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RECREATIVE NATURAL HISTORY. explore and investigate such countries as they might find, and
take note of all valuable productions. On the discovery of BRITISH PEARLS AND PEARLY SHELLS.
the Cassiterides by the Phoenicians, tin and probably pearls It would be difficult to find, among the multitudes of strangely formed important objects for commercial enterprisea; but the formed and deeply-interesting inhabitants of our lakes, rivers, situation of the new treasure-lands was for a long time successand the sea which girds our coasts, a wider field for study and fully concealed by the fortunate discoverers. The Romans, research than is presented by an examination of the habits and however, at length discovered the secret, and there appears little peculiarities of the shell-bearing Mollusca. Whether we select doubt that the glowing accounts given of the fabulous quanti. for investigation the tiny creature in his glass-like dwelling ties of pearls possessed by the inhabitants of "Baratanac," among the green water-weeds freshly called from the clear brook or Britain, first led Julius Cæsar to plan his second invasion, (a familiar type of which is to be found in the Lyminea stagnalis, and decide on its capture and subjugation. That pearls were the subject of the annexed illustration, Fig. 1); or dredge up the great and main attraction is proved by the fact of one of his from the rock-fastnosses at the sea's bottom some stout and first offerings to the shrine of Venus Genitrix as a successful strong sea-castle, like that inhabited by the Triton, figured in conqueror being a shield or buckler covered with pearls from the annexed engraving (Fig. 2); or search the grass and herbs his new possession. Pliny, in writing of this offering, says that growing in some sheltered hedge-row, where the snails and other the pearls from Britain were of small size, devoid of lustre, and land-shells love to dwell, we find the same admirable fitness and very inferior to those of Eastern origin; Tacitus also speaks of marvellous adaptation to the position and conditions under which them in much the same terms. It is fair, therefore, to infer each had existed : and notwithstanding that the one possesses that the description of pearl known in those early days was the power of supporting and carrying out the various functions obtained from the common edible mussel (Mytilus edulis, the subof existence in water far removed from the sea, the other beneath ject of the accompanying illustration, Fig. 4), which is only met the salt waves of the ocean, and the third in situations far re- with at the mouths of tidal rivers where the water is strongly moved from water either fresh or salt, a perfect shell, exquisite impregnated with salt, or in the sea itself. An investiin form, admirable in design, and very nearly of identical com- gation of the contents of these palatable bivalves will often position, is secreted in each instance. Many of these terres- lead to the discovery of small pearls of little or no commercial trial shells are, notwithstanding the position assigned them by value. Some years since, when pearls formed an important nature, capable of assimilating elements productive of rich, element in the prescriptions of medical men, they were far more admirable, and varied colouring. The annexed sketch of Helix eagerly sought after than now. The common oyster of our hemastoma (Fig. 3) will serve to show this. Few of our readers coasts is also occasionally found to yield small or seed pearls, will have failed to observe the beauty of tint and variety of which are of value only to the curious. The great silk mussel shading to be found on the shells of the common banded and (Pinna nobilis, a representation of which is shown at Fig. 5, on golden-yellow snails of our hedges, lanes, and thickets.
a reduced scale) is the largest bivalve shell found in our seas. Few natural processes are more extraordinary and mysterious It not only produces a tuft or tassel of silk-like material, than that by which colour and quality of product are produced known as the "byssus," which is at times spun into gloves by living creatures, and even the lowest orders of plants. We and stockings, but is often found to contain coloured pearls of take a grain of wheat, the seed of the poppy, the nux vomica, considerable value. Some of these are of a steel-grey tint, and the deadly nightshade ; we prepare a suitable tub or other others are lead-coloured, reddish, and occasionally even black. vessel for them to grow in; we furnish soil, water, heat, and it is not to this shell, however, that we have to look for the shelter; and in due time, when the plants from each of these true precious pearl of Britain : that is produced by a shell seeds have arrived at maturity, we shall find that no two much larger than the edible mussel, bearing no silk, and dwelling will be alike either in colour of blossom, form foliage, or exclusively in running streams of fresh water. The rivers of Wales, shape of plant. We go a step farther, and subject them and Ireland, Germany, and Switzerland have been long celebrated their products to chemical analysis, and we find food suitable for their pearl mussels. The Unio margaritiferus, as it is called for man associated with a plant-stalk covered with a sheath by naturalists, represented at Fig. 6 in the accompanying illusof pure flint in the wheat; whilst the poppy, with its rich tration, is the true fresh-water pearl-shell. It has been found scarlet tints and soft stem, yields the useful alkaloid morphia; measuring five inches and a half in length, and two inches ands and the nux vomica furnishes to us the deadly poison, half in breadth across the valves; but it is very rarely so large, the strychnia—all these wondrous elements and compounds being great majority of specimens but little exceeding five inches long drawn from the one simple tub of earth, and the water with by about two inches broad. Some curious information relating which it was supplied. So it is with the shells of the earth, the to Irish pearls was communicated by Sir Robert Redding, river, and the sea : by processes the nature of which we know through a Dr. Martin Lister, to the Philosophical Transactions nothing, results of the most extraordinary nature and magni- of 1673. He states that the rivers of Derry, Donegal, Tyrone, tude are brought about. Not only the spined and gaily-painted Wexford, and Kerry contained the pearl mussels, and that the shell of the coral reef, but the very reef itself, destined at some poor people in the neighbourhood of the streams fished for time to form a home for man, is slowly but surely being built them during the warm weather preceding harvest, when there up and massed together by the living labourer, who works by was little water flowing, and that they made use of either their laws far beyond our ken. The eggs of birds, too, are marvellous toes, wooden tongs, or sharp-pointed sticks for dislodging in their form and colouring, and possess a crust or shell closely them from their retreats on the bottom or among the stones. resembling that of the shells we have been describing, both in The sharp sticks were, he says, thrust between the open valves texture and component parts. Dealing with shells and struc- of the shells “as they lay in part opened, with the white foot tures allied to them, we can easily pile such beautiful works of protruded like a tongue ont of the mouth.” He then states an all-wise Creator together, apply fire and reduce them to lime; as follows :-"Some gentlemen of the country made great but with all our boasted skill in science and art, no human advantage thereof; and I myself, whilst there, saw one pearl power or ingenuity could, from the materials thus formed, cause bought for fifty shillings that weighed thirty-six carats, and the building up of that which has been so readily torn down. was valued at forty pounds. Everybody abounds with stories Pearls, after all, are merely lime which has passed through the of the good pennyworths of the country, but I will add one laboratory of that most wonderful of chemists, the shell-bearing more. A miller took out a pearl, which he sold for four pounds mollusk. For the early history of English pearls, and the shells ten shillings to a man, who sold it for ten pounds, who sold it which yield them, we
must go back to a period when Britain was to the late Lady Gleneally for thirty pounds, with whom I saw known to other nations as a mere group of islands vaguely it in a necklace. She refused eighty pounds from the lata known as the Cassiterides. This supposed group was, no doubt, Duchess of Ormond for it." formed by the Scilly Islands and the projecting land of the coast Scotland, too, particularly in past times, had reason to boast of Cornwall. This region was probably first discovered by a of the importance of her river pearls, the Tay, from Perth to band of Phænician voyagers who were dispatched about 600 B.C., Loch Tay, being one of the richest streams. Captain Brown, by Pharaoh-Necho, king of Egypt (the same who slew Josiah, in recording the particulars of the Scottish pearl-fishing, says, king of Judah). These bold adventurers were directed to set “The pearls sent from Scotland to London from
the years 1761 sail from the Red Sea, to voyage round Africa, and
enter the to 1764 were estimated at ten thousand pounds' Falue.” The northern seas by the Straits of Hercules, when they were to Isle of Man, too, has had its river harvest, and a peculiar
variety of the unio (U. roissyi) was found to produce a very appears no reason why they should not be found as abundantly noteworthy number of pearls. The river flowing near Braddon as when Sir Robert Redding wrote: speaking of the proportion was that most successfully fished. The river Conway, in of prizes to blanks, he says, “Although, by common estimate, North Wales, has for ages been known to be one of the chosen not above one shell in a hundred may have a pearl, and of these homes of the pearl shell, as both the salt-water mussel at the pearls not above one in a hundred be tolerably clear." Yet a river's mouth, and the unio high up among the brawling rills vast number of fair merchantable pearls, and too good for the which ripple among the hazels and yellow furze blossom, bear apothecary, are offered for sale by these people every summer with them ever and anon the much-coveted treasure. Bettws. assize." y-Coed has, so tradition says, the honour of being the locality near The streams of Bavaria at the present day produce from which the bold and handsome Welsh nobleman, Sir Richard time to time pearls well worth obtaining, and about thirty Wynne, obtained the rich and costly pearl which he presented years since a most important find of them was made by mere to the queen of Charles II. The term "Cregin diluw" has been chance in Norway. An unusually dry summer had caused the by the Welsh given to the Conway shells from an idea, which waters of the Zeddern Channel to become nearly dry. A they appear to have entertained, that they were brought to the peasant who chanced to be wandering about over the shingle river at the time of the delage. The formation of pearls in the land pebbles, seeing a dead and partially dried unio laying in its
L. LIUNEA STAGNALIS. 2. TRITON. 3. HELIX HEMASTOMA. 4. MYTILUS EDULIS (THE EDIBLE MUSSEL). 5. Pinna NOBILIS (THE
SILK MUSSEL). 6. UNIO MARGARITIFERUS (THE FRESH-WATEE PEARL SHELL). 7. DAMAGED SHELL REPAIRED BY PEARLY DEPOSIT. 8. ADONTA (POND MUSSEL).
tissues of this or any other mollusk can be only viewed in the wide-spread shell, stopped, and picked it up, when, much to his light of a diseased or abnormal secretion, caused in the majority wonder and delight, out rolled a pearl worth £50. Specimens of cases by the presence of some foreign and irritating cause of even greater value than this were soon after discovered by the Linnæus discovered by actual experiment that grains of sharp people, who rushed from far and near to the treasure-yielding sand introduced between the valves of the shell in such a way sands, which were thoroughly searched until the return of the that they rested between the body of the animal and the water to its accustomed level put a stop to the search. A shell "mother-of-pearl,” or shell-lining, caused in a short time the closely resembling the Unio margaritiferus is to be found in deposition of a coating or crust of pearl on the sand grain, most of the ponds, brooks, and rivers of England;
it is known which, acting as a nucleus, gathered the shielding matter as the " pond mussel," or Adonta. A reference to Fig. 8 will at around it, and so guarded the delicate tissues of the mollusk once show the particulars of external form in which the two shells from friction and injury. It has also been found that by differ. The Adonta, so far as we have observed, yields no pearls, drilling a small hole through the outer coatings of the sheli, but produces an incredible number of young adontas, which are and leaving the lining untouched by the boring instrument, carried within the parent shell completely valved and ready to that a pearl nodule was in a short time formed, as shown in the shift for themselves when cast on the world of waters. It is annexed illustration (Fig. 7), so as to defend the weak point, just said that an American naturalist has succeeded in computing as a skilful armourer would patch a weak place in breast or back one Adonta family at 600,000 in number. There are many more plate. It is somewhat remarkable that the search for home shell-dwellers interesting in habits
and curious in form, and to pearls should be so rarely followed at the present day, as there these we hope to refer in another paper.
LESSONS IN GREEK.-XXVII.
Second Aorist.-Tense-stem λιπ-. PARADIGM OF THE REGULAR VERB Aww, I loose (MIDDLE
Sing. λιπ-ου, -εσθω, remain behind. (Like the Present.)
INFINITIVE MOOD. .
Present, , λυ-ε-σθαι, to loose one's self, or to be loosed. Present.-Tense-stem λυ-. Imperfect.-Tense-stem ε-λυ-.
First Aorist, λυ-σ-ασθαι, to have loosed one's self. Sing. 1. λυ-ομαι, I loose myself, or ε-λυ-ομην, I was loosing my
Second Aorist, λιπ-εσθαι, to hαυe remained behind. am loosed, etc. self, etc.
PÅRTICIPLES. 2. λυ-η.* ε-λυ-ου.
Present, , λυ-ομενος, loosing one's self. 3. λυ-εται. E-λυ-ετο.
First Aorist, λυ-σ-αμενος, Μανίης ίoosed. Dual. 1. λυ-ομεθον. ε-λυ-ομεθον.
Second Aorist, λιπ-ομενος, λαυϊng remained behind. 2. λυ-εσθον.*
ε-λυ-εσθον. 3. λυ-εσθον, * ε-λυ-εσθην.
EXERCISE 76.-GREEK-ENGLISH. Plur. 1. λυ-ομεθα.
1. Λοιμην. 2. Λυσoιμην. 3. Λυομαι. 4. Λυωμαι. 5. Ελυομην. 2. λυ-εσθε,* ε-λυ-εσθε. 6. Ελυσαμην. 7. Λυσομαι. 8. Ελιπομην.
9. Λυονται. 10. 3. λυ-ονται. ε-λυ-οντο.
Ελνοντο. 11. Ελυσαντο. 12. Λυσαισθε. 13. Λιπoιμην. 14.
15. Λιπομενος. 16. Λυσασθαι. 17. Λυεσθαι. 18.
Λυομενος. 19. Λυσασθε. 20. Λιπωμαι. 21. Ελνσω. 22. Λυσηται. Sing. 1.. λυ-σ-ομαι, I shall loose myself.
| 23. Λυεσθων. 24. Λυοισθον. 25. Λυομενου. 26. Ελυεσθε. 27. (The Person-endings are like the Present.)
Λυσαμενοι. 28. Λυοιντο. 29. Λυσαιμεθα.
EXERCISE 77.-ENGLISH-GREEK. Sing. 1. ε-λυ-σ-αμην, I loosed Dual.1, ε-λυ-σ-αμεθον. 1. I might loose myself. 2. He might loose himself. 3. They 2. ε-λυ-σ-ω. [myself.
2. ε-λυ-σ-ασθον. might loose themselves, 4. To loose one's self. 5. Loosing 3. ε-λν-σ-ατο.
3. ε-λν-σ-ασθην. one's self. 6. Loose yourselves. 7. He would loose himself. Plur. 1. ε-λυ-σ-αμεθα. 2. ε-λυ-σ-ασθε. 3. ε-λυ-σ-αντο. -8. Let him loose himself. 9. We may have loosed ourselves.
10. They will loose themselves. 11. He may loose himself. 12. Second Aorist.-Tense-stem ε-λιπ-.
You two might have loosed yourselves. 13. You may have Sing. 1. ε-λιπ-ομην, I remained behind.
loosed yourself. 14. They remained behind. 15. He may have (Like the Imperfect Indicative.)
remained behind. 16. Do ye remain behind. 17. To have loosed
one's self. SUBJUNCTIVE MOOD.
Conjugate, according to the active and middle paradigms, Present.-Tense-stem λυ-.
these verbs :-παιδευω, I instruct, educate ; βασιλευω, I reign. Sing. 1. λυ-ωμαι, I may loose Dual. 1. λυ-ωμεθον.
The chief parts are-παιδευω, παιδευσω, πεπαιδευκα, πεπαιδευμαι, 2. λυ-η.* [myself, etc.
2. λυ-ησθον. and βασιλεύω, βασιλευσω, βεβασιλευκα, βεβασιλευμαι.
THE PASSIVE VOICE OF λνω.
(The Present and Imperfect are the same as in the Middle Voice.) First Aorist.-Tense-stem λυ-σ..
First Aorist.-Tense-stem ε-λυ-θ-.
Sing. 1. ε-λυ-θ-ην, I was loosed, etc.
Dμαι. 2. ε-λυ-θ-ητον. (Like the Subjunctive Present.)
3. ε-λυ-θ-ητην. OPTATIVE MOOD.
Plur. 1. ε-λυ-θ-ημεν.
2. ε-λυ-θ-ητε. Imperfect.--Tense-stem λυ-. First Aorist.--Tense-stem λυ-σ-.
3. ε-λυ-θ-ησαν. Sing. 1. λυ-οιμην, I might loose λυ-σ-αιμην, I might have myself, etc. loosed myself, etc.
First Future.-Tense-stem λυ-θή-σ-. 2. λυ-οιο. λυ-σ-αιο.
Sing. 1. λυ-θή-σ-ομαι, I shall be loosed, είc. 3. λυ-οιτο. λυ-σ-αιτο.
(Like the Indicative Present Middle.) Dual.1. λυ-οιμεθον.
λυ-σ-αιμεθον. 2. λυ-οισθον. λυ-σ-αισθoν.
Second Aorist.-Tense-stem e-τριβ-. 3. λυ-οισθην. λυ-σ-αισθην.
Sing. 1. ε-τριβ-ην, I was rubbed, etc. Plur. 1. λυ-οιμεθα. λυ-σ-αιμεθα.
(Like the Indicative First Aorist Passive.) 2. λυ-οισθε.
λυ-σ-αισθε. 3. λυ-οιντο. λυ-σ-αιντο.
Second Future.-Tense-stern τριβ-η-σ-.
Sing. 1. τριβ-η-σ-ομαι, I shall be rubbed.
(Like the Indicative First Future Passive.) Sing. 1. λυ-σ-οιμην, I would loose myself, etc. (The person-endings like the Optative Imperfect.) Perfect.-Tense-stem λε-λυ». Pluperfect.-Tense-stem e-Af-Ar.
Sing. 1. λε-λυ-μαι, I have been
ε-λε-λυ-μην, I had been Second Aorist.-Tense-stem λιπ-.
loosed, etc. Sing. 1. λιπ-οιμην, I might or would, etc.
ε-λε-λυ-σο. (Like the Optative Imperfect.)
ε-λε-λυ-το. Dual. 1. λε-λυ-μεθον.
ε-λε-λυ-μεθον. IMPERATIVE MOOD.
ε-λε-λυ-σθον. Present.--Tense-stem Avo. First Aorist.-Tense-stem λυ-σ-, 3. λε-λυ-σθον.
ε-λε-λυ-σθην. Sing. 2. Av-ov, loose thou thyself, etc. Au-r-01,* loose thyself, etc.
Plur. 1. λε-λυ-μεθα.
ε-λε-λυ-μεθα. 3. λυ-Εσθω. λυ-σ-ασθω.
ε-λε-λυ-σθε. Dual. 2. λυ-εσθον.*
3. λε-λυ-νται. λυ-σ-ασθον.
ε-λε-λυ-ντο. 3. λυ-εσθων.* λυ-σ-ασθων.*
Note that when the tense-ending uat of the perfect passive is Plur. 2. λυ-εσθε.*
preceded by a consonant the third person plural is supplied, for 3. λυ-εσθωσαν, commonly λυ-σ-ασθωσαν, commonly euphony's sake, by the perfect participle with εισι-for τετυπνται, εσθων.* ασθων,και
τετυμμενοι εισι-and in the pluperfect τετυμμενοι ησαν.
Perfect Future, or Third Future.-Tense-stem Ae-Av-o..
Aureos, one who ought to be loosed. (Like the Indicative Present.)
1. Ετριβη. 2. Τριβη. 3. Τριβειης. 4. Τριβειη. 5. Λυθειητην. First Aorist.-Tense-stem λυ-θ-. Perfect.-Tense-stern λε-λυ-.
6. Λυθειεν. 7. Λυθητω. 8. Λυθηναι. 9. Λυθησομενος. 10. Τριβηναι. 11. Τριβησομενος.
12. Ελυθης. 13. Ελυθητε. 14. Sing. 1. λυ-θ-ω, Imay have been λε-λυ-μενος, -ω, I may have loosed, etc. been loosed, etc.
Λυθηση. 15. Λυθωμεν. 16. Λυθειημεν. 17. Λυθωσι. 18. Λυθεις.
19. Λυθησεσθαι. 20. Τριβεις. 21. Τριφηθητω. 22. Λελυμαι. 2. λυ-θ-ης. λε-λυ-μενος, -ής.
23. Ελελυμην. 24. Λελυσομαι. 25. Λελυνται. 26. Ελελυντο. 3. λυ-θ-η. λε-λυ-μενος, -η.
27. Λελυμενος ειης. Dual. 2. λυ-θ-ητον.
λε-λυ-μενω, -ητον. 3. λυ-θ-ητον. λε-λυ-μενω, -ητον.
EXERCISE 79.-ENGLISH-GREEK. Plur. 1. λυ-θ-ωμεν.
1. He was loosed. 2. He may have been loosed. 3. He might 2. λυ-θ-ητε. λε-λυ-μενοι, -ητε.
have been loosed. 4. He shall be rubbed. 5. They shall be 3. λυ-θ-ωσι. λε-λυ-μενοι, «ωσι.
loosed. 6. He was rubbed. 7. I have been loosed. 8. Thou Second Aorist.-Tense-stem τριβ-,
mayest have been loosed. 9. They shall have been loosed. Sing. 1. τριβ-ω, Immay be rubbed.
Of the participles in the middle and passive voice, those
which end in os (uevos) are declined like ayafos, -1), -ov. Of (Like the Subjunctive First Aorist Passive.)
those which end in eus, take the following as a model : OPTATIVE MOOD.
DECLENSION OF λυθεις, λυθεισα, λυθεν, loosed. First Aorist.-Tense-stem λυ-θ-, Perfect.-Tense-stem λε-λυ-.
λυθεις, λυθεισα, λυθεν. 2. λυ-θ-ειης. λε-λυ-μενος, -ειης.
λυθεντος, λυθεισης, λυθεντος. 3. λυ-θ-ειη. λε-λυ-μενος, -ειη.
λυθεντι, λυθειση, λυθεντι. Dual. 2. λυ-θ-ειητον. λε-λυ-μενω, -ειητον.
λυθεντα, λυθεισαν, λυθεν. 3. λυ-θ-ειητην. λε-λυ-μενω, «ειητην.
Dual. Plur. 1. λυ-θ-ειημεν. λε-λυ-μενοι, -ειημεν.
Nom. and Acc. λυθεντε, λυθεισα, λυθεντε. 2. λυ-θ-ειητε. λε-λυ-μενοι, -ειητε,
Gen. and Dat. λυθεντoιν, λυθεισαιν, λυθεντοιν. 3. λυ-θ-ειεν. λε-λυ-μενοι, «ειησαν.
λυθεντες, λυθεισαι, λυθεντα. Sing. 1. λυ-θή-σ-οιμην, I would be loosed.
λυθεντων, λυθεισων, λυθεντων. (Like the Optative Imperfect Middle.)
λυθεισι, λυθεισαις, λυθεισι. Acc.
λυθεντας, λυθεισας, λυθεντα. Second Aorist.-Tense-stem τριβ-.
PERSONAL ENDINGS OF THE MIDDLE VOICE.
HISTORICAL TENSES. (Like the Optative First Aorist Passive.)
1st Pers. 2nd Pers, 3rd Pers 1st Pers, 2nd Pers. 3rd Pers. Second Future.-Tense-stem τριβ-η-S..
Duαι. -μεθον, -σθον, -σθον. -μεθον, -σθον, -σθην. Sing. 1. τριβ-η-σ-οιμην, I would be rubbed.
Ρίur. «μεθα, -σθε,
•μεθα, -σθε, (Like the Optative First Future Passive.) Perfect Future, or Third Future.-Tense-stern λε-λυ-σ..
KEY TO EXERCISES IN LESSONS IN GREEK.-XXVI. Sing. 1. λε-λυ-σ-οιμην, I would have been loosed.
EXERCISE 74.-GREEK-ENGLISH, (Like the Optative Imperfect.)
1. Loosing. 2. To be about to loose. 3. He is loosing. 4. I have
loosed. 5. I had loosed. 6. I shall loose. 7. Ye two would loose. IMPERATIVE MOOD.
8. Thou wouldest loose. 9. Let him loose. 10. Loose ye. 11. I was
loosing. 12. He shall loose. 13. We are loosing. 14. Ye two were First Aorist.-Tense-stem λυ-θ-. Perfect.— Tense-stem 26-du.. loosing. 15. I might loose. 16. I loosed. 17. He has loosed. 18. Sing. 2. λυ-θ-ητι, be thou loosed, λε-λυ-σο.
He loosed. 19. I might have, loosed. 20. Loose thou. 21. Let them 3. λυ-θ-ητω. [etc. λε-λυ-σθω.
two loose (aor.). 22. Having loosed. 23. I may have loosed. 24. Dμαι. 2. λυ-θ-ητον.
Thou hast loosed. 25. They had loosed. 26. They loosed. 27. They 3. λυ-θ-ητων. λε-λυ-σθων.*
have loosed. 28. Ye might have loosed. 29. Thou mayest have loosed. Plur. 2. λυ-θ-ητε.
30. Thou hast appeared. 31. Thou didst leave. 32. Thou mayest
have left. 33. Thou mightest have left. 34. Let him leave. 35. Hay. 3. λυ-θ-ητωσαν. λε-λυ-σθωσαν, commonly
ing left. 36. To have appeared. 37. Thou hadst appeared. 38. He Second Aorist.-Tense-stem τριβ-η.
might have appeared. 39. He might loose. 40. They might looso. Sing. 1. τριβ-η-θι, be thou rubbed.
EXERCISE 75.- ENGLISH-GREEK. (Like the Imperative First Aorist Passive.)
1. Πεφηνα. 2. Ελιπετην. 3. Λειποι. 4. Λειποιτε. 5. Aυουσι. 6. Ανωσι.
7. Ανοιεν. 8. Ανσαιτε. 9. Ανe. 10. Λιοντων. 11. Λελυκα. 12. Λυσετε. 13. INFINITIVE MOOD.
Λυσωσι. 14. Λυσεις. 15. Λυειν. 16. Λυσειν. 17. Λυσων, 18. Ανσας. 19. First Aorist. . λυ-θ-ηναι, to have been loosed."
Αυη. 20. Ελελυκειτην. 21. Ανοιτην. 22. Αυητον. 23. Πεφηνασι. 24. ΠεφηFirst Future. λυ-θή-σ-εσθαι, to be about to be loosed. νατον. 25. Πεφηνε. Second Aorist.
τριβ-ηναι, to have been rubbed. Second Future. τριβ-η-σεσθαι, to be about to be rubbed.
LESSONS IN ALGEBRA.—XVII. Perfect.
λε-λυ-σθαι, to have been loosed. Perfect Future, or λε-λυ-σ-εσθαι, to be about to be loosed.
SOLUTION OF PROBLEMS. Third Future.
171. For the solution of problems in Simple Equations, wo
derive from the preceding principles the following general rule:PARTICIPLES.
RULE.-1. Translate the statement of the question from the First Aorist. λυ-θ-εις, λαυϊng been loosed.
ordinary language into algebraic language, in such a manner as First Future.
λυ-θή-σ-ομενος, being about to be loosed. to form an equation; that is, put the question into the form of an Second Aorist. Tp.B-ers, having been rubbed.
equation. Second Future.
τριβ-η-σ-ομενος, being about to be rubbed. 2. Clear the equation of fractions by multiplying every term in Perfect. λε-λυ-μενος, λανίng been loosed.
both members by all the denominators successively, or by their Perfect Future, or A6-Av-o-ouevos, being about to be loosed. Least common multiple. Third Future,
3. Transpose all the terms containing the unknown quantity to
the one side of the equation, and all the known quantities to the 2. Divide 39 into four parts, such that if the first be increased other, taking care to change the signs of the terms transposed, and by 1, the second diminished by 2, the third multiplied by 3, and incorporate the terms that are alike.
the fourth divided by 4, the results may be all equal. 4. Remove the co-efficient of the unknown quantity, by dividing 3. If a certain number is divided by 12, the quotient, all the terms in the equation by it; the result will be the solution dividend, and divisor, added together, will amount to 64. What roquired.
is the number? PROOF.-Substitute the value of the unknown quantity for the 4. An estate is divided among four children, in such a manner letter which stands for it in the equation ; and if the number that the first has £200 more than of the whole, the second satisfies the conditions of the question, it is the answer sought. has £340 more than of the whole, the third has £300 more
PROBLEM 1.-A man being asked how much he gave for his than of the whole, the fourth has £400 more than of the watch, replied: If you multiply the price by 4, to the product whole. What is the value of the estate ? add 70, and from this sum subtract 50, the remainder will be 5. What is that number which is as much less than 500, as a equal to 220 pounds.
fifth part of it is greater than 40 ? In order to solve this question, we must first translate the 6. There are two numbers whose difference is 40, and which conditions of the problem into such an algebraic expression as are to each other as 6 to 5. What are the numbers ? will form an equation.
7. Suppose two coaches to start at the same hour, one from Let æ be the price of the watch.
London for Glasgow, and the other from Glasgow for London, This price is to be multiplied by 4, which makes 4x; to the the former travelling 10} and the latter 91 miles per hour. product 70 is to be added, making 4x + 70; from this, 50 is to Where will they meet, the distance between the two cities being be subtracted, making 4x + 70 — 50.
400 miles ? Here we have a number of the conditions, expressed in 8. Suppose everything to be as in the last question, except algebraic terms; but we have as yet no equation. We must that the coach from Glasgow starts two hours earlier than the observe, then, that by the last condition of the problem, the other. Where will they meet ? preceding terms are said to be equal to 220.
9. A dealer purchases 60 yards of cloth for £30; and by We have, therefore, this equation, 4x + 70 — 50 = 220; selling one part of it at 12s., another, twice as great, at 14., which reduced, gives æ= 50. Ans.
and the rest at 10s. per yard, he gains £8. How many yards Here the value of w is found to be 50 pounds, which is the were in the several lots ? price of the watch.
10. Suppose two dealers each annually to double his capital, PROOF.-The original equation is 4x + 70 - 50 = 220; sub- except an expenditure of £100; and that at the end of three stitating 50 for x, it becomes 4 X 50 + 70 — 50 = 220; that years the capital of one is found to be doubled, while the other is, 220 = 220.
has only half what he had at first. How much had each to comPROBLEM 2.-What number is that to which, if its half be mence with ? added, and from the sum 20 be subtracted, the remainder will 11. If a person each year double his capital, except an expenbe a fourth of the number itself ?
diture of £300 the first year, £400 the next year, and £500 the In stating questions of this kind, where fractions are con- third, and at the end of three years be found to be worth £5,500, cerned, it should be recollected that jx is the same as that
what was his original capital ? 2x
12. A father's age is now treble of his son's, while five years 5'
ago it was quadruple. What are their present ages ? Let æ be the number required.
13. Divide £1,000 between A, B, and C, giving A £100 more,
and B £50 less, than C. Then by the conditions, we have x +
, and re 14. A spirit merchant finds that if he add 10 gallons to a cask 2
of brandy, the mixture will be worth 21s. per gallon; but that ducing the equation, we have <= 16. Ans.
if he had ten gallons more, the value will be reduced to 188. 16
16 PROOF.—Thus 16 + - 20
How many gallons were in the cask ?
15. Find a number, such that if it be divided successively by PROBLEM 3.—A father divides his estate among his three sons 2, 3, 4, 5, 6, 7, 8, 9, and 10, half the sum of the first four in such a manner, that the first has £1,000 less than the quotients increased by 20 shall be equal to the sum of the whole; the second has £800 less than one-third of the whole ; remaining five. the third has £600 less than one-fourth of the whole. What is 16. Find two numbers differing by 6, and such that three the value of the estate ? Ans. £4,1147.
times the less may exceed twice the greater by 7. PROBLEM 4.--Divide 48 into two such parts, that if the less be 17. Find a number, such that if it be increased successively divided by 4, and the greater by 6, the sum of the quotients by 1, 2, and 3, the sum of one-half of the first result and onewill be 9.
third of the second shall exceed one-fourth of the third by 8. Let æ be the smaller part; then 48 — x is the greater part; and,
48 by the conditions of the problem, we have + - 9.
LESSONS IN ITALIAN.-XIV Whence x= 12; therefore, 12 is the less part, and 36 the
EXERCISES FOR PRACTICE. greater part.
We resume in this lesson our series of exercises which will 172. Letters may be employed to express the known quantities afford the student sufficient practice in translating simple senin an equation, as well as the unknown. A particular value is tences in Italian into English, and turning English into Italian. assigned to the letters, when they are introduced into the calcu- The copious vocabularies will afford the learner a useful opporlation ; and at its close, the numbers are restored.
tunity of storing his mind and memory with Italian words. EXAMPLE. If to a certain number 720 be added, and the sum be divided by 125, the quotient will be equal to 7392
VOCABULARY. divided by 462. What is the number?
E's-so, m., ès-sa, f., L'0-ro-16-gio, the watch
he, she, it (of perLet æ be the number required ; and let a=720, b=125, Che, who, whom, that,
sons and things).
Ma, but. d=7392, and h=462.
Il cap-pel-lo, the hat. M6l-to, very. Then, by the conditions of the problem, we have a ta d. E-gli, he.
Il ca-vdl-lo, the horse. Per, for. and reducing, we have <=
ñi E'lla, she, it (in refe. I fan-ciúl-10, the child. Per-du-to
, lost. bd - ah
rence to a feminine I tem-pe-ri-no, the pen. Tro-ta-to, found. h (125 x 7392)-(720 x 462)
knife. Restoring the numbers, we have x= =1280.
1. Mí-o pá-dre è buô-no ; é-gli ha án-che un buôn fra-těl-lo. EXERCISE 29.-MISCELLANEOUS PROBLEMS IN SIMPLE 2. Mi-a má-dre è buð-na; él-la ha án-che ú-na bud-zia sorel-la. EQUATIONS.
3. Ab-bia-mo ve-du-to
rổ-stro zi-o; e-gli ha com-pra-to un gràn 1. Divide 11 into two parts, such that the sum of twice the lubro. 4. A-véte voi ve-dú-to il no-stro gior-di-no ? és-soe first and half the second may be 16.
5. Hô com-prá-to ú-na pén-na; és-sa è mol-to