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LESSONS IN GEOLOGY.-IX. LITHOLOGY-PETROLOGY-GEOLOGICAL TERMS. UNDER the general term Geognosy is included all that can be said in relation to the structure of the matter composing the earth's crust. Such a description readily permits of a subdivision.

The rock-masses may be treated of as to their mineral, their internal structure, and those characters which may be determined by handling specimens, such as texture, construction, hardness, etc. All this is Lithology.

Petrology describes the larger characteristics of rock; the relative positions they occupy, and the disturbances they have undergone.

Neither of these sub-divisions treats of rocks arranged in geological groups. Hence this forms a third part of the subject, and to enable us to classify rocks chronologically-that is, to determine which rocks were deposited at or about the same time-we must appeal to their organic contents. The mineral composition is of little service. For instance, two sandstones, identical in their composition, may be found, which we know must have been formed at two periods separated by vast intervening ages; and this we discover by their fossil contents. Hence a study of fossils is of the greatest importance, and this has received the name of Palaeontology.

Mineralogy is a further sub-division of Lithology.

larger quantity were treated in the same manner, the basalt returned to its former stony appearance; but in doing so, it was observed that the molten mass congregated into little balls, and these increased in size by the continuous addition of more matter to their external coating. In due time these balls touched each other; but as their increasing capacity still continued, they were squeezed together; and as the expansive force progressed, their curved surfaces were flattened. Presuming the force in each ball to be exactly the same, by this process hexagonal (six-sided) short prisms would be produced. This will be sufficiently evident from Fig. 15.

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Fig. 14.

Lithology, as we have said, treats of the mineral composition of the rocks, but does not enter into the chemistry, etc., of these mineral elements. Thus we find the remark we made in the opening lesson is true. To be a perfect geologist we must begin with Chemistry. This teaches us the elements whereof all bodies are composed, and the laws of their combination. A step higher, and we reach Mineralogy, by which we are taught how those elements are arranged in bodies contained in the solid crust of the earth; the forms in which minerals appear, and their characteristics. Lithology groups these minerals into rocks, and forms the third division of our subject; Petrology tells how the rocks lie on the surface, their contortions, interstratifications, etc.; while Palæontology, from the fossils the rocks contain, groups them according to their ages, and writes a history of the animal life of the globe. Mineralogy will be treated separately; and for a further description of the minerals we shall have occasion to name, we refer the reader to the forthcoming lessons.

For some reason or other these spheres arranged themselves one above the other, so that a straight line would pass through their centres. This explains the formation of the columnar structure.

Certain green stones are found which appear in spherical masses. When exposed to the weather they are liable to exfoliate; that is, one coat after the other peels off, thus demonstrating their concretionary character, or that they were made by successive layers accumulating round a nucleus, probably in the same manner as the globules of basalt, in which the columnar structure originated.

All masses of rock are intersected by regular sets of cracks, which are termed joints. Without these it would be difficult to quarry stratified rocks, and impossible to hew out hard primary rocks.

Joints generally traverse rocks at right angles to each other. In granite quarries three sets frequently cut the stone into cubical

masses.

Their existence can only be accounted for by supposing they result from the shrinkage of the mass upon its consolidation. When these joints are very close to each other, and pass through the rock-mass in the same direction, the phenomenon is termed cleavage, and the rock splits into slates. Some stratified rocks readily divide into horizontal slabs, the planes of division coinciding with those of stratification. Such slabs are called flags or flagstones.

Fig. 15.

Technical Terms descriptive of the Structure and Internal Characters of Rocks.-Although the particles of a mineral may be arranged in a symmetrical order, forming a crystal, this formation never extends to large masses. No crystal has been discovered more than one or two feet long; but when a rock is composed of particles which are either crystals or fragments of crystals, it is said to be crystalline. Such is the structure of loaf-sugar. The granites and many of the primary rocks exhibit it. Occasionally a uniform structure is developed in large masses of rock; this is always columnar (Fig. 14), as in the basaltic rocks of the Giant's Causeway, in the north of Ireland, and in Fingal's Cave, on the opposite shore of the Isle of Staffa.

The number of the sides of the columns varies from three to ten. They fit so closely to each other that the blade of a knife is with difficulty inserted between them. When broken horizontally they exhibit a conchoidal fracture; that is, the surface of one piece is concave, the corresponding surface of the other being of course convex-like a ball-and-socket joint.

The origin of the columnar structure of rocks was proved experimentally by Mr. Gregory Watt. He caused a quantity of basaltic rock to be fused in a blast furnace. When a small portion of this was removed and allowed to cool, it assumed a vitreous character; that is, like glass, but not transparent. If a

VOL. III.

When the rock exhibits a disposition to break up into thin leaves, it is said to be laminated. Shales are clayey deposits which were once soft and plastic, but upon drying became intersected by numerous joints, which cause the mass to split up into small pieces.

Crystalline rocks are frequently found possessing a laminated structure; they are then schists, or of a schistose structure. Occasionally the term foliated is applied to rocks of this nature, from the leaf-like manner in which the layers overlie each other. Fissile is a general term which characterises all rocks which show any tendency to break up into small parts.

When a layer of rock reposes on a stratum of different material, its under surface must partake of smoothness or inequality of that stratum; this is denominated bedding. A stratum of rock is sometimes called a bed, but the word is becoming geologically obsolete. Seam, unfortunately, has two meanings; sometimes it is used to indicate the line which marks in a section the junction of two strata, and also it is applied to thin layers of mineral matter which traverse a series of strata. For example, thin beds of coal, a few inches or even feet thick, are frequently found at intervals in many strata; these would be called seams of coal. It is evident how the word has become applicable to each case. The thin bed was considered the line which divided the two layers of strata.

The above terms are descriptive of the structure of rockmasses. On examining a specimen in the hand, a closer inspection reveals to us its internal characters. If it be made up of the same kind of matter, the rock is homogeneous; when its particles are in grains, perceptible to the touch or plainly visible, the specimen is granular. Occasionally the material is arranged in fibres, as asbestos; it is then fibrous. When the fibres are distinct, long, fine crystals, it is said to be acicular (needle-like).

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A compact rock has its particles in close and firm proximity, but one which is friable permits of being crumbled. A porous specimen is full of holes, like pumice-stone, but when the pores are small it is said to be cellular or vesicular. Rocks are hard or soft, but beyond a general application these terms are not much in vogue. In mineralogy we shall find that much stress is laid on the comparative hardness of minerals.

coverings, mixed with the shells of larger inhabitants of the ocean. Marble is also carbonate of lime which has been submitted to the action of heat, and thereby rendered crystalline. Mountain limestone is so called because it appears in ranges of hills. It is very compact and dark-coloured. The walls in many parts of Ireland are built of this admirable material, which is found in great quantity in that island. In Sweden there is an instance where a vein of granite has passed through a mass of mountain limestone. This it rendered like marble where it had contact with it, and the white crystalline rock gradually shaded away to its original dark condition. The colour of this stone is considered to be due to carbon in a state of minute sub-division; but the quantity is so small as to evade detection by chemical means. Oolite is a species of limestone which appears in little round A stratum which has been deposited by aqueous agency is of grains, like the roe of fish ; hence its name. Each of these one of three characters. It is either of an arenaceous quality-grains has a particle of sand for a nucleus, round which the that is, a sandstone; or it is argillaceous-that is, a clay; or it limestone seems to have congregated. is a limestone.

Rocks which are composed of water-worn pebbles cemented together are conglomerates. If angular fragments take the place of the pebbles, a breccia is the result, which word is the Italian for "fragment." A pebble is a small piece of mineral matter, worn round by the action of water. When the sea-beach is not sand, but stones rounded by the waves, the accumulation of pebbles is a shingle.

If the size of the pebble exceed a few pounds in weight, it becomes a boulder.

In each of the great systems in which rocks are classified, these three species of rocks appear. Each system has its limestone, its sandstone, and its argillaceous rocks, or its clay beds. Sand, of which arenaceous rocks are composed, is properly small particles of quartz, which is the hardest constituent of granite, and therefore most successfully resists the process of attrition.

Quartz is pure silex or flint, and may at once be recognised in a specimen of granite, as those clear, semi-transparent grains. When granite decomposes, these grains remain intact, or nearly so; for silex is most difficult to dissolve. Particles of sand are always rounded, as if by the action of running water.

Sandstone is an aggregate of these particles, which are held

together in some cases without any apparent cement; but often calcareous or siliceous matter is present in a small quantity, which binds the arenaceous particles together. Sometimes clay or the oxide of iron forms this cement, and to this latter substance the red colour which frequently tints sandstones is due. Some fine-grained sandstones are found which contain minute scales of shining matter; this is mica, another constituent of granite, and such rocks are termed micaceous sandstones. sandstones are found among the earlier formations.

These

Grit is applied to sandstones whose grains are very coarse. Argillaceous Rocks.-Any earth which is sufficiently plastic to be kneaded by the hand is, in common language, a clay. Strictly speaking, clay is composed of siliceous and aluminous particles. Kaolin, or porcelain clay, is the finest of the clays. Its composition is given in this table, in which it is compared with other specimens::-

When magnesia is present in a quantity as much as thirtyfive per cent., the rock is termed dolomite.

When clay and sand are mixed in a considerable quantity with lime, a loam is formed. When only a little sand is present, and the mixture is of a more firm texture than a loam, it is denominated a narl. It is not a usual thing to find any limestone pure; they all contain an admixture of foreign matter.

These are the general characteristics of the great divisions of rocks. Those deposits which are peculiar to the various formations will be alluded to in their proper places.

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11. ένδεκακις.

Kaolin.

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Clay.

Clay.

12. δωδεκακις.

13. τρισκαιδεκακις.

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[σαρεσκαιδεκακις.

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15. πεντεκαιδεκακις.

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16. έκκαιδεκακις.

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17. ἑπτακαιδεκακις.

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All clays are formed by the very fine disintegrated particles of water-worn rocks. Mud is matter also formed of such particles, but it contains a mixture of animal or vegetable matter, or both. Shale is hardened clay, but if it be softened by water it will exhibit the plastic properties of that body. All clays when breathed upon emit a peculiar earthy smell.

Calcareous Rocks. All rocks of this description may be at once discovered by the application of a few drops of any acid. Effervescence at once takes place, owing to the escape of carbonic acid gas, which is always associated with lime, forming a carbonate of that base.

There are many varieties of limestone. Chalk, as we have said, is due to the incessant work of minute animalcules, which separate the lime from the sea-water to form their calcareous |

18. οκτωκαιδεκακις. 19. εννεακαιδεκακις.

20. εικοσακις.

30. τριακοντακις.

40. τετταρακοντακις οι [τεσσαρακοντακις.

50. πεντηκοντακις.

60. ἑξηκοντακις.

70. ἑβδομηκοντακις.
80. ογδοηκοντακις.
90. ενενηκοντακις.
100. ἑκατοντακις.
200, διακοσιακις.
300. τριακοσιακις.
1000. χιλιάκις.
2000. δισχιλιακις.

10,000. μυριάκις.
20,000. δισμυριάκις.

RECAPITULATORY EXERCISES FROM THE CLASSICS.

1. Αναχαρσις κρειττον ελεγεν, ένα φίλον εχειν πολλου αξιον, η πολλους μηδενος αξίους. 2. Αννων, ὁ πρεσβύτερος, εκ της Λιβυης επέρασε μεγαλην δυναμιν εις Σικελίαν, πεζων μυριάδας πεντε, ἱππεις δε εξακισχιλιους, ελέφαντας δε έξηκοντα. 3. Τους Σηρας ἱστορουσι μέχρι τριακοσιων ζην ετων, και τους Χαλδαίους ὑπερ τα έκατον ετη βίουν λόγος (εστι). 4. Αργανθώνιος, ὁ Ταρτησσιων βασιλευς, πεντηκοντα και έκατον ετη βίωσαι λεγεται. 5. Ο Πλατων ετελεύτησε τῳ πρωτῳ της ογδόης και εκατοστής Ολυμπιαδος, βιους ετος ἐν προς τοις ογδοήκοντα. 6. Δημήτριος τις είπε τῳ Νέρωνι συ μεν απειλεις εμοι τον θάνατον, σοι δε ἡ φυσις. 7. Σχολαστικος απόρων, τα βιβλια αυτου επιπρασκε, και γραφων προς τον πατερα έλεγε, συγχαιρε ἡμιν, πατερ, ηδη γαρ ήμας τα βιβλια τρεφει. 8. Αναχαρσις ὁ Σκύθης ερωτηθεις ύπο τινος, τι εστι πολεμιον ανθρωποις; αυτοι, έφη, ἑαυτοις. 9. Σχολαστικός οικιαν πωλων, λιθον απ' αυτης εις δειγμα περιέφερε. 10. Κρίτης ων, αει ταύτα περι των αυτών γιγνωσκε, ουδεν προς χαριν ποιων. 11. Vuxns etiμeλov τns σEAUTOV. 12. Βουλου αρεσκειν πασι. 13. Παντων μάλιστα σεαυτον αισχυνου. 14. Ῥᾷστον ἁπάντων εστιν

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1. Αξιος, -α, -ον, worth, worthy ; πολλ. αξ., of great value. 2. Αννων, -ωνος, δ, Hanno, the Carthaginian general. Επέρασε (from πέρας, beyond), transported, carried over; πεζων (from πεζος), of foot-soldiers; ἱππεις (ίππευς), horsemen, cavalry.

3. Σηρας (Σηρ, -os), the Seres, an Eastern people who produced alk; ζην (infin. of Qaw, I live), to live: Χαλδαίους, the Chaldeans; τα έκατον ετη, literally, above the hundred years (so with either number the article is used when a whole is contemplated, in construing into English you must drop the article in such cases) : βιουν (from βιοω, I live, Bios, life), to live.

4. Βιώσαι, to have lived; λεγεται, is said.

5. Ετελεύτησε (from τελος, an end), came to an end, died; Ολυμπίας, άδος, ή, an Olympiad, a period of five years (the Greeks reckoned time by Olympiads, as we date from the birth of Christ, A.D.); βιους, having lived; ετος έν, etc., one year to eighty, that is 81 years.

6. Ειπε, said; Νερων, -ωνος, δ, the Roman emperor Nero; απειλεις (from απειλεω, I threaten), threatenest.

7. Σκολαστικός, -ου, δ, an idler, a witling; απορων, being in dificulties ; επιπρασκε, sold.

8. Ερωτηθείς (ερωταω, I ask), being asked; εφη, said, answered.

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αναπεσειν (πιπτω, I fall), to sit down; χορτος, -ου, δ, grass ; ανέπεσον, they sat down; τον αριθ., as to number, that is, in number, or to the number; ώσει, about.

2. Των ακουσαν. (ακουω, I hear), of those who heard; επιστευσαν (πίστις, faith), believed; εγενήθη (γινομαι, I become), was, rose to.

3. Ειδον (είδος, appearance, shape), I saw ; ηκουσα, I heard; αρνιον, -ου, το, lamb ; εσφαγόμενον (σφάγιον, a victim).

4. 'O έχων νουν, . let him who has; ψηφισάτω (ψηφος, α pebble; the Greeks usually reckoned with beans, as the Latins did with pebbles, calculi, whence calculate), calculate.

5. Διεκώλυε (κωλύω, I hinder), tried to hinder; βαπτισθηναι, to be baptised; βαπτω, I dip; ερχῃ, comest thou ?

6. Βαστάζετε (βαστάζω, I carry), bear; οὕτως, thus ; αναπλη. (ανα, up, πληρόω, I fill), fill up, fulfil.

7. Καυχησις, εως, ή, boasting; συνειδησις, εως, ή, conscience; 'απλότης, ητος, ή, simplicity; ειλικρίνεια, -ας, ἡ, sincerity; σαρκικος (σαρξ, flesh), fleshly ; ανεστράφημεν, we have behaved (conducted) ourselves, we have acted; περισσότερως (περι, denoting abundance), more exceedingly.

8. Παράκλησις, εως, ή, exhortation, comfort, παραμυθιον, -ου, το, solace, soothing; κοινωνία, -ας, ἡ, community; πνεύμα, ατος, spirit; σπλαγχνον, -ου, το, bowels; οικτιρμος, -ου, δ, pity; πληρώσατε (πληρόω, I fill), fulfil; φρενητε (φρενες, the mind), that ye desire, aim at, love; συμψυχοι (ψυχη, the soul), being of the same soul, of one soul; ερίθεια, -us, ή, strife; κενοδοξία (κενος, empty), vainglory; ταπεινοφροσυνη, -ης, ἡ (ταπεινος, humble), lowliness of mind, ἡγουμενοι, thinking, considering; ὑπερέχειν, to be superior; σκοπούντες (σκοπειν, to look, hence επισκοπείν, το overlook, whence our word bishop), looking at.

REMARKS.

The pronouns are among the oldest words in every language.

9. Δειγμα, ατος, το, a specimen, περιέφερε (περι and φέρω), Consequently, if in two languages the pronouns are found to

carried about.

10. Γιγνωσκε, pronounce the same judgment; προς χάριν ποιων, doing nothing for favour.

12. Αρεσκειν, to please ; βουλου, wish (try). 13. Αισχύνου (αισχυνομαι), reverence.

14. Εξαπαταν, to deceive, cheat.

15. Αγνοεί, be thou ignorant.

16. Σκυτοτομος, -ου, δ, a leather cutter (from σκυτος, -ους, το, α hide, leather), ευγενης, well-born; αρχετ. απ. εμου, literally begins from me, that is, with me ; παύεται, comes to an end. 17. Απεκρινατο (απο and κρίνω), answered; ελπις, hope; και γαρ, for.

19. Φέρεται, carries itself (middle voice), flows ; εκβολη, ης, ή, a falling out of; μέχρι, up to, down to, until. 21. Εξελαύνει, marches.

EXTRACTS FROM THE NEW TESTAMENT.

have strong marks of resemblance, we may safely conclude that those two languages are akin to each other. Such marks of resemblance may be found by comparing the Greek and the English personal pronouns together. Thus the Greek εγω, through the Latin ego, is clearly the English I (also the German ich and the French je). Look at the Greek accusative με, the Latin me, and the English me. Again, compare the Greek συ, namely, σε, te, thee. The f (the e aspirated and so made he) i the Latin tu, and the English thou; also the accusatives,

obviously our he.

Similar remarks may be made with regard to the numerals. Obviously in structure, as well as in individual numbers, the Greek numeral system is the same as our own.

The student, if he has well attended to these lessons, may now rejoice in having made some considerable progress; and the progress he has made he may in a measure estimate by the comHyparative ease with which he has just read passages from the Greek New Testament.

1. Είπε δε ὁ Ιησους, Ποιησατε τους ανθρωπους αναπεσειν. δε χορτος πολύς εν τῳ τόπῳ. Ανέπεσον ουν οἱ ανδρες τον αριθμόν ώσει πεντακισχιλιοι (John vi. 10). 2. Πολλοι δε των ακουσαντων τον λόγον επιστευσαν και εγενήθη δ αριθμός των ανδρων ώσει χιλιάδες πέντε (Acts iv. 4). 3. Και είδον και ηκουσα φωνην αγγελων πολλών κυκλῳ του θρόνου και των ζωων και των πρεσΒυτέρων και ην δ αριθμός αυτών μυριάδες μυριάδων και χιλιάδες | χιλιάδων, λεγοντες φωνῇ μεγαλῃ, Αξιον εστι το αρνιον το εσφαγο μενον λαβειν την δυναμιν και πλούτον και σοφίαν και ισχυν και τιμήν και δοξαν και ευλογίαν (Rev. v. 11, 12). 4. Ο έχων νουν ψηφισάτω τον αριθμόν του θηριου αριθμος γαρ ανθρωπου εστι, και ο αριθμός αυτού (understand εστιν) χξς (Rev. xiii. 18). 5. Ο δε Ιωάννης διεκώλυεν αυτον, λεγων, Εγω χρειαν εχω ύπο σου βαπτισθήναι, και συ ερχῇ προς με; (Matt. iii. 14). 6. Αλληλων τα βαρη βασταζετε, και ούτως αναπληρωσατε τον νόμον του Χριστού (Gal. vi. 2). 7. Ἡ γαρ καυχησις ἡμων αύτη εστι, το μαρτύριον της συνειδήσεως ἡμων, ὅτι ἐν ἁπλοτητι και ειλικρινεια Θεον, ουκ εν σοφια σαρκική αλλ' εν χαριτι Θεού, ανεστράφημεν εν τῷ κόσμῳ, περισσότερως δε προς ύμας (2 Cor. i. 12.) ουν παράκλησις εν Χριστῳ, ει τι παραμύθιον αγαπης, ει τις κοινωνία πνεύματος, ει τινα σπλαγχνα και οικτιρμοί, πληρωσατε μου την χαραν, ίνα το αυτο φρονητε, την αυτην αγαπην έχοντες, συμψυχοι, το ἐν φρονούντες, μηδεν κατα εριθειαν η κενοδοξίαν, αλλά τη ταπει νυφροσύνη αλλήλους ἡγουμενοι ὑπερεχοντας ἑαυτων, μη τα έαυτων έκαστος σκοπουντες, αλλά και τα ἑτερων έκαστος (Philippians ii. 1-4).

VOCABULARY.

8. Ει τις

1. Ιησους, Jesus; ποιησατε (ποιεω, I make, do), make, cause to;

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KEY TO EXERCISES IN LESSONS IN GREEK.-XXI.
EXERCISE 70.-GREEK-ENGLISH.

1. The river Euphrates is four stadia in breadth. 2. The stadium of the Romans contains one hundred and twenty-five steps, or six hundred and twenty-five feet. 3. To Cyrus there were present thirty-five ships from Peloponnesus. 4. The breadth of the Sarus, a river of Cilicia, was three plethra. 5. The plethron contains a hundred feet. 6. Cydnus, a river of Cilicia, is two plethra wide. 7. The

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breadth of the Meander, a river of Phrygia, is twenty-five feet. 8. The parasang, that is, Persian measure, contains thirty stadia, or eighteen thousand seven hundred and fifty feet. 9. The calculation of the entire journey, the expedition and retreat, which is described by Xenophon, was two hundred and fifteen stadia, one thousand one hundred and fifty-five parasangs, thirty-four thousand six hundred and fifty stadia; and the length of time of the expedition and retreat was a year and three months. 10. The friendship of one intelligent person is better than the friendship of all unintelligent people. 11. This was the number of the army of Cyrus: of the Greeks there were ten thousand four hundred hoplites, two thousand five hundred targeteers; but of the Barbarians with Cyrus, there were one hundred thousand, and scythe-bearing chariots about twenty.

EXERCISE 71.-ENGLISH-GREEK.

1. Εἰς σύνετος φίλος εστι κρείττων πολλών ασυνετών. 2. Ta en éẞdounκοντα ποιει αμφι τας ήμερας δισμυρίας πέντε, πεντακοσίας και πεντήκοντα και πεντε. 3. Όλος ο αριθμός της όδου απο της μάχης εν Βαβυλώνι εις τα Κοτύωρα ύπο Ξενοφώντος συγγράφεται σταθμοι έκατον είκοσι, δυο παρασάγγαι εξακόσιοι είκοσι σταδια μύρια οκτακισχίλια εξακοσία, χρόνου δε το πλήθος οκτώ μήνες. 4. Ο αριθμός του στρατεύματος εστι τρισμύριοι ενιακισχίλιοι OKTAKOGIOL KAι ЯEVTпkovтa. 5. Eisi TeoσаPES σтPATNYOL TOV σTрATOV ÉKαTEP ́s των στρατιωτων τρισμυρίων εννακοσίων και εξήκοντα, 6. Пapnav ev Ty μαχη τρις τρισμύριοι και εξακισχίλιοι εξακόσιοι και πεντήκοντα των στρατιωτών, και άρματα δρεπανηφορα αμφι έκατον και πεντήκοντα.

GEOMETRICAL PERSPECTIVE.-XII.

DEL

upon the PP diminishes. Turn to Fig. 24, Vol. II., page 360, where the slabs of the pavement touching the PP are drawn to the size given by the scale; also fe, the perpendicular edge of the cube in Fig. 33, Vol. III., page 9, is another example. After this remark, it will be seen that the object may be made to touch the PP in more than one place, if it is placed at a distance from the PP, by means of one or more of its lines being produced to the PP as points of contact. Therefore, if we have the option of placing a line representing the PP anywhere in conjunction with one of these points of contact, besides our usual practice of putting it below the drawing, we have the advantage of distributing the measurements, which might be crowded upon this one line, upon other lines similarly placed for the same purpose. Any further remarks will be made as we proceed with the method of drawing the following problem :

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PROBLEM XXXV. (Fig. 57).-Two slabs or rectangular blocks, each of the same dimensions, 6 feet long, 4 feet broad, and 1 foot thick. One block is above the eye, the other below, resting on the ground; in every other respect the conditions of each are the same. Their long sides are 40° with the PP; their nearest angles 3 fest to the left of the eye, and 2 feet within the PP. Height of the eye, 4 feet, and distance of nearest angle to the eye 10 feet. The vertical space between the blocks is 6.feet.

Our motive for employing two blocks of the same dimensions and position, with the one exception named, is that we shall find it easier to explain; and we hope our pupils will more clearly understand the use of the PP when placed above the eye, and by which we intend to show that the proportions of the object can with equal capability be arranged upon a line above the HL, as upon one below it. By this use of two lines to represent the PP, the base of a column can be worked from the PP below, and the capital from the one above. The same may be observed when representing windows, balconies, etc.,. in the upper storeys of a large building. From PS on the HL draw the semicircle

E

400

a

PP

Fig. 57

PS

[blocks in formation]

VP2

DVP

VP2

IN proportion as the number of lines and angles increase, which compose the subject to be represented in perspective, so there will follow a greater amount of working lines, drawn in various directions from the picture plane. Under these circumstances it will frequently be necessary to use more than one line to represent the PP, in order to prevent the confusion which must occur when working all the details from one PP only. Therefore we are at liberty to use any number of lines as picture planes an advantage fully appreciated by every draughtsman when engaged in making highlyfinished drawings of very elaborate subjects. The kind of work to which these lessons are but an introduction, and which must fall to the lot of those who have studied perspective for some practical purpose, will not be restricted to cubes, blocks of wood, and the simple objects we have selected for our practice, and to assist us in explaining the prinWe know ciples. the same rule for drawing a block in perspective is applied again in drawing a church or a palace; but respecting the latter, that which increases the labour, and not unfrequently perplexes the student, is the increased amount and the great variety of details. We intend still to confine ourselves to simple examples, so long as we have any new rule to give or fresh principle to explain; let these be well learnt, then the application of them to more extensive and important subjects will be easy. We now, therefore, introduce the practice of additional picture planes, and that our explanations may, we trust, be clearer, we will simplify the process by proposing a problem with reference to two slabs or blocks only, of the same size, and each in the same position with regard to the PP. By this time our pupils will be prepared with the fact, that if an object touches the picture plane its real length is represented upon the picture; and as it retires from or beyond the picture, the space it occupies

n

T b

u

PP

DE E DE3. (We have stated the distance of sight in a way frequently done, in some of the military enmination papers, for the purpose of drawing attention to it. It is said that the distance from the rarest angle to the eye is 10 feet, and that the object is 2 feet within or beyond the PP; therefore the eye will be 8 feet from the PP, which length will be the radius for deseribing the semicircle through E.) The distance of the nearest angle of the object to the left of the eye will be at b; e

the nearest point of the object to the PP, from which lines must be drawn to both vanishing points; the perspective lengths of c d and c e must be cut off by lines to their respective distance points in the way already explained in Lesson IX., Vol. III., page 271. The line cd, which has been drawn to VP', must be produced to the PP in h. The thickness of each block is 1 foot, that being added to the verti cal space between them will be 8 feet; therefore the perpendicular line, or line of contact, must be 8 feet from to i Another PP through i must be drawn parallel to the HL. Now, as the blocks in this case are the same in their dimensions and positions, the upper one could be very quickly and conveniently drawn from the lower one, by raising perpendicular lines from the angles; but we avoid this for a special reason: that is, wo wish our pupils to go through the construction again, upon and from the upper PP, in the same way as they did from the lower;

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