8. If 55 tons of hemp cost £660, what will 220 tons cost at LESSONS IN ARITHMETIC.-No. XXXVII. the same rate? ANALYSIS. THE term Analysis, in physical science, signifies the resolving of a compound body into its elements, or component parts. ANALYSIS, in arithmetic, signifies the resolving of numbers into the factors of which they are composed, and the tracing of the relations which they bear to each other. In the preceding lessons the student has become acquainted with the method of analysing particular examples and combinations of numbers, and thence deducing general principles and rules. But analysis may be applied with advantage not only to the development of mathematical truths, but also to the solution of a great variety of problems, both in arithmetic and practical life. Indeed, it is the method by which business men generally solve practical questions. A little practice will give the student great facility in its application. No specific directions can be given for solving examples by analysis. None, in fact, are requisite. The judgment, from the conditions of the question, will suggest the process. Hence analysis may, with propriety, be called the COMMON SENSE RULE. In solving questions analytically, it may be remarked in general, that we reason from the given number to 1, then from 1 to the number required. Ex. 1. If 60 yards of cloth cost 240 crowns, what will 85 yards cost? Analytic Solution.-Since 60 yds. cost 240 crowns, 1 yd. will cost of 240 crowns; and of 240 crowns is 4 crowns, or £1. Now, if 1 yd. costs 4 crowns, 85 yds. will cost 85 times as much; and 4 crowns X 85-340 crowns, or £85. Ans. Or, we may reason thus: 85 yds. are of 60 yds.; therefore, 85 yds. will cost of 240 crowns (the cost of 60 yds.), and of 240 crowns is 240 crowns X340 crowns, or £85, the same as before. Other solutions of this example might be given; but our present object is to show how this and similar questions may be solved by analysis. The former method is the simplest and most strictly analytic, though not so short as the latter. It contains two steps: First, we separate the given price of 60 yds. (210 crowns) into 60 equal parts, to find the value of 1 part, or the cost of i yd., which is 4 crowns. Second, we multiply the price of one yd. (4 crowns) by 85, the number of yds. whose cost is required, and the product is the answer sought. This and similar questions are usually placed under the rule of Simple Proportion, or the Rule of Three. The operation of solving a question by analysis, is called an analytic solution. In working the following examples, each one should be analysed, and the reason for every step given in full. 2. A man bought a horse, and paid £15 down, which was of the price of it: what did he give for the horse? Analysis. Since £45 is of the price, the question resolves itself into this: £45 is of what sum? If £45 is of a certain sum, is of £45; and of £45 is £9. Now, if £9 is 1 seventh, 7 sevenths are 7 times as much; and £9X7=£63. Ans. £63. PROOF. of £63£9, and 5 sevenths are 5 times as much, which is £15, the sum he paid down for the horse. In solving examples of this kind, the learner is often perplexed in finding the value of, etc. This difficulty arises from supposing that if of a certain number is 45, of it must be of 45. This mistake will be easily avoided by substituting in his mind the word parts for the given denominator. Thus, if 5 parts cost £45, 1 part will cost of £45, which is £9. But this part is a seventh. Now, if 1 seventh cost £9, then 7 sevenths will cost 7 times as much. 3. If 40 bales of wool cost £120, how much will 100 bales 9. If 165 bushels of apples cost £32, how much will 31 bushels cost? 10. If 72 bushels of peas cost 253 crowns, what will a pint cost at the same rate? 11. If 150 acres of land cost £7,000, what will a square rood cost? 12. If 2 pipes of wine cost £315, what is that per gill? how much did his land cost per acre? 17. If a stack of hay will keep 350 sheep 90 days, how long will it keep 525 sheep? 18. If 440 barrels, of flour will last 15 men 55 months, how long will the same quantity last 28 men? 19. If 136 men can build a warehouse in 120 days, how long will it take 15 men to build it? 20. If of a pound of tea cost 1s. 8d, what will of a pound cost? 21. If of a yard of broadcloth cost 8s. 6d., how much will of a yard cost? 22. Bought of a ton of hay for £3 5s.: how much wi of a ton cost? 23. Bought of a hogshead of molasses for £38: how much will of a hogshead cost? 24. If of an acre of land cost £108, how much will ¦ of an acre cost? 25. If of a barrel of flour cost £2 10s., how much will ef a barrel cost? 26. Paid £4,200 for of a vessel: how much can I afford to sell of the vessel for? 27. Sold 18 baskets of peaches for 34 crowns: how much would 654 baskets come to? 28. If I pay £12 10s. for building 20 rods of wall, how much must I pay for 215 rods? 29. A man can hoe a field of corn in 6 days, and a boy ca hoe it in 9 days: how long will it take them both together t hoe it? Analysis. Since the man can hoe the field in 6 days, in! day he can hoe of it; and since the boy can hoe it in 9 days, in 1 day he can hoe of it; consequently, in 1 day they can both hoe + of the field. Now, if of the field requires them both 1 day, 1s of it will require them of a day, and will require them 18 times as long, or of a day, which is equal to 33 days. Ans. 30. If A can chop a quantity of wood in 4 hours, and B in 6 hours, how long will it take them both to chop the same quantity? 31. A can dig a trench in 6 days, B in 9 days, and C in 13 days: how long will it take all of them together to dig it? 32. A man bought 25 pounds of tea at 6s. a pound, and paid for it in corn at 48. a bushel: how many bushels did it take! Analysis.-If 1 lb. of tea costs 6s., 25 lbs. will cost 25 times as much, which is 150s. Again, if 48. will buy 1 bushel of corn, 150s. will buy as many bushels as 4s. is contained times in 150s.; and 1508.4 37: Ans. 37 bushels. The last and similar examples are frequently arranged under the rule of Barter. Barter signifies an exchange of articles of commerce at prices agreed upon by the parties. Such examples are so easily solved by Analysis that a pt. cific rule for them is unnecessary. 33. A cheesemonger bought 110 lbs. of sugar at id pound, and paid for it in lard at 8d. a pound: how much lard did it take? 34. How much butter, at 12 d. a pound, must be given for 250 lbs. of tes, at 3s. a pound? 35. How many pounds of tea, at 2s. 6d. per pound, must be given for 56 yds. of cloth, at 4s. 3d. per yard? 36. How many pairs of boots, at 15s. a pair, must be given for 50 tons of coal at £1 10s. per ton? 37. A, B, and C, united in business; A put in £250-B When two or more individuals associate themselves together for the purpose of carrying on a joint business, the union is called a partnership or copartnership. The process by which examples like the last one are solved, is often called Fellowship. 38. A and B join in a speculation: A advances £1,500 and B £2,500; they gain £1,200: what was each one's share of the gain? 39. A, B, and C, entered into partnership; A furnished £3,000, B £4,000, and C £5,000; they lost £1,800: what was each one's share of the loss? 40. A's stock is £4,200; B's £3,600; and C's £5,400; the whole gain is £2,400: what is the gain of each ? 41. A's stock is £7,560; B's £8,240; C's £9,300; and D's £6,200; the whole gain is £625: what is the share of each ? 42. A bankrupt owes one of his creditors £400; another £500; and a third £600; his property amounts to £1,000 how much can he pay in the pound; and how much will each of his creditors receive? The solution of this example is the same in principle as that of Ex. 37. Examples like the preceding are commonly arranged under the rule of Bankruptcy. A bankrupt is a person who is insolvent, or unable to pay his just debts. 43. A bankrupt owes £5,000, and his property is worth £3,500: how much can he pay in the pound? 44. A man died owing £1,640, and his effects were sold for £410: how much per cent. did his estate pay? 45. If a man owes A £624, B £876, and C £900, and has but £1,150, how much will each creditor receive? 46. If I owe £4,800, and have property to the amount of £3,200, how much per cent. can I pay? 47. How much. per cent. can a man pay, whose liabilities are £12,000, and whose assets are £4,500? 48. How much per cent. can a man pay, whose liabilities are £150,000, and whose assets are £15,000? It often happens in storms and other casualties at sea, that masters of vessels are obliged to throw portions of their cargo overboard, or sacrifice the ship and their crew. In such cases, the law requires that the loss shall be divided among the owners of the vessel and cargo, in proportion to the amount of each one's property at stake. The process of finding each man's loss, in such instances, is called General Average. The operation is the same as that in solving questions in bankruptcy and partnership. 49. A, B, and C, freight a ship from Liverpool to New York; A had on board 100 tons of iron, B 200 tons, and C 300 tons; in a storm 240 tons were thrown overboard: what was the loss of each? 50. A packet worth £36,000 was loaded with a cargo valued at £65,000. In a tempest the master threw overboard £25,250 worth of goods: how much per cent. was the general average? 51. A steam ship being in distress, the master threw of the cargo overboard; finding she still laboured, he afterwards threw overboard of what remained. The steamer was worth £12,000, and the cargo £24,000; how much per cent. was the general average, and what would be a man's loss who owned of the ship and cargo? 52. A man mixed 25 bushels of peas, worth 6s. a bushel, with 15 bushels of corn worth 48. a bushel, and 20 bushels of oats worth 3s. a bushel: what was the mixture worth per bushel? Analysis.-25 bu. peas at 6s. 15 bu. corn at 48. and 20 bu. oats at 3s. The mixture=60 bu. and 270s., value of whole mixtr. Now, if 60 bu. mixture are worth 270s., 1 bu. mixture is worth of 270s., and 270s. 60=4s. Ans. PROOF.-60 bu. at 48.-270s., the value of the whole mixture. The process of finding the value of a compound or mixture of articles of different values, or of forming a compound which shall have a given value, is called Alligation. Alligation is usually divided into two kinds, Medial and Alternate. When the prices of the several articles and the number or quantity of each are given, the process of finding the value of the mixture, as in the last example, is called Alligation Medial. When the price of the mixture is given, together with the price of each article, the process of finding how much of the several articles must be taken to form the required mixture, is called Alligation Alternate. Alligation Alternate embraces three varieties of examples, which will be pointed out in the following notes, 53. If you mix 40 gallons of sperm oil worth 8s. per gallon, with 60 gallons of whale oil worth 3s. per gallon, what will the mixture be worth per gallon? 54. At what price per pound can a grocer afford to sell a mixture of 30 lbs. of tea worth 4s. a pound, and 40 lbs. worth 78. a pound? 55. If 120 lbs. of butter at 10d. a pound are mixed with 24 lbs. at 8d. and 24 lbs. at 5d. a pound, what is the mixture worth? 56. A tobacconist has three kinds of tobacco, worth 3s. 9d., 4s. 6d., and 6s. 3d. a pound: what is the mixture of 100 lbs. of each worth per pound? 57. A liquor dealer mixed 200 gallons of gin worth £1 a gallon, with 100 gallons of brandy worth £1 5s. a gallon: what was the value of the mixture per gallon? 58. A grocer sells the finest souchong tea at 10s. a pound, and hyson at 4s.: what part of each must be taken to form a mixture which he can afford to sell at 6s. a pound? Note.-1. It will be observed in this example that the price of the mixture and also the price of the several articles or ingredients are given, to find what part of each the mixture must contain. Analysis. Since the souchong is worth 10s. and the required mixture 6s., it is plain he would lose 4s. on every pound of souchong which he puts in. And since the hyson is worth 4s. a pound and the mixture 6s., he would gain 2s. on every pound of hyson he puts in. The question, then, is this: How much hyson must he put in to make up for the loss on 1 lb. of souchong? If 2s. profit require 1 lb. of hyson, 4s. profit will require twice as much, or 2 lbs. He must, therefore, put in 2 lbs. of hyson to 1 lb. of souchong. PROOF.-2 lbs. of hyson, at 48. a pound, are worth Ss., and 1 lb. of souchong is worth 10s. Now 8s.+10s. 18s. And if 3 lbs. mixture are worth 18s., 1 lb. is worth of 18s., which is 6s., the price of the mixture required. 59. A farmer has oats which are worth 20s. a quarter, rye 55s., and barley 60s., of which he wishes to make a mixture worth 50s. per quarter: what part of each must the mixture contain? Analysis.-The prices of the rye and barley must each be compared with the price of the oats. If 1 quarter of oats gains 30s. in the mixture, it will take as many quarters of rye to balance it, as 58. (the loss per quarter) are contained times in 30s., viz. 6 quarters. Again, since 1 quarter of oats gains 30s., it will take as many quarters of barley to balance it, as 10s. (the loss per quarter) are contained times in 30s., viz. 3 quarters. Hence, the mixture must contain 2 parts of oats, 6 parts rye, and 3 parts barley. 60. If a man have four kinds of currants worth 8 9 11 and 1 12 pence a pound respectively, how much of each kind must | he take to form a mixture worth 10d. a pound? Note.-2. In examples like the preceding, we compare two kinds together, one of a higher and the other of a lower price than the required mixture; then compare the other two kinds in the same manner. In selecting the pairs to be compared together, it is necessary that the price of one article shall be above, and the other below the price of the mixture. Hence, when there are several articles to be mixed, some cheaper and others dearer than the mixture, a variety of answers may be obtained. Thus, if we compare the highest and lowest, then the other two, the mixture will contain 1 part at 8d.; 1 part at 9d.; 1 part at 11d.; and 1 part at 12d. Again, by comparing those at 8d. and 11d., and those at 9d. and 12d. together, we obtain for the mixture 1 part at 8d.; 2 parts at 11d.; 2 parts at 9d. ; and 1 part at 12d. Other answers may be found by comparing the first with the third and fourth; and the second with the fourth, etc. 61. A goldsmith having gold 16, 18, 23, and 24 carats fine, wished to make a mixture 21 carats fine: what part of each must the mixture contain? 62. A farmer had 30 bu. of corn worth 6s. a bu., which he wished to mix with oats worth 3s. a bu., so that the mixture might be worth 48. per bu.: how many bushels of oats must he use? Note.-3. In this example, it will be perceived that the price of the mixture, with the prices of the several articles and the quantity of one of them are given, to find how much of the other article the mixture must contain. Analysis.-Reasoning as above, we find that the mixture (without regard to the specified quantity of corn) in order to be worth 4s. per bu, must contain 2 bu. of oats to 1 bu. of corn. Hence, if 1 bu, of corn requires 2 bu, of oats to make a mixture of the required value, 30 bu. of corn will require 30 times as much; and 2 bu. X 30-60 bu., the quantity of oats required. 63. A merchant wished to mix 100 gallons of oil worth 68. 8d. per gallon, with two other kinds worth 2s. 6d. and 3s. 4d. per gallon, so that the mixture may be worth 5s, per gallon: how many gallons of each must it contain? 64. A merchant has Havanna coffee at 18. and Java at 18. 6d. per pound, of which he wishes to make a mixture of 150 lbs., which he can sell at 1s. 4d. a pound: how much of each must he use? LESSONS IN GREEK.-No. LVIII. By JOHN R. BEARD, D.D. THE PREDICATE WITH A DOUBLE ACCUSATIVE. THERE may be a double accusative with a transitive verb when the action of the verb operates equally on a person and on a thing. Such verbs, in Greek, are the following: 1. Verbs which have as their object the abstract idea conveyed in the verb, take also in the accusative the person affected by the verbal action. This construction is most frequent in cases where the abstract object is indicated by an adjective or pronoun in the neuter gender: eg. Σωκράτης έκαστον επειράτο ευεργετείν την μεγιστην ευεργεσίαν τοιαῦτα εγκωμιάζουσι την αρετήν With verbs denoting to divide, μepn (parts), and similar τρεις μοιρας the accusative of the person," Accusative of the person. Sometimes the person appears in the dative, when the parson does not immediately receive the action of the verb: if αγαθόν έπραξε τη πόλει he did a good thing for the state. Thus arises a difference between these two phrases: τι σοι ποιήσουσιν οἱ μάρτυρες; 3. The following verbs also take an accusative of the person and an accusative of the thing; namely, didarkav, to learn; aicever, to educate; arappynokELY, Toppnokeev, to re mind; puπTELY, KOUTTEGbaι, ATOKOURTEOUL, Reefer, to conceal; Epwrav, spectat, to ask, inquire; erase, to inves tigate; aureir, airtio0ai, aior, to request, to claim; par Tεi, πрarrεovai, to carry on, to manage, to take from, as a fe or tribute: e.g. Σωκράτης σωφροσύνην εδίδαξε τους συνόντας Socrates taught his scholars soundmindedness, Οἱ στρατηγοι τους πολίτας έκατον ταλαντα έπραξαν the generals made the citizens pay a hundred talents. Several of these verbs admit of another construction. Th αναμιμνήσκειν and ὑπομιμνήσκειν commonly take the thing is the genitive. Instead of tpwrav riva ri, to ask some one some thing, we find spwrāv Tiva Tepi Tivos, to ask some one respect ing something; and instead of αιτείν οι αιτεῖσθαι τινα τις πε End αιτεῖν τι παρά τινος. 4. Verbs which signify to put on, to clothe, as ever. aμpievvvvai; to put off or take off, tkdver; to take away deprive, apaiptiotal, orEPICKELY, ATOOTEDεiv; to plunder, tai, put both the person and the thing in the accusative: eg. Τα ήμεταρα ήμας αποστερεί Φιλιππος Philip deprives us of our own. Together with αποστερεῖν τινα τι, we find also very ofte αποστερεῖν τινα τινος, and sometimes αποστερεῖν τινος της αφαιρείσθαι τινος τι. A double accusative is found also with those verbs the ide of which in the predicate is too wide to be fully expres without the addition of an explanatory attribute; this attribute stands in agreement with the object, and is accordingly for the most part put into the accusative. Such verbs, are to name of appoint, to bring up for, to declare as, to show yourself so and so, etc. e.g. Σοφιστήν ονομάζουσι τον άνδρα τούτον The Accusative of the End and of Dimension. The end toward which an action is directed is generally p in the accusative in union with a preposition, &c, po, The poets, however, especially of the epic class, with the verts denote the end or object which a person strives for, whe to come, reach, go, sometimes employ the accusative alone attained: e.g. the time during which a condition lasts, are indicated by the | διελεῖν ; εἶπε ; αναμνησω; κρύψω; κατένειμε, αφείλετο ; You accusative without a preposition : Ο Φωκικός πόλεμος αειμνηστον παιδειαν τους Θηβαίους | επαίδευσεν. Σωκρατης, ηδη Μελήτου γεγραμμένου αυτον την γραφην, περι παντων μαλλον η περί της δικης διελέγετο. Θρασύβουλος άρκωσε παντας τους στρατιωτας τους μεγιστους όρκους, ου χρη μιμήσεις πονηρας μιμεῖσθαι τους πολεμίους. Όνομα ποιον αυτόν ονομάζει πατηρ ; καλοῦσι με τοῦτο το ονομα. Ο Σωκράτης δικαιος όντως ην, ώστε βλαπτειν μηδε μικρόν μηδένα, ωφελεῖν δε τα μεγιστα τους χρωμένους ἑαυτῷ. Πολλά αν τις έχοι Σωκράτην επαινεσαι. Ουδε ταδε αιτιῶμαι τον Θεόν. Των συμμοριῶν ἑκαστην διελεῖν κελευω πεντε μέρη. Η γη τους αριστα θεραπευοντας αυτην πλεῖστα αγαθα αντιποιεῖ. Oi πονηροι αει τι κακον εργαζονται τους εγγυτατω έαυτων οντας. Πολλα κακα εἶπεν ανθρωπους. Πᾶς τις το γυναικεῖον φύλον κακα πολλ' αγορεύει. Ταυτα με ποιοῦσιν. Ταύτα μοι ποιοῦσιν. Ου φροντιστέον ὁ τι εροῦσιν οἱ πολλοὶ ἡμᾶς. Ο χρόνος και η εμπειρια τα μη καλῶς ἔχοντα εκδιδάσκει τους ανθρώπους. Ποιοῦσιν οἱ τεχνῖται ὁ οἱ διδασκαλοι αυτους επαιδευσαν. Τρια μονα τους παῖδας παιδεύουσιν οἱ Πέρσαι, ίππευειν και τοξεύειν και αληθιζεσθαι. Αναμνησω ύμας τους τῶν προγονων τῶν ἡμετέρων κινδυνους. Ου σε κρύψω την εμην γνωμην. Ερωτῶ σε τας των φίλων τύχας. Νῦν δε εμε πολλοι οικεται σῖτον αιτοῦσι, πολλοι δε ἱματια. Τἀγαθα αιτοῦμεν τους θεους. Σωκράτης ουδένα των συνόντων επράξατο τῆς συνουσίας μισθον. Γλώτταν τε την Αττικήν και τροπους τῶν Αθηναίων εδιδασκον | τους παῖδας. Κῦρος το στρατευμα κατένειμε δωδεκα μέρη. Τον μονον μοι και φιλον παῖδα αφειλετο την ψυχην. Την τιμην αποστερεί με; κρυπτω σε το ατύχημα. Παῖς μεγας, μικρον ἔχων χιτῶνα, ἑτερον παῖδα μικρον, μεγα εχοντα χιτῶνα, εκδύσας αυτόν, τον μεν εαυτοῦ ἐκεῖνον ημφιεσε, τον δε εκείνου αυτος ενεδυ. Ο Κυρος τον Γωβρύαν απέδειξε στρατηγον. Πλουτον και τιμην και δόξαν αγαθα νομίζουσιν οἱ πολλοι. Τον θάνατον ου κακον ἡγεῖσθαι χρη, αλλά κακών απαλλαγήν. Θεμιστοκλής Κλεοφαντον τον υἱὸν ἱππεα εδιδαξατο αγαθόν. Το ψεῦδος ου δύνασαι αληθες ποιεῖν. Η Εφεσος απέχει από Σαρδέων τριῶν ἡμερων δέον. Ο Αρχέλαος κατασχων τρεῖς η τέτταρες ήμερας | την τυραννίδα ετελεύτησεν. Ευδαιμονέσταται πόλεις λέγονται αἱ αν πλείστον χρόνον εν ειρηνη διατελῶσιν. Αἱ σπονδαι συμμορίαι, or classes. Το γυν. φύλον, “ the female tribe;” spoken contemptuously. Σωκ. επρα, της συνουσίας, Socrates took no fee, “no reward Ίππευς, εως, a horseman " taught him to be a good horseman.” Why is αειμνηστος in the form of αειμνηστον, while its noun, παιδεια, is of the feminine gender: What parts of the verbs are these-επαιδευσα ; γεγραμμενου ; διελέγετο ; ώρκωσε; μιμεῖσθαι; επαινεσαι; αιτιῶμαι ; are to give the root in each case, and conjugate the part. Explain the augment in these verbs--αφειλετο, εδιδάξατο; ετελεύτησεν ; ὡρκωσε; εἶπεημφιεσε. Explain in full the constructions, Μελήτου γεγραμμένου αυτόν την γραφήν ; ου σε κρύψω την εμήν γνώμην. Mark exactly how the English differs from the Greek in καλοῦσι με τοῦτο το όνομα. To which class of verbs does Kaλour belong? Write out the verb in full; including the middle voice and the passive as well as the active. Explain the construction (what case they represent, and why of the verbs ἱππεύειν, τοξεύειν, αληθίζεσθαι. Decline these nouns - Σωκράτην ; φύλον; πατηρ ; τεχνῖται γνώμην ; Αθηναίων; γλῶτταν; χιτῶνα; τέλος; σφαιρα. ENGLISH-GREEK. The The father taught his son a lesson he would not forget. Of what (τι) did Miletus accuse Socrates? Miletus accused Socrates of impiety (ασέβεια). They discourse respecting the trial. Pericles makes the Athenians swear an oath. Boys imitate the bad deeds of boys. (By) what name do they call Helen. I assist my associates in the best things. They ask your father? They call me Alexander. They call my sister all good from God. I divide the kingdom into five parts. Good men do good to good men; bad men to bad, wicked speak ill of the good. That bad boy spoke ill of his father. Good children will always speak well of their parents. He takes no fee from his pupils. He took the coat from the much good. I teach my children one thing, virtue. They man and put it on himself. He will deprive his family of reminded the soldiers of their valour of old. Ask truly good things from God. I have asked God for wisdom and virtue. Thou teachest young men the Attic language. They hide their misfortune from all men. The queen appointed Wellingand honour He tries to make the lie true. The city con ton general. I consider knowledge and self-controul riches tinued at war six months. POETIC IDIOM. These lessons are chiefly designed as an introduction to the reading of Greek prose. For the most part, in consequence, been confined to Greek prose, and specially to the Attic the remarks, the paradigms, the rules and the examples, have writers. Yet, as something like completeness is aimed at, now and then an observation has been made as to poetic usage. In older manuals, the diction of prose and the diction of poetry were confusedly blended together. In the rich treasury of Grammar, very many are from the poets. But in all languages examples of Greek usage found in Matthiæ's excellent Greek poets take great licence; and a construction, or a word, which is very good in poetry, may be inadmissible in prose. Hence, the necessity of distinguishing between the two in grammatical treatises, and of limiting the matter to prose usage in a manual intended to instruct students in the art of reading prose. Nevertheless, as poetic usage is-as poetic usage-good Greek, so a student should not, even at an early period of his studies, be left entirely ignorant of it, especially as it is only by some acquaintance with it that he can appreciate the difference of poetic usage from prose usage. And the rather is some knowledge of poetic idiom desirable, because the words of the language are often presented by it in their simpler forms, so as to lead the pupil to an acquaintance with the primitives of the Greek, which, as I have already intimated, are not very numerous, learners, to form some faint conception (more, here, I cannot In order, therefore, to assist you, my fellowhope for) with the idiom of Greek poetry, I shall lay before you a number of Γνώμαι, that is, apothegms, proverbs, or pithy sayings, taken from ancient Greek writers. Γνωμαι. 1. Αρχὴν ἀπαντων και τέλος ποιει Θεός. 3. Αγιοι εν χορῳ ἁγιων αγαλλονται. 4. Σφαιρᾳ ὁ κόσμος είκει. 5. Χωρίς αγκυλης τοξον και αφου ελπίδος ητος, όμοιως πράττουσι. 12 pence a pound respectively, how much of each kind must | he take to form a mixture worth 10d. a pound? Note.-2. In examples like the preceding, we compare two kinds together, one of a higher and the other of a lower price than the required mixture; then compare the other two kinds in the same manner. In selecting the pairs to be compared together, it is necessary that the price of one article shall be above, and the other below the price of the mixture. Hence, when there are several articles to be mixed, some cheaper and others dearer than the mixture, a variety of answers may be obtained. Thus, if we compare the highest and lowest, then the other two, the mixture will contain 1 part at 8d.; 1 part at 9d.; 1 part at 11d.; and 1 part at 12d. Again, by comparing those at 8d. and 11d., and those at 9d. and 12d. together, we obtain for the mixture 1 part at 8d.; 2 parts at 11d.; 2 parts at 9d.; and 1 part at 12d. Other answers may be found by comparing the first with the third and fourth; and the second with the fourth, etc. 61. A goldsmith having gold 16, 18, 23, and 24 carats fine, wished to make a mixture 21 carats fine: what part of each must the mixture contain? 62. A farmer had 30 bu. of corn worth 6s. a bu., which he wished to mix with oats worth 3s. a bu, so that the mixture might be worth 4s. per bu.: how many bushels of oats must he use? Note.-3. In this example, it will be perceived that the price of the mixture, with the prices of the several articles and the quantity of one of them are given, to find how much of the other article the mixture must contain. Analysis.-Reasoning as above, we find that the mixture (without regard to the specified quantity of corn) in order to be worth 48. per bu, must contain 2 bu. of oats to 1 bu. of corn. Hence, if 1 bu. of corn requires 2 bu. of oats to make a mixture of the required value, 30 bu. of corn will require 30 times as much; and 2 bu. × 30=60 bu., the quantity of oats required. 63. A merchant wished to mix 100 gallons of oil worth 6s. 8d. per gallon, with two other kinds worth 2s. 6d. and 3s. 4d. per gallon, so that the mixture may be worth 5s. per gallon : how many gallons of each must it contain? 64. A merchant has Havanna coffee at 18. and Java at 1s. 6d. per pound, of which he wishes to make a mixture of 150 lbs., which he can sell at 1s. 4d. a pound: how much of each must he use? LESSONS IN GREEK.-No. LVIII. By JOHN R. BEARD, D.D. βασιλέως αγαθου έργον έστι τους αρχομένους αγαθα παν it is the office of a good king to do good to his subjects. τα έσχατα έλεγον αλλήλους they said the worst things of each other. Instead of the definite terms αγαθα, κακα, etc., you ma have a demonstrative, relative, or interrogative pronoun τί μ' ειργάσω ; what hast thou done to me? Sometimes the person appears in the dative, when t son does not immediately receive the action of the v r. αγαθόν έπραξε τη πόλει he did a good thing for the state. Thus arises a difference between these two pr Σωκρατης σωφροσύνη, the genitive. I αμφιενι THE PREDICATE WITH A DOUBLE ACCUSATIVE. THERE may be a double accusative with a transitive verb der when the action of the verb operates equally on a person and put on a thing. Such verbs, in Greek, are the following: ject is indicated by 1. Verbs which have as their object the abstract idea conveyed in the verb, take also in the accusative the person affected by the verbal action. This construction is most fre quent in cases where the adjective or pronoun in Σωκράτης έκαστον επεί Socrates endeavoured t You must sometime form of the Greek in into good English. i lation just given. Sor be made dependent or τοιαῦτα ἔγι in such th With verbs den 1 words, are to be reg sative; and, accordi sion is made are a accusatives, the one. and the other, "the a Accusative of the th τρεις μοιρας three parts r: eg. • μεγιστην ενε holy from prono ען, . |