in fig. 20. An angle which is less that a right angle is called acute, Fig. 20.

from the Lat. acutus, having a sharp edge, as in fig. 21. An angle which is greater than a right angle is called obtuse, from the Lat. obtusus, blunt, as in fig. 22. When one straight line meets another at any point between its extremities, it always makes either two right angles, as in fig. 18, or two angles which are together equal to two right angles, as in fig. 23, one being acute, and the other obtuse. When two straight lines cross each other, they always make either four right angles, as in fig. 19, or four angles which are together equal to four right angles, as in fig. 24, two being acute and equal to each other, and two being obtuse and equal to each other. Thus, the three kinds of angles, right, acute, Fig. 21. and obtuse, are all that are spoken of in distinguishing plane angles from each other. It may also be

observed, that two right angles occupy all the space about a point on one side of any straight line and four right angles all the space about a point on both sides of it. Hence all the space made by any number of straight lines meeting in a point, are together equal to four right angles.

D

A circle is well defined to be a figure such that its boundary, called its circumference (from the Lat. circumferens, carrying round) or outline, is a line everywhere, that is, at all points, equally distant from a fixed point within the figure, which is called the centre (from the Greek kentron, a point), see fig. 25. The straigh line drawn from the centre to the circumference is called the radius of the circle (from the Lat. radius, a rod, or spoke of wheel), see fig. 25. The straight line drawn through the centre, Fig. 26.

a

When a triangle has its three sides all unequal information to the ornamental and architectural draughtsman; and it is called a scalene triangle. Scalene means unequal-legged.

A triangle is also said to be rightangled when it has one right angle; it

cannot have more than one right angle.

An obtuse-angled triangle is that which

it is of nearly equal utility in all landscape drawing which comprises buildings,-the buildings being actually constructed by strict geometrical rules. The architect, indeed, cannot work without them. Should we not, then, in our representations or drawings bear this in mind? We cannot fail to do so, if the principles be well understood, and it is only then that we can be said to draw

has one obtuse angle; it cannot have more than one with unimpeachable accuracy.
obtuse angle.

An acute-angled triangle is that which has three acute angles; it cannot have less than these, otherwise it would become one or

other of the preceding two triangles.

A square has four sides and four angles, all its sides being equal, and all its angles right angles.

An oblong has all its angles right angles, and has four sides, but the sides are unequal. It is sometimes called a long square, but this is an absurd name. No side of a square can be longer than another.

A rhombus, or lozenge, sometimes called a diamond, or diamondshaped figure, has all its sides equal, but its angles are oblique, i. e., not right angles.

A rhomboid has its sides equal in pairs, opposite to one another; but

the one pair is not equal to the other pair, and its angles are oblique.

These four figures are all parallelograms (pa-ra-lel'-o-gram), the first two being right-angled parallelograms-the square having this distinction, that all its sides are equal.

All other four-sided figures are called trapeziums, or trapezoids, the trapezoid having one pair of its opposite sides parallel, and the trapezium none of its sides equal nor parallel. Trape'zium means a table or slab.

A five-sided figure is called a pentagon; and a sixsided figure, a hexagon. A seven-sided figure is a heptagon; a

figure with eight sides is an octagon; one with nine sides is an enneagon; and one with ten sides is a decagon. Accent the first syllable in all these names, thus: pen'-ta-gon, dek'-a-gon. When the sides are all equal, and the angles also all equal, the figures are said to be regular; as a regular pentagon, a regular hexagon, &c. When the sides are not all equal, or the angles not all equal, the figure is called irregular; as, an irregular heptagon, decagon, &c. A many-sided figure is sometimes called a multilateral figure, and a triangle, a trilateral figure, and four-sided figures are very commonly called quadrilaterals.

By fixing these definitions in your memory, you will get distinctly-shaped images in your mind, which will last you through your whole life, and become clearer the oftener you refer to them.

It is scarcely possible to overrate the importance of geometrical

True, it is not absolutely necessary that you should study Euclid along with these lessons; but if you have any inclination for the study of geometry at greater length than can be given in these lessons, we cannot too strongly advise you to follow that inclination. For, if well followed up, you will thus make an acquisition of which the importance cannot be conceived until it be attained. The proportions of form and of quantity regulate all the works of nature.

The old Greeks assigned to the Graces and to the Muses the origin and the patronage of the arts. There is, indeed, a verbal connexion between the Graces and gratitude; and it may be truly said that all the arts are grateful as well as graceful. They return to the student, in the amplest manner, every attention he bestows upon them; and from them, at last, he receives his crown of laurel.

Endeavour to commit the greater part of this lesson to memory, as we shall have to refer to it from time to time throughout this course, Give it your early and best attention; and read, also, the lessons in practical geometry already mentioned. If you make yourself well acquainted with geometry, you will find in drawing natural objects that you know the leading characteristics of an immense nun.ber of forms at a glance, while in the most complex forms and outlines you will be able to dissect them, and to separate one component part from another with comparative ease. Read, again, what is said of outline in the first lesson, and you will see that, as outline is necessarily composed of lines, geometry must so far govern outline,-not, indeed, rigidly in all cases, as nature possesses a free hand; but you will still find yourself compelled to go to geometry for the forms and principles which nature handles with such freedom.

In our next lesson we shall treat of the drawing of curved and mixed outline. In the meantime, we recommend you to read both these lessons over again, and to practise them with the utmost care until you acquire a readiness in them which will be a prelude to future success.

LESSONS IN LATIN.-No. XXXVII.
By JOHN R. BEARD, D.D.

DEVIATIONS IN THE THIRD CONJUGATION.
7. Perfect with Reduplication.

THE reduplication in the verbs, the first vowel of whose stem is i, o, or u, consists in the repetition of the first consonant of the stem, together with that vowel; in the rest, however, it consists in the repetition of the first consonant of the stem, together with e. The compounds have, in the perfect, no reduplication; except those from curro, I run; disco, I learn; and posco, I demand.

Com

i. Cado, cadere, cecidi, casum, to fall, happen. pounds are in cido, cidere, cidi, casum, thus: occido, I go down, die; incido, I fall on (E. R. incident); recido, I fall back; the rest want the supine; as, concido, concidere, concidip to fall together.

ii. Caedo, caedere, cecidi, caesum, to cut, to kill. Compounds are in cido, cidere, cidi, cisum; as, occido, I put to death.

iii. Cano, canere, cecini, cantum, to sing. Compounds in cino, cinere, cinui; so concino, to sing together; and occino, to sing inauspiciously; the rest are without perfect and supine. iv. Curro, currere, cucurri, cursum, to run. Most of the compounds in the perfect have, but oftener have not, the reduplication.

V.

Disco, discere, didici (no supine, but disciturus), to learn; so the compounds, as perdisco, perdiscere, perdidici, to learn thoroughly. vi. Fallo, fallere, fefelli, falsum, to deceive; fallit me, it escapes me, I am not aware, I am unconscious. The participle falsus, false, is mostly employed as an adjective; compound, refello, refellere, refelli (no supine), to refute.

vii. (Pango) pangere, pepigi, pactum, to conclude a treaty. | eggs a-day (in dies) do your hens lay? thy mother has borne a son; The present, with this meaning, is supplied by paciscor; but pango, in the sense I strike, fasten, has panxi (seldom pegi), panctum (pactum, E. R. pact). Compounds, pingo, pingere, pegi, pactum; as, compingo, I put together; depango, to fix in; and repango, to set into (without the perfect)..

In eodem prato pascebantur tres boves in maxima concordia, et The hen has laid an egg; the hens will lay eggs; how many sic ab omni ferarum incursione tuti erant. Sed dissidio inter illos

boni sit in concordiâ

orto, singuli a feris petiti et laniati sunt.-Fabula docet quantum trammelled by past conclusions, as they will impede their exercise and hinder their growth; thus forethought will enable us to profit by experience, and experience teach us to exercise forethought.

ASINUS.

Asinus pelle leonis indutus territabat homines et bestias, tanquam leo esset. Sed forte, dum se celerius movet, aures eminebant; unde agnitus, in pistrinum abductus est, ubi poenas petulantiae dedit. Haec fabula stolidos notat, qui immeritis honoribus super

biunt.

Vulpes, is, f, a fox; perterreo, ere, ui Itus 2, to alarm; conspicor, ari, atus sum, dep. to behold; nequaquam, by no means; cancer, cri, m. a crab; obliquus, oblique, across, sidewise; gressus, ûs, m. a step; pergo, pergere, perrexi, perrectum 3, to proceed; rectâ, viâ, in a straight path, straight forward; dissidium, i, n. disagreement; lanio, are 1, to cut up like a butcher, tear, rend; quantum boni, literally, how much of good, that is, how much good; tanquam, as if; emineo, eminére, eminui 2, to show one's self; pistrinum, i, n. a mill; petulantia, ae, f. impudence; inhio 1, to grasp at, to long for, to covet; perdo, perdere, perdidi, perditum 3, to lose, destroy.

THE PHILOSOPHY OF STUDY.-No. II.

"Industry is the law of our being: it is the demand of nature, of reason, and of God."

ADVICE is good or bad according to the result which it produces. The advice which we gave in our last lesson on the necessity of forethought may be good advice to some, but it is likely, if left alone, to prove bad advice to others. Men when driven from one extremity are ever apt to fly to another, or rather, they carry their old principle into their new course of action, and instead of the result desired, produce a new one as opposed to it as the course they have left.

Reflection rightly exercised is opposed to rashness, but those who have been accustomed to act inconsiderately, will, when called to reflect, carry their want of consideration even into the act of reflection.

We are not prepared to enter here into a full consideration of the nature of forethought and the manner in which it ought to be exercised, but it is necessary that we should say something of it in order to prevent the misapplication of the advice which we have already given. Nothing will better serve this purpose than to inculcate the necessity of patience, both for learning the nature and acquiring the habit of this kind of reflection.

We have said that forethought is a consideration of the advantages and disadvantages of the course which you propose to pursue; we may add that it is a consideration of every possible course in order that you may choose the best.

From these statements we may make the two following deductions. That as the exercise of forethought implies the consideration of many things with which we are imperfectly acquainted, it is not fitted to lead to conclusions of absolute certainty, or to give the assurance of dogmatical accuracy; and, that even if possessed of all the materials for a correct decision, it were idle to expect an unpractised judgment to lead at once to the proper conclusion.

Trusting that these hints will be sufficient to prevent any hasty misapplication of what we have said on the exercise of forethought, we will now proceed to the next part of our subject, the consideration of the plan of study.

He whose eye has scanned the boundary of a mighty forest till he has formed a conception of its grandeur and magn.ficence, or whose footstep has measured its depths till he has familiarised himself with its variety of form and foliage, may form a conception of the power of development in material things, when he conceives it shrunk up into a single seed for each species which it incloses in its countless combinations. From the effects of development in the world of matter, we may form an idea of its power in the world of mind. There is no better test of truth than its productiveness. One correct idea rapidly branches forth into others; it attracts to itself nourishment from all around it, and grows on the materials of everyday observation and experience. The first principles of knowledge are few, simple, and obvious; so are the first principles of the art of acquiring it. Let it not be supposed, then, that in treating study as a science, we are introducing you to vague and abstract discussions on matters of remote or uncertain import; it is our object, on the contrary, to set before you those simple and obvious elementary truths, which, if fairly received and fully carried out, will secure for themselves a development which will put our labour in inculcating, and yours in receiving them, at as great a disproportion to their results as is the single seed to the stately forest.

Whoever studies must of necessity have a plan of study,that is to say, he must have something which he proposes to do, and a certain way in which he proposes to do it. There is labour to be undergone, and he must have the expectation of advantages to be derived from it; there is an end to be gained, and he must have the conception of means to attain it.

Let us see what extent of consideration is necessary to lead to this result.

The choice of a plan of study may be arbitrary, or it may be intelligent. By an arbitrary choice we understand one which is formed without a decisive reason; by an intelligent choice one which proceeds on a full knowledge and accurate understanding of everything that affects its wisdom or folly. From this it will be seen that an arbitrary choice is not necessarily an unreasonable one. Where there is sufficient ground for the decisive choice of one of two courses, it is unreasonable not to adopt it; but where it is necessary to make a choice without such reasons as to render the adoption of one of the alternatives imperative, it is proper to choose that which appears the best, although the choice is arbitrary to the extent to which the grounds for it are imperfect. An arbitrary choice, then, is reasonable only when an intelligent one is impossible.

The choice of a plan of studies is arbitrary when the grounds of its adoption are derived from a partial consideration of the end for which it is intended, and the circumstances in which it is made. Let us consider how far such a choice is reasonable. The object with which we enter on this investigation is to show the importance of an intelligent choice of studies. To effect this there are two objections which it is necessary to answer,first, that which questions the possibility of such an investigation as this supposes; and second, that which questions its propriety. The first may be very summarily disposed of. We only ask an Our object in making these observations is to show that investigation to the extent to which it is possible, and the diffiforethought does not render us independent of experience; at culty of carrying it to a state of absolute completeness does the same time it must be remembered, that, while it is only a not hinder it from being pushed to the utmost limit which the degree of uncertainty which attaches to the exercise of fore-intelligence of the student renders practicable. It only remains thought, all is uncertain without it. Whether your information to show that it is advisable to do so. be great or small, whether your judgment be strong or weak, you may be sure of arriving at a better conclusion as the result of deliberation, than you could reach without it, and this while you are maturing your judgement, and rendering its decisions more unerring for the future.

We should learn from this the necessity of distinguishing between persistence and perseverance, and the danger of imagining that when once we have decided on a course of action, we may adhere to it for ever after. We should exercise forethought continuously, and study to keep our judgments un

In every practical undertaking we meet with those who are fonder of action than of reflection; to such, an arbitrary decision presents a ready way of cutting short a long investigation, and they may be ready to object that there are shorter and better ways of reaching the same result than that which we propose. It is true there are certain considerations which occur obviously to every one who proposes to enter on a course of study, and on which it may be easy for him to found a plan of procedure; and we readily admit that these considerations are usually the most valuable, but they are not the only one, and the object to be

gained by them may frequently be defeated by a want of proper metropolis retains its etymological signification, for Athens (for attention to others; and even these considerations themselves instance) was the mother of the colonies she planted. But now the have a much deeper import, and require a more extensive metropolis of England, namely, London, stands in no strictly investigation, than is apparent from any view of them which maternal relation to the provinces or even to the colonies of the may present itself to the unreflecting. empire. London is not the mother-city of the population of Lancashire, or of Calcutta, and its claim to bear the name metropolis arises almost exclusively from the fact that it is the centre of the empire, and the seat of its central government. So marked an instance of the departure of a word from its primitive meaning may teach you how cautious you should be in the etymological study of words, and how necessary it is in such studies to call in the aid of history and general knowledge.

Our word pyre is from the Greek pyr.

"When his brave son, upon the fun'ral pyre

He saw extended, and his beard on fire."

Dryden.

From pyr and latreia (Gr. worship) is formed pyrolatry, or fireworship, and from the same, with manteia (Gr. divination), is formed pyromancy, or divination by fire.

"Divination was invented by the Persians, and is seldom or never taken in good sense; there are four kinds of divination, hydromancy, pyromancy, aeromancy, geomancy."-Ayliffe. These four kinds you ought now to be able to make out for yourself, if I tell you in addition that aer is the Greek for air, the two terms being different forms of the same word.

From pyr we have also pyrotechnics, the art of making fireworks. Pyramid is derived from the same, as appears from the following instructive quotation :

There are three objections to which any plan of study founded on merely obvious considerations is liable. First, it involves a waste of time; second, it involves a risk of failure; and third, it involves a sacrifice of enjoyment. We will take a single illustration of these objections from what is perhaps the most common consideration in the choice of studies-that of taste. There are two things to be gained in the prosecution of any study; in order to obtain the full advantage of either, it is necessary that it should be kept in view both in its selection and pursuit. The one is the knowledge which we derive from the study itself, the other the facility which it gives us for the pursuit of other studies. Taste has regard only to its immediate object; therefore if we make it the sole consideration in the choice of our studies, we overlook altogether the half of the object of study; and no one who knows what study is will suppose that the advantages which are thus overlooked, will be gained to the same extent in the mere course of study which takes no cognisance of them, as if they were made one of its primary objects; and it is obvious that when two objects are to be gained, it is a waste of time to gain only one of them. But taste not only leads to the neglect of part of the aim of study, it leads also to the choice of inappropriate studies. There is a tendency among students to prefer the more advanced studies as apparently the most attractive, and this tendency constantly leads to the selections of studies for which they are not prepared. Hence, repeated and vexatious failures, and the ultimate risk of becoming disgusted with study altogether. From this it will be obvious that by making taste the sole guide to our studies we frequently defeat our own end, which is to increase the enjoyment of study; and a little further consideration will serve to show that we always do so. If enjoyment were merely its origin in the fact that a stone (alumen schisti) was employed for Sarcophagus, or flesh-devourer, the Greek name for coffin, had a contingent of study, we might at least be certain that in the purpose, which had the quality of accelerating decomposition. consulting our taste we were taking the best means to secure According to Pliny, bodies put into such coffins were, except the it; but it is not so. The student has a right to expect enjoy-teeth, totally destroyed within forty days. Perhaps from religious ment in his studies. There is enjoyment in the exercise of his considerations the Greeks took means to hasten the breaking up of powers, enjoyment in their expansion, enjoyment in the dis- the frame, as is instanced in their practice of burning the dead. covery of truth, and enjoyment in the contemplation of the beautiful. All these enjoyments, study is fitted to give, and we have a right to look for them at every step of our progress. But how and in what proportion? In proportion certainly to the progress we make; and as by studying taste alone, we lessen our progress in knowledge, we lessen also our enjoyment of study.

Whether the choice of studies be arbitrary or not, it usually proceeds from a complication of reasons. It is possible, therefore, that the simple consideration which we have presented in this illustration, may not be the sole one of any particular student; but the principle which it serves to illustrate holds good in every case where any important consideration is omitted, namely that such an omission is certain to occasion a similar deficiency in the plan of study. We may therefore generalise the deficiencies brought out in this particular case, and say that every plan of study chosen on arbitrary grounds is liable to these three objections:

First. The danger of omitting part of the object of study;
Second. The danger of choosing inappropriate studies; and,
Third. The certainty of lessening the enjoyment of study.

LESSONS IN ENGLISH.-No. XXIX.
By JOHN R. BEARD, D.D.

GREEK STEMS. (Concluded)

THE word metropolis, literally mother-city, shows how much terms, while they retain a trace of their primitive meaning, in process of time, deviate greatly therefrom. Metropolis originally had reference to the Greek system of colonisation, and was equivalent to our term mother-country; that is, the country to which each colony belonged. Properly, then, metropolis is the mother-country (in German, father-land), and the counterpart was colony. Here,

in how long a time and with what difficulty they were brought up so high, "The seven pyramids that are become wonders of the world; which Herodotus sheweth; towers they be, erected to such an height as exceedeth the handywork of man; of a huge breadthe in the bottome, and rising to a most sharp-pointed top; which figure in geometry is tearmed pyramis, for that [like] to the form of fire, it cometh to be small in the head, in fashion of a cone or pine-apple."-Holland.

song which was sung in the Greek theatre while the chorus moved Strophe, which properly signifies a turning, was the portion of a from one side of the stage to the other; when they began to move in the opposite direction, they sang the antistrophé, or opposite strophé.

To some it may not appear that enthusiast comes from theos; in

the Greek original, however, the derivation is clear. Enthusiasm, according to its derivation, denotes the presence of God in the soul, and an enthusiast was one who had God in his soul. Hence, word fell into bad odour, as may be seen in these words :anciently, enthusiasm was the same as inspiration. By degrees the

"I mean enthusiasm, which, laying by reason, would set up revelation without it. Whereby in effect it takes away both reason and revelation, and substitutes in the room of it the ungrounded fancies of a man's own brain, and assumes them for a foundation both of opinion and conduct."

-Locke.

Zoology is the science of life, that is, of animal life, as may appear in the quotation :

"Zoology is the noblest part of natural history, as it comprehends all sensitive beings, from reasonable man, through every species of animal life, till it descends to that point where sense is wholly extinct, and vegetation commences."-Pennant, "British Zoology.”

Azote, literally life-less, is also the name of the gas called nitrogen, in which animal life cannot be sustained.

The Greek a privative is found in several other words which form part of our language. It appears in azymes, mentioned in the preface to King James's translation of the Bible, and in the Rheims version of 1582. The word is made up of a, not; and zyme, leaven.