feeding bird. The swallow, which plunges with such reckless impulse through the air, will nevertheless seize a small insect as it dashes along with almost unerring certainty. Usually the prey is so small, that the wonderful powers of the bird displayed in the chase cannot be observed; but sometimes, when the insect has large wings, this dexterity may be seen. The writer has seen a swallow seize, while in headlong flight, the beautiful, scarce swallow-tail butterfly, and shear out its sapid body from between the wide wings, and let them float severally down; and then, not satisfied with a feast so little proportioned to the splendour in which it was dished up, glance round and seize again the several pieces before they had time to reach the ground. How, then, is a long sight and a keen short sight to be obtained from the same eye? This is done mainly by the aid of the bony plates already described. These are so disposed that the edge of one is capable of sliding over the edge of its next neighbour, so that when the fibres of the muscle which unites them contract they compress the eye all round and make it more tubular, while the humours of the eye, thus subjected to pressure, cause the cornea to protrude more, and also the retina to be removed further from the lens. These motions are, in addition to the adjustment for distance, found in mammals. in small quantity, and the result of this is that the fish can see distant objects as well through the air as through the water; and this is important, because almost all fish are surface fish; many feed on flies, and most have to be on their guard against aerial foes. The reader, then, need not be surprised when the sun-loving shoals of carp or chub all plunge headlong into the depths when he appears on the river bank. As a singular instance of the adaptation of means to ends, it is found that all animals, whether reptiles, birds, or brutes, which are amphibious, or which spend much time in the water, have eyes which, though they differ from those of fish, in some things have the same relation of the cornea and lens. Thus the whale and the dolphin (which are but brutes which have taken to the sea), the cormorant and diver, the frog and the crocodile, have all spherical lenses and flat corneæ. Fish and frogs have on the outer layer of the choroid a layer of silvery or golden crystals, and this layer, which is continued round till it occupies the front layer of the iris, gives to the toad so metallic and bright an eye as to countenance the legend that it has a jewel in its head. So Shakespeare "The toad, ugly and venomous, Wears yet a precious jewel in its head." LESSONS IN GERMAN.-IV. SECTION VIII.-INDEFINITE ARTICLE. Intimately connected with this pressure upon and alteration of the dimensions of the humours of the eye, is another peculiarity in the eye of a bird. This is a puckered, purse-like membrane, which is attached to the optic nerve, which in this class enters into the eye by a slit-like opening. This membrane THE indefinite article is less varied than the definite, having for is sometimes called a marsupium, from its resemblance to a the masculine and neuter nominative but one form, aspurse, and sometimes a pecten, from its supposed likeness to a comb. It stretches to the interior of the eye to a different extent in different birds, and is composed of a tangled mass of blood-vessels, mixed with pigment granules. Whether this is simply an erectile organ, which can rapidly contract and enlarge suddenly as it is deprived of or injected with blood, or is capable of feeding the vitreous humour with liquid strained by it from the blood, and draining it off again as circumstanees require, is not known. The eyes of reptiles are so different from one another, ranging in structure between the eye of the bird and that of the fish, that it is better at once to pass on to a description of an eye adapted to sight in water. A fish, living as it does in an atmosphere which is many hundred times denser than air, and by no means so transparent, must have an eye suited to look at near objects. It must therefore be able to concentrate the rays of light rapidly; yet it is under this disadvantage, that as it is only when passing from a rare into a dense transparent convex substance that diverging rays are bent towards one another, and the original rays pass through a dense medium, the cornea and aqueous humours can play no part in the bending of the rays towards one another, for they are of about the same density as water. The whole duty of refraction must thus be done by the lens. This is very dense, and of the sheets of which it is made up the inside are denser than the outside, while it is so convex both before and behind as to become a perfect globe. Both the consistence and shape of the round lens may be seen by squeezing it out of the eye of a cooked fish, even by those whose taste for comparative anatomy is only stimulated at the dinner-table. In connection with this kind of lens we have a shallow eye. In other words, if the cornea, through which light enters, be turned upwards, the back of the eye on which the retina is spread resembles a saucer, and not a cup as it does in animals and birds. This is so much the case, that even though the hard capsule is shallower than in brutos, there is still left a large space between this and the choroid, and even this latter has between two of its layers a horse-shoe shaped "gland" composed of blood-vessels, something like the pecten of a bird, though in a different place, and with exactly a converse function. The hard outer coat is strengthened and held to its form by a cup-shaped bone or cartilage, which occupies the parts which are left unoccupied by the bird's eye-bones; because while the latter are used to elongate the eye this maintains a shortened axis. The cornea, or window, and the watery fluid behind it being usele collect the rays, are left, the one flat and the other Masculine: ein Mann, a man. Neuter: ein Glas, a glass. DECLENSION OF THE INDEFINITE ARTICLE MASCULINE AND Masculine. NEUTER WITH NOUNS. N. Ein Mann, a man ; D. Neuter. ein Kint, a child; eines Kintes, of a child; OF THE COMPOUNDING OF NOUNS IN GERMAN. 1. Nouns are more frequently compounded in German than in English; and accordingly one word in German often requires for its full translation several in English, as :— Wirkungskreis, sphere of action (action sphere); 6. Der Vater dieses Geld des Kaufmanns? 9. Haben Sie den Gewehr. 5. Wer hat den Pflug des Bauers? SECTION IX.-DECLENSION OF ADJECTIVES. The adjective has thus far been employed only predicatively, Manches schön-e Märchen ist eitel. in which use it is unvaried in form, as Stahl ist hart, steel is hard, Blei ist weich, lead is soft. The terms attributive and predicative have, in grammar, a strictly conventional sense, and should be distinctly understood. If we say, The deep river is here (der tiefe Fluß ist hier), the adjective deep is attributive: for the quality, depth, is there referred to as a known and recognised attribute of the river. If we say, The river is deep here (ter Fluß ist hier tief), the adjective is predicative, for we then merely affirm or predicate of the river that it has the quality, depth. When used attributively, the adjective is varied by the addi tion of suffixes. 1. When not affected by a preceding word, the adjective is inflected according to Solcher fein-e Stahl ist kostbar. Yonder (that) large horse is Many a good man is poor. EXERCISE 10. 1. Ist dieser junge Mann der Sohn des Capitains? 2. Nein, er ist der SECTION X.-DECLENSION OF ADJECTIVES (continued). Ein, ein (a or an); Mein, mein (my); Dein, dein (thy); Neuter. Masculine. Erlicher, the adjective adds, in the nominative masculine and in the nominative and accusative neuter, the letter c, and in all the other cases en; and is inflected according to the adjective has, in the nominative masculine and in the nominative and accusative neuter, the terminations of the old declension, and, in all the other cases, those of the new, and is said to be of 1. In the preceding list of words, ein, mein, dein, x, it will be seen that their form for the masculine and neuter is the same; and hence that they do not (like the previous class, der, dieser, ., and like adjectives of the old declension) indicate the gender of the nouns which they precede. The adjective, therefore, by taking the characteristic terminations (er for the masculine and cs for the neuter) assumes the office of pointing out the gender of its noun, as Masculine: Gin groß-er Stein, a great stone. ENDINGS OF Aber, but. 3. RÉSUMÉ OF EXAMPLES, SHOWING ADJECTIVES IN THE NOMINATIVE, AFTER DECLENSION. Faul, lazy, idle. Holländer, m. Dutch man. Jhr, your. 2. RÉSUMÉ OF EXAMPLES, SHOWING THE ENDINGS OF ADJECTIVES IN THE NOMINATIVE AFTER THE MIXED DECLENSION. Attributive. Predicative. Gin warm-er Neck ist gut. 2. n n m A warm coat is good. 1. Ist Ihr guter Freund, der Capitain, noch ein junger Mann? 2. Ja, er ist noch jung, aber jein guter Freund, der Holländer, ist alt. 3. Haben Sie einen schönen, großen Hund? 4. Nein, ich habe ein schönes, großes Pferd. 5. Hat Ihr kleines Kind mein neues Messer? 6. Nein, aber Ihr guter Sohn hat Ihren neuen Stock. 7. Hat der Fleischer ein fettes Schaf? 8. Ja, und sein guter Sohn hat ein schönes, weißes Lamm. 9. Ist Ihr Freund, der junge Holländer, reich oder arm? 10. Er ist nicht reich, aber er ist zufrieden. 11. Ein zufriedener Mann ist auch reich. 12. Ein reicher Mann ist nicht stets ein zufriedener Mann. 13. Ihr großes Haus hat ein steiles Dach und einen tiefen Keller. 14. Von wem haben Sie Ihr neues Sopha? 15. Ich habe es von einem guten Freunde. 16. Das Schwein ist ein faules, fettes Thier. 17. Ein treuer Freund ist ein starker Schuß. LESSONS IN PENMANSHIP.-V. HITHERTO the attention of the learner has been confined to letters based on the elementary stroke called the "pot-hook" or "bottom-turn." He may now proceed to copy the next elementary stroke, called the "top-turn" or "hanger," as shown in Copy-slip No. 11. This stroke will be found to enter into the composition of three letters only, and therefore plays by no means so important a part in the formation of the writing alphabet as the bottomturn, which, as it has been already said, enters into the composition of no less than nine. It consists of a fine hairstroke, commenced on the central line e c, and carried upwards in a direction bending gradually towards the right, as far as the upper line a a, where it is turned and changed into a broad down-stroke, which is brought downwards, with an equal pressure of the pen throughout, as far as the lower line bb. The top-turn may be described as being precisely the reverse of the bottom-turn; or, in other words, the bottom-turn reversed, as may be seen by turning the page upside down, and examining the stroke n. It is only used in combination with other forming letters, for unlike the bottom of the writing alphabet which is even by its repetition or any formed 'modi** It is needful, therefore, for the learner to become acquainted with a third elementary stroke before he can proceed to the formation of any new letters, and this he will find in the top and bottom-turn shown in Copy-slip No. 12. This stroke enters into the composition of six letters of the writing alphabet, as the learner will find in future lessons. It consists of a fine hair-stroke, commenced at the central line e c, brought upwards towards the right in a gentle curve, and turned at the upper line a a into a broad down-stroke, which is again narrowed as it approaches the lower line bb into a fine hair-stroke that is turned and carried upwards towards the right. It may be described as being formed of the upper half of the top-turn and the lower half of the bottom-turn, joined together on the line c c. When the learner can make these strokes with ease, he will find that he is in a position to form two more letters of the writing alphabet without any difficulty whatever, while he has also advanced more than half-way towards the formation of the seven other letters that are partly made by the aid of these strokes. He may now proceed to copy the letters n and m, as shown in Copy-slips Nos. 13 and 14, observing that the letter n consists of a combination of these two strokes only, the topturn being made first, and the top-and-bottom-turn added to it, while in the letter m the top-turn is repeated twice, and the letter is then completed by the addition of the top-andbottom-turn. LESSONS IN ARITHMETIC.-V. DIVISION. 1. THE process of finding how many times one number is contained in another is called Division. The number to be divided is called the Dividend. The number by which we divide is called the Divisor. The result-viz., the number of times which the Dividend contains the Divisor-is called the Quotient (Latin quoties, "how often "). The sign placed between two numbers means that the first is to be divided by the second. Thus, 195 means 19 divided by 5. If the Dividend does not contain the Divisor an exact number of times, it will contain it a certain number of times (the Quotient) with a number left over, which will be less than the Divisor. The number left over in this case is called the Remainder. Thus, when we say that 5 is contained in 19 3 times and 4 over, 19 is the dividend, 5 the divisor, 3 the quotient, and 4 the remainder. This fact may be exhibited in the following form :— 19 = 3 × 5 + 4 2. It will readily be perceived that division is, in reality, only a short method of performing a series of subtractions, in the same way as multiplication is a convenient method of perform ing a series of additions. For instance, to find how many times 5 is contained in 19, subtract 5 (the divisor) continually from 19 (the dividend), until the number is exhausted, or a number less than 5 is left; then, counting the number of these subtractions, we shall get the quotient. Thus, 5 from 19 leaves 14, 5 from 14 leaves 9, 5 from 9 leaves 4. Since 5 has been subtracted 3 times from 19, leaving 4 as a remainder, we see that 19 divided by 5 has 3 for its quotient, leaving 4 as a remainder. N.B. It is evident, from the nature of division, that the product of the quotient and divisor, added to the remainder, is equal to the dividend. 3. Method of Division.-The method we are about to explain depends upon the truth of the following principle: If the dividend be split up into any number of parts, of which the sum is equal to the dividend, then, if we divide each part separately by the divisor, the sum of all the quotients so obtained will be the quotient required. For instance, 18 is equal to the sum of 9 and 6 and 3. The quotients of these, divided respectively by 3, are 3, 2, and 1, which, added together, make 6, the quotient of 18 divided by 3. Similarly, 36 is 28 +8, and therefore 36 divided by 4 is the sum of the separate quotients of 28 and 8 by 4, which are 7 and 2 respectively. Hence 7+ 2, or 9, is the required quotient. It must be observed that if, the quotient of a given dividend and divisor being known, the dividend be increased by annexing any number of ciphers to it, the new quotient is obtained by annexing the same number of ciphers to the quotient. Thus, 28 divided by 4 has the quotient 7; and 28000 divided by 7 is 4000. 4. To divide 5356 by 4. 53565 thousands + 3 hundreds + 5 tens + 6 units. Now 5 contains 4 once, with remainder 1; therefore 5 thousands contain 4 one thousand times, with remainder 1 thousand. Add this remaining 1 thousand to the 3 hundreds, thus making 13 hundreds. Now 13 contains 4 three times, with remainder 1; therefore 13 hundreds contain 4 three hundred times, with remainder 1 hundred. Add this remaining 1 hundred to the 5 tens, thus making 15 tens. Now 15 contains 4 three times, with remainder 3: therefore 15 tens contain 4 thirty times, with remainder 3 tens, or 30. Add this remaining 30 to the 6 units, thus making 36 units. Therefore 1 thousand, 3 hundreds, three tens, and 9 units are the number of times the parts into which 5356 has been divided contain the divisor 4 respectively. Their sum, therefore, is the required quotient: this is 1 thousand +3 hundreds + 3 teas + 9 units, i.e. 1339. 5. The above is the analysis of the following shorter process, and will be seen fully to explain it : Write Write down the dividend and divisor as in the margin; 4)5356 then say 4 in 5 is contained 1 time, with 1 over. the quotient 1 under the 5, and placing the remaining 1 before the next figure of the dividend 3, say, 4 in 13 1339 Write the quotient 3 is contained 3 times and 1 over. under the second figure in the dividend, and prefixing the remaining 1 to the 5, say, 4 in 15 is contained 3 times and 3 over. Write the quotient 3 under the third figure in the dividend, and prefixing the remaining 3 to the 6, say, 4 in 36 is contained 9 times, with no remainder, and write down the 9 under the last or unit's figure of the dividend. It will be seen that when, to get the first figure of the quotient, we say 4 in 5 is contained once, with remainder 1, we really indicate that 4 is contained in 5000 1000 times, with remainder 1000, which 1000 we carry on to add to the next three of the dividend, which really indicates 300, and so on; as will be seen by comparing the process with the analysis of the method in Article 4. 6. To divide 7499 by 9. 9)7499 833-2 Here, since 7, the first figure of the dividend, is less than the divisor, 9, we take two figures of the dividend, and say, 9 in 74 is contained 8 times, with a remainder 2, and put down the 8 under the second figure of the dividend (reckoning from the left 9 in 29 is contained 3 times and 2 over; and again, 9 in 29 is hand). Then, proceeding as in the previous example, we say, contained 3 times and 2 over. This last 2 is 2 units, and is therefore the remainder left after dividing 7499 by 9. It is generally written after the quotient, as above. This method, which is only conveniently applicable when the divisor is a small number (generally one figure), is called Short Division. EXERCISE 8. (1.) Divide 658 by 2; 537 by 3; and 7891011 by 6. (2.) Divide 4389127 by 8; 407792 by 11; and 5349279 by 9. (3.) Divide 41239789 by 12; and 54937862 by 5. (4.) Divide each of the numbers contained in the square in Ex. 4, page 23, successively by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. (5.) Divide each of the numbers contained in the square in Ex. 4, page 23, successively by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. (6.) Divide each of the numbers 1010421690, 7689768432134, 54932684736856, and 428571428571496, by all the numbers from 2 to 12 inclusive. 198 175 23 contained in 229 is 6 (which must be found by trial). Then say, the greatest number of times that 35 is Put down the 6 to form the next figure in the times 35-i.e., 210-from quotient, and subtract 229, leaving a remainder 19. To this annex the last figure (8) of the dividend, making it 198. Then say, the greatest number of times which 35 is contained in 198 is 5. Write down the 5 to form the next figure in the quotient, and subtract 5 times 35-i.e., 175-from 298, leaving 23. 265 is the required quotient, and 23 is the remainder. Hence 9298265 × 35 + 23. 8. A careful examination of the above process will show that what we have really done is equivalent to saying: 35 is contained in 92 hundreds two hundred times, with a remainder 22 hundred; then, subtracting 200 times 35-i.e., 7 thousand--from 9298, we have 2298 left. Next we say: 35 is contained in 229 tens sixty times, with a remainder of 19 tens; then subtracting 60 times 35-i.e., 2100 -from 2298, we have 198 left. Next we say 35 is contained five times in 198, with a remainder 23. the dividend, again, 60 times from what is left, and again, 5 times Hence we see that after taking away 35, first, 200 times from from what is left, we have 23 units over, a number which is less than 35. Hence we see that 35 is contained in 9298 200+60 + 5-i.e., 265 times-with a remainder 23. We might have written down the process thus:— 35)9298 (200 35)2298(60 2100 35) 198(5 23 The quotient is therefore 200+ 60+5, or 265, and the remainder 23. 9. The above explanations will sufficiently elucidate the following Rules for Division: (1.) When the divisor contains only one figure, write the divisor on the left of the dividend, with a curved line between them. Beginning at the left hand, divide successively each figure of the dividend by the divisor, and place each quotient figure directly under the figure divided. If there be a remainder after dividing any figure, prefix it to the next figure of the dividend, and divide the number so formed as before. If there occur any figure which does not contain the divisor, place a cipher in the quotient, and prefix this figure to the next one of the dividend, as if it were a remainder, and proceed in the same manner to the last figure. (2.) When the divisor contains more than one figure, beginning on the left of the dividend, find how many times the divisor is contained in the first fewest figures of the dividend which will contain it, and place the quotient figure on the right hand of the dividend, with a curved line between them; then multiply the divisor by this figure, and subtract the product from the figures divided. To the right of the remainder bring down the next figure of the dividend, and divide the number so formed as before. If this number be less than the divisor, annex a cipher to the quotient, and bring down the next figure continuing this process until the number thus obtained be equal to or greater than the divisor. Proceed in this manner until all the figures of the dividend are exhausted. 10. Tests of Correctness of Division :— (1.) Multiply the divisor by the quotient, and add the remainder to the product. This should, as already explained, give the dividend. 7. 18. Tacent et laudántur. 19. Mórdeor et vúlneror. EXERCISE 6.-ENGLISH-LATIN. 20. Si 1. Thou fearest and art frightened. 2. If I am silent I am blamed. 3. He rejoices. 4. We rejoice. 5. They rejoice. 6. He tries to bite. We try to educate. 8. Thou obeyest and art praised. 9. We bite. 10. If we bite we are blamed. 11. They exercise. 12. You are moved. 13. He dances. 14. They are delighted. 15. You are adorned. N.B. In this exercise, and in those which follow, words and forms previously given are repeated for the sake of practice. Regimur, we are ruled (2) Subtract the remainder, if any, from the dividend, and 1st per. Regimus, we rule divide the difference so obtained by the quotient. The result should be equal to the divisor, if the working be correct. EXERCISE 9. 1st per. Rego, 2nd 3rd 33 I rule 1st per. Regor, 2nd Regeris, 3rd Plural. Regimini, you are ruled 3rd Reguntur, they are ruled. (1.) Divide 47839 by 42; 75043 by 52; and 93840 by 63. (2.) Divide 325000 by 85; 421645 by 74; and 999999 by 47. Fallo, 3 (3.) Divide 145260 by 1345; and 1912500 by 425. (4.) Divide 8893810 by 37846; and 9302688 by 14356. (5.) Divide 9749320 by 365; 65358547823 by 2789; and 908070605040 by 654321. (6.) Divide 10000000000000000 by 111; 100000000000 by 333; and 10000000000000000 by 11111. (7.) Divide the product of 12345 multiplied by 67890 by 97, 213, 4351, 59, 847, and 6939. LESSONS IN LATIN.-III. PRELIMINARY INSTRUCTIONS IN THE VERBS OF THE FOUR writes well. 5. They paint ill 6. They dance well. 7. I rejoice if he |