blocks of many substances on account of their shape or physical and, as before, we first find the weight of water required to fill properties, and many other bodies are too small or too valuable. it to a certain mark, and then the weight of the liquid we are We cannot, then, compare their densities in this way, but we operating upon. may take some substance as a standard, and compare the The details of an actual experiment will make this clearer. weights of all others with this. A sample of nitric acid was taken, of which it was desired to Now any substance might be chosen for this purpose, the ascertain the specific gravity. The main requisites being that it shall be easily procurable in a small bottle was first put in the state of purity, and easy of manipulation. Water has been scales and found to weigh 80 grains. chosen as this standard, and is found to answer well. When, On being filled with the acid it therefore, we speak of the specific gravity of any body, we weighed 159 grains. The acid was mean this-the proportion which exists between its weight next emptied out, the bottle rinsed, and that of an equal bulk of distilled water at a temperature and filled to the same height with of 60°. water, the weight being then 136 The reason why we thus fix on a certain temperature is that grains. B water expands by heat, and therefore a cubic inch of hot water Now, since the bottle weighed Frighs less than an equal bulk of cold. The temperature of 80 grains, we subtract this amount 640® is chosen merely as a matter of convenience, that being from its weight when filled with about the average, and therefore involving less trouble. When, the different liquids, and thus see Fig. 13. then, we say the specific gravity of mercury is 13.6, we mean that the water in the bottle weighed that any amount of mercury weighs 13:6 times as much as an 56 grains, while the weight of the same bulk of acid was 79 equal bulk of distilled water at 60°. Now, as we have seen, grains. We have, then, the following equation by which we the weight of a cubic inch of distilled water is 252:5 grains; a can determine the specific gravity of the liquid :cubic inch of mercury therefore weighs 252-5 grains x 136, As 56 : 79 :: 1 : 1:41. Op 3,434 grains, which is nearly 8 oz. We can in this way, if we know the specific gravity of a body, tell the weight of any This, then, is the specific gravity of the acid, and from this we balk of it. Questions like the following frequently occur, and can form an idea of its strength. In our next lesson we shall can thrus be solved :-What is the weight of a block of coal see how to proceed in the case of solids. 3 feet x 5 x 4, the specific gravity of coal being 1.270 ? EXAMPLES. Since the specific gravity of the coal is 1.270, the weight of 1. A cubic foot of glass weighs 166 pounds; what is its specific a cabic foot is 1.270 times that of an equal bulk of water. But a gravity ? cubic foot of water weighs about 1,000 oz.; a cubic foot of coal 2. A flask holds 8 ounces of water and 10} of another liquid; what most then weigh 1,270 ounces. Now the total bulk of the coal is the specific gravity of the latter ? is 3 X 5 X 4 = 60 cubic feet. Its weight, therefore, is 3. A small flask weighs when empty 150 grains, when full of an oil 60 X 1,270 ounces=76,200 ounces, or 42 cwt. 2 qr: 2 lb. Again, 290 grains, and when full of water 315 grains; what is the specific strong oil of vitriol has a specific gravity of 1-850; how much gravity of the oil ? 4. A rectangular block of timber measures 14 in. x 14 x 10. Its will 6 lb. measure? A fluid ounce of water, it must be re- specific gravity is •850. If it floats with its largest surface horizontal, membered, weighs one ounce avoirdupois; 6 lb. of water, how deep will it be immersed? Also, how deep if it be vertical! then, would measure 96 oz.: but since oil of vitriol is heavier 5. A block of chalk 3 feet 30" x 30" X 2'6" is suspended in water. than it, in the proportion of 1,850 to 1,000, it will measure pro- Taking its specific gravity as 2.660, what is the strain on the rope portionately less. Hence the following proportion will give us supporting it? the balk :As 1,850 : 1,000 :: 96 : the required volume.. ANSWERS TO EXAMPLES IN LESSON II. (Vol. II, page 398). On working this out, we shall find that the vitriol will measure tion of the squares of their diameters, the larger has 144 times the 1. Since the areas of the pistons are to one another in the propor51-89 oz., or nearly 34 ordinary pints. area of the smaller. There is also a gain of 6 by the lever. Thus the We see thus the importance of knowing the specific gravity advantage gained is 144 * 6 or 864. If we divide 20 tons by this, we of any substance, and there are several modes of ascertaining find the required pressure is 51.85 pounds. it , one or other of which is more applicable according to the 2. The area of the sides is together 144 feet, and the mean depth circumstances of the case. If, however, we bear in mind 2 feet. The total pressure on them is thus equal to the weight of exactly what it is we wish to know, we shall find little difficulty 144x2 or 324 cubic feet of water. This is nearly 324,000 ounces, or in remembering which way to proceed. 9 tons and 90 pounds. The pressure on the bottom is 6x10x 44*1,000 We will consider, first, how to proceed in the case of a liquid. ounces, or 7 tons 10 cwt. 2 qrs. 19 ib. 3. Rather more than 19; tons. Procure a thin glass flask (Fig. 13, A) provided with an accurately 4. The area of the large piston is 38} square inches. The required fitting stopper. Instead, however, of this being solid, let it be pressure is therefore nearly 40 pounds. drawn out, as shown at B, into a long tubular neck, so that when 5. Just over 15 tons. it is put in its place any excess of liquid may escape through it. 6. The additional pressure will be that of a column of water having The flask is best made of such a size as to hold 1,000 grains up an area of 6 square inches, and a height of 3 feet. This will be of to the mark o in the neck. Now procure a small piece of metal, a cubic foot, and therefore weigh 7 lb. 13 oz. The total pressure is and file or grind it till it exactly balances the flask and stopper therefore 10 lb. 13 oz. eben empty. If the flask, filled with distilled water to the level o, be pat in one pan of a balance and the counterpoise or LESSONS IN GREEK.-XIV. weight in the other, we must add just 1,000 grains to balance the water. Empty this out, and fill it with the liquid whose REVIEW OF THE THREE DECLENSIONS. specifio gravity we want to know-say, for instance, the strongest With the nouns of the first and second declension, the student, alcohol-and weigh again; we shall now find that only 792 if he has thoroughly mastered the foregoing lessons, will find no grains are required to balance it. The weight, then, of any difficulty in any attempt he may make to construe classical volume of alcohol is to that of an equal bulk of water in the Greek. It is somewhat different with nouns of the third deproportion of 792 to 1,000; or, in other words, the specific clension, the discovery of the nominative of which is necessary gravity of the alcohol is :792. The reason why we chose a flask in order to consult a Greek lexicon with ease and effect. I containing 1,000 grains is now clear, for all trouble in calcula- therefore subjoin the following, which will enable him from the tion is thas avoided. We have only to take the weight of the genitive case to find the nominative ; in which form substanliquid in grains, and point off three figures as decimals, and we tives and adjectives appear in dictionaries. I give the genitive, have the specific gravity: because the genitive is, as it were, the key to the remaining Thus, if we fill the bottle with sea water, we shall find it oblique cases. Thus, if you meet with avopa, you know the will weigh 1,028 grains; the specific gravity is therefore 1.028. genitive must have two of these letters, namely, Op; if you meet Sometimes, however, it is difficult or costly to procure a with xeluwes, you know the genitive will have the letters officient quantity of the liquid to fill such a largo fiask. We meuwv; if you meet with ueraves, you know the genitive will then nes a much smaller one, usually made out of a glass tube, have the letters menar. Now, from the genitive you may get no ears. 11. Tiportidet, adds, from a portionis, I add ; ETLOTIUN, -ns, , days, but by nights. 24. It is hard to speak to the stomach, as it has understanding. 25. Vulcan was lame in his feet. 26. Medea is painted as 27. Time is the test of men's 12. Bovkepw, having the horns of an ox, from Bovkepws, -w, and scowling fiercely at her children. that from Bous and repa ; lovs, Io, from Iw, -olls; tavai, wander- character. 28. Serpents have a poison in their teeth. 29. Parnassus is a great and shady mountain, 30. In Bæotia are two remarkable ings, from Fiam, -ns, y. mountains, the one called Helicon, and the other Cithæron. 31. The 14. Aindas, truly; ús aanbws, very truly. Nile has all kinds of fishes. 32. Honour your parents. 33. Anacharsis 15. 'HÖLotny, sweetest, the superlative degree of hous, sweet ; said that the vine bore three branches; one of pleasure, one of intoxispopapov, pleasant, from tpoo pupos, -ov, suitable to (npos and cation, and the third of disgust. 34. Toil is the rent of glory. φερα). 35. Inachus was the son of Oceanus and Tethys. 36. Grasshoppers 16. Apiatur, the best, that is, noble, from aplotos, a superlative feed on dew. 37. Cleanthes used to say that uneducated men differed of ayatos. in form only from wild beasts. 38. Anacharsis being reproached be17. Zipos, -OUS, TO, a sword; TiTpwrket, wounds, from TiTpWoKW, 99. In hell the bad are punished, (whether) kings, slaves, satraps, cause he was a Scythian, said he was so in race but not in character. I sound. 18. Merlotov, the greatest, superlative from meyas, great. poor, rich, or beggars. 40. The daughters of Phorcus were old women even from their birth. 41. Zenon used to say that it was right to adorn 20. Tuparvis, -idos, i, usurped power, tyranny; aðlkias, of in- cities, not with monuments, but with the virtues of the inhabitants. justice (a privative, and Siky, right, justice). 21. Δειλος, -η, -ον, owardly, ο δειλος, the coward; προδοτης, KEY TO EXERCISES IN LESSONS IN GREEK.-XIII. -*, ¢, a betrayer, traitor. (Vol. II., page 390.) 22. E.koves, images ; Elkwy, -ovos, /, an image. EXERCISE 47.--GREEK-ENGLISH. 23. Nouaoes, the nomads, or wandering tribes, from vouas, sãos, and that from yeuw already explained ; ape@uovoiv, they Poseidon, and Apollo, and other gods. 3. Modesty becomes women. 1. Women rejoice in ornament. 2. The Greeks worship Zeus, and number, from ap@new, I number, our arithmetic. 4. The dogs guard the house. 5. The pilot directs the ship. 6. The 24. Exovray, having, present participle from exw, I have; it droppings of water make the rock hollow. 7. It is a woman's duty to agrees with yootepa. watch her home. 8. It is the part of a good wife to keep house. 9. 25. 'HPALITOS, Vulcan ; xwios, -, -ov, lame. The dice of Jove always throw luckily. 10. Dogs always afford men 26. Mndera, -as, f, Medea; OBAerovoa, scowling at, from aid and pleasure. 11. The evidence of witnesses is often trustless. ise, under, and BAETw, I look. (Compare the Latin suspicari = 12. Cerry, my child, the key of the chest. 13. O Zeus, receive the sub, specio.) prayers of the unfortunate man. 14. Castor and Pollux were the saviours 16. The Æthio27. Heous, of character, from to nbos; Bavaros, -ov, , a touch of ships. 15. Silence brings adornment to woman. pians have dark hair. 17. O woman, preserve your house. 18. We stone, test. comb our hair with a comb. 19. Æăcus keeps the keys of Hades. 28. Oous, opeus, d, a serpent; los, -ov, a dart, sting. 29. Tlapvascos, Parnassus, a mountain of Phocis, on which EXERCISE 48.- ENGLISH-GREEK. Tas Delphi ; συσκιος, -ον, ουerhung oth clouds, from συν, witle, 3. Φερουσι κλεις της οικίας. 4. Κλειδες της οικιας φερονται τη μητέρι. 5. Τους 1. Κοσμος πρεπει την γυναικα. 2. Εργον εστι γυναικων φυλαττειν την οικιαν. and chie, a shade. Αθηναιοις ησαν πολλαι νηες. . 6. Διί ησαν πολλοι ναοι. . 7. οι ιχθυες 30. Erlojuos, -oy, distinguished, remarkable, from enti, on (here ανακύπτουσιν εκ του ύδατος. . & ο κυβερνητης ιθυνει την ναύν. 9. Η ναυς an intensive), and onua, a sign, whence our semaphore, that is, a Ouverai UNO TOU Kußepuntov. 10. Lebeis Ata kai Atol Awwa. telegraph ; EAixwv, Helicon ; Kidaipwy, Cithæron ; kalovjevov, EXERCISE 49.-GREEK-ENGLISH. called, named, participle agreeing with to, that is opos; étepos, 1. To drink much wine is an evil. 2. Kings have large revenues. 5-09, other, the other. 3. In Egypt is abundance of corn. 4. The sea is great. 5. Croesus had 33. Asaxeppis, Anacharsis ; EIT€, said; ģdovns depends on great wealth. 6. From a slight joy often arises great anguish. 7. To Borpus ; peon, -ns, n, intoxication; andła (from a, not, and nous, gentle words we yield with pleasure. 8. The great gifts of fortune street), disgust. bring terror. 9. The tempers, of many men are gentle. 10. Toil 34. EVKAEIG, -as, ñ, glory, distinction, is a great aid to virtue. 11. Children love gentle fathers and gentle 35. Saeiros, -ov, d, Oceanus, Ocean considered as a divinity; mothers. 12. Keep up an acquaintance with gentle-hearted men. 13. Treus, -35, 1, Tethys, a sea-goddess. The women are gentle. 14. The majority of mankind call Alexander, 36. Στεομαι, I feed on ; δροσος, -ου, ή, deco. King of Macedonia, Great. 37. KAxarons, Cleanthes; eon, said ; anaideuros, -ov, untaught, EXERCISE 50.-ENGLISH-GREEK. weducated; popor, -ns, i, form ; diapepw, I differ. 1. Απεχου πολλου του οινον. . 2. Οι κακοι χαιρoυσι πολλώ τω οινό. 3. 38. Ονειδιζω, I reproach, Anacharsis being reproached; Σκυθης, Πολυν ο οινο: βλαπτει τους ανθρωπους. 4. Τους βασιλευσι εισι μεγαλα a Scythian. προσοδοι, 5. Η προσοδος των βασιλεων εστι μεγαλη. 6. Αιγυπτος έχει πολυν 39. Kolace, I punish ; ev qdov, douw is understood, in the σιτον. 7. Πολλοις εστι πολυς πλουτος, ολιγος δε νούς. 8. Ορεγεσθε πρα€ων abode of Hades, in hell και σατραπης, -ου, δ, α εαtrap or governor | Αλεξανδρος, ο των Μακεδονων Βασιλευς, πολλακις μεγας προσαγορεύεται. εθεων. 9. Τα εθη των γυναικων εστι πραεα. 10. Καλλος εστι πραεσ ιαθεσι. 11. da province ; ferns, -ntos, poor ; #twxos, -77, -ov, begging, oi Texet, beggars. EXERCISE 51.-GREEK-ENGLISH. 40. r paa, , old, an old woman, grey-haired. 1. Speech is a mirror of the mind. 2. Men have intellect as a 41. Aely, that it was necessary, proper; avaonua, -TOS, TO, an master. 3. Cherish a well-disposed friend. 4. Good friends have a dering, public monument, from ava, up, and Tionut, I place; with discretion. 7. The mob has no discretion. 8. Do not quarrel faithful mind. 5. The voyage is uncertain to sailors. 6. Lead a life TEY OUKOUVTAY, of their inhabitants, from Olkew, I inhabit (com with people. 9. The good are well disposed to the good. 10. Seek pare aukos and okia). for good friends. 11. The bones of Orestes were in Tegea. 12. The female servants carry bread in baskets, 13. The gods give both the KEY TO THE RECAPITULATORY EXERCISES FROM THE fair and foul voyage to sailors. 14. The intellect is the soul's curb, GREEK CLASSICS. 15. Often the tempers of men reveal their abilities. 16. The speech 1. Ose swallow does not make a spring. 2. Time brings all things of truth is simple. 17. A kind word lessens grief. 18. The cup is to light. 3. Atreus and Thyestes were the sons of Pelops. 4. Many silver. 19. Death is called a brazen sleep. things happen to men contrary to expectation. 5. Women's ornament EXERCISE 52. ENGLISH-GREEK. a Trind) disposition, not jewels. 6. Grasshoppers are said to be 1. Ο νούς εστι διδασκαλος ανθρωπου. 2. Ο ευνοος φιλος θεραπευεται. 3. sriotous. 7. Ants and bees have a laborious life. 8. Thief knows Oi evvoor didor Depanevovtar. 4. Tois envoois eloi Todo pilot. 5. Anexou thief, and wolf (knows) wolf. 9. It is the use and not the possession Tov avoov. 6. Opeyou twv evrow pilnv. 7. Komse tov Aptov ev TOIS kavos. 8. e books that is the means of education. 10. Nature without instruc- Devyete tous avoove veavias. 9. oi veavia avoou pevnovrat. 10. TO KUTENOV ta is a blind thing, and instruction with nature is a defective thing. IL Time brings knowledge to old age. 12. Many were the wanderings εστι χρυσούν. 11. Τα κυπελλα αγγαρεα εστι καλα. 12. Βιον αγε το ν. 13. the cow-borned Io. 13. Man saves man, and city city. 14. Very Mn epide our tous avoaus. traly was Epaminondas a hero amongst heroes. 15. An old man has the setest topgne for an old man, a child for a child, and a woman GEOMETRICAL PERSPECTIVE.-Y. has tongue suitable for woman. 16. All the children of the noblest Persians are educated at the king's court. 17. The sword wounds the We have said in a previous lesson that if we are able to debody, but speech wounds the mind. 18. Intellect is the greatest good. termine the perspective position of one point, we can of more ; 1. Laws are a city's soul. 20. Tyranny is the mother of injustice and should these points be considered as the extremities of L. The coward is the betrayer of his country. 22. Good men are the straight lines, we can, by drawing lines to unite them, repreEzenkause of deity. 23. The nomad Lybians reckon (time) not by. I sent the lines themselves. We repeat this statement for the 40° ar purpose of placing before our pupils one or two cases to show how all its angles equal; an irregular polygon has unequal sides and this principle, when put into practice, will simplify the work in unequal angles. many questions which may appear to be difficult. Let the pupil PROBLEM XII. (FIG. 31).—To draw the perspective of a circle. turn to Prob. I., Fig. 7 (Vol. II., p. 225)-of course we presume Diameter of the circle, 4 feet; height of eye, 5 feet; distance of that this problem has been learnt, and, for the sake of practice, the eye from the P P, 10 feet, and opposite the centre of the circle. lines have been placed at other angles and worked out also- Scale, 1 inch to the foot. Draw the B P and also the H L 5 feet becanse this problem contains the key to the whole theory of above it; anywhere (at a) draw the semicircle b c d, with a ground-plan perspective. Now, if the pupil consider for a radius of 2 feet; from a erect a perpendicular to B P, and from moment the principle exemplified in that problem of putting a the point where this line cuts the H L in P s describe the semiline only into perspective, he will see that it is nothing more circle D E 1, E, D E 2, with a radius equal to the distance than finding the positions of c and B. For as a straight line of the eye from the picture plane. About the semicircle extends between the two points in the plan, therefore, when the dcb describe the rectangle defb; draw a e, af, and through the perspective of these two points is determined by drawing a line points in the semicircle cut by the lines a e and a f, draw the lines between them, we shall have the perspective of the line. In giand h k parallel to acord e. From the points d, k, a, i, b, draw order that we may be fully prepared to go further into the lines to the P s. Draw a line from d to D E 2, and also one from subject, we will take a point only, independent of any line, and 6 to D E 1, and call them distance lines; notice where these last place its plan anywhere beyond the P P, Fig. 27. Let a be the lines cut b p s and d P s, between these intersections the line point. From A draw a line at any angle with the P P, and meet m n must be drawn. We have now a square in perspective, in ing it in a. Find the vanishing point of a A, bring down the which the circle is to be drawn. Through the intersection of point of contact a perpendicularly, to b, and join b v P; a visual the distance lines draw o p parallel to m n. With the hand draw ray from a cutting this line will give the perspective position of through the points t, u, p, q, a, , 0, s, to t again, the perspecA at c. We will now make an applica tive circle required. This latter part tion of this principle, and show how, of the process—that is, drawing the cir. with only one vanishing point, we may cle-will be the most troublesome; as it work out a problem which in plan is Fig. 33. does not admit of the use of compasses, composed of a great number of lines, it must be done by the hand only, and and none of them parallel with each will require much practice to do it other. We will propose a very simple neatly. case (Fig. 28), composed of three lines PROBLEM XIII. (FIG. 32) is the ab, b c, and c d. Draw a line a e from first example of elevations. A row of a to the PP, and from the extremities of 7 rods, perpendicular to the ground, 6 each ine draw others parallel with a e; feet high, and 1 foot apart; the plan find the v P for PP 55° with the picone of these ture p'ane. Their lines, which will distance apart be the v P also must be for the rest, be ranged in the cause parallel AL plan 1, 2, 3, 4, retiring lines -5, 6, 7; their VP.2 VPL have the same heights must be V P; bring down set off on the the points of line of contact, contact e, f, g, h, bc; therefore a to B P, the base line drawn from of the picture, c to the v P will and then join them with the v P, represent their retiring position on Upon these last lines respectively the ground, and a line from b to the will be the perspective positions of V P will represent the perspective of the points or extremities of the lines their heights; their widths apart abcd found by the visual rays as in will be found by the visual rays Fig. 27, viz., a'u c' d'; unite these drawn from 1, 2, 3, etc., on the plan. points by straight lines corresponding PROBLEM XIV. (FIG. 33). A cube with the plan, and then will be pro 4 feet edge has one of its faces at duced the perspective view of that represented by the plan. The an angle of 40° with the PP; its nearest angle touches papil must practise this by giving himself a similar combination the PP. Draw the plan of the cube a b c d, making dc of lines, and of greater number. We will add another position of at an angle of 40° with P P. Find the vanishing points of line to this figure. A line, a b, is drawn across the arrangement the sides a d and d c, viz., v P 1 and v P 2. Proceed as in (Fig. 29). There is no necessity to repeat that which has been Prob. VII., Fig. 19, for the extent of the base. For the already shown in Fig. 28, so we will proceed to explain the elevation, as the cube touches the P P at d, therefore a permethod of representing the line a b. It will be understood pendicular line from d brings down the point of contact to e, that the perspective of c d is d ď' and of e f, ef. Now making the line d e the line of contact. As all heights are the given ling a b crosses these lines in the plan through measured upon the line of contact, therefore the height of m and n; it will be necessary, then, to find the projection of the cube must be represented by e f equal to d c (as all the these points m and n, which will be done if visual rays are edges of a cube are equal). Draw lines from f and e to each bronght down from these points to cut the perspective lines vanishing point; then the visual rays from a and c will de&& in o, and e' f' in p; then, to complete the problem through termine the outer and perpendicular edges of the cube gh and these points o and p, the line a' b'must be drawn to the extent i k. Again, as parallel retiring lines have the same vanishing each way as determined by visual rays from the extremities point (and opposite sides of a cube are parallel), draw a line a and b. These figures may in themselves have no particular from i to v P 1, and another from g to v P 2, where these lines meaning, we merely employ them to illustrate a principle, be- intersect at m will complete the upper horizontal face of the cause the perspective of any other object of an intelligible cube, viz., 9 fmi. Make all these lines dark as in the diagram. character may be worked out by this method. To find the perspective of the centres of any of the faces of Fig. 30 is the plan of a hexagon (see Lessons in Geometry the cube, it will be only necessary to draw the diagonals on the XIX., Problem LI., Vol. II., page 192), having one of its edges faces of the perspective projection--viz., from f to k and i to e, at an angle of 200 with the PP. We will only give the figure, or from f to b and g to e. If a line is required to be drawn and recommend the papil to work it out; afterwards he should across the centre of a face, in a horizontal position, the abovo make other regular or irregular polygons for practice also. Re- central point must first be found, and then the line must be member that a regular polygon is one that has all its sides and drawn through this point to the v r of the face respectively. 9 |