hearing would be wanting to them. Yet, strange to say, while the ears of the cuttle-fish and the slug have been satisfactorily detected, the seat of hearing in insects is still undetermined. The antennæ, or jointed appendages of the head, have been usually looked upon as the seat of the sense of hearing, but whether it be in the basal joint or the terminal one is a matter of dispute; and in one instance it was supposed to have been found in the hip joint of the front pair of legs-a singular position, it must be confessed. To show the difficulty of determining these matters, we have given a sketch of the external orifices of two supposed organs of sense in the common lobster. The little conical protuberance, with a hole through the shell at the summit, which is closed by a membrane, beneath which is a little bag of fluid with a nerve running to it, which is found on 4 III. VI. problems may be thus propounded:-What structures, in the fish, are the representatives of the ossicles of the tympanum called the hammer (malleus) and anvil (incus) in the mammal ? To this question an answer is given by some of our best anatomists which is almost startling from its strangeness, but which, on further examination, has much to support it. These anatomists affirm that the two bones, which form the joint of the lower jaw in the fish, are the representatives of the hammer and anvil, taken out, so to speak, of the ear-drum, much enlarged and applied to quite a different purpose. Such questions as these require much research to determine them, and are only mentioned here to give a slight insight into the difficulties found in unravelling the plan of Nature, though there is undoubtedly a plan in all her works. L. BONE CONTAINING THE EAR OF A RABBIT. VII. UPPER SIDE OF II. EAR-BONE OF THE WHALEBONE WHALE, ONE-FOURTH NATURAL SIZE. III. INTERNAL EAR OF A BIRD. IV. EAR OF A COD. V. EAR-STONE OF COD. VI. UNDER SIDE OF LONG ANTENNA OF A LOBSTER. SHORT ANTENNA OF A LOBSTER. Bel, to Nos. in Figs.-II. 1, tympanic bone; 2, its point of attachment to the skull. III., IV. 1, cochlea; 2, vestibule: 3, oval hole; 4, 5, 6, semi-circular canals; 7, sack of ear-stone. VI., VII. 1, organs of sense. be the true ear. the under side of the first joint of the first, or long, pair of antenna, has been long considered the organ of hearing. Now, however, the opinion seems to prevail that this is an organ of smell, while that found opening on the upper side of the first joint of the second, or short, pair of antennæ, is now thought to In searching for the ear, the presence of hard bodies suspended by threads in a sack containing liquid, and capable of striking upon a nerve filament, is considered as characteristic and indicative of an ear, just as the expansion of a nerve in front of black pigment and behind a transparent membrane is thought to denote an eye. The first-named structure is found in the organ of the lobster last described, but not in the other. It will be seen that much remains to be made out about the ear, and the subject is extremely difficult to study. Indeed, some of the most perplexing problems of the comparative anatomist seem to be associated with the ear. One of the The temporal bones-which, in man, lodge the internal and support the external ears, and besides these functions, close in the brain-case at the sides, send out strong buttresses forward to strengthen the bones of the face, and others to sling the throat. bones upon, and also give attachment to the lower jaw-are the most difficult bones in the body to describe and remember. Many vessels and nerves enter them by numerous holes, and these subdivide and find their way out in such, strange ways, that many a poor medical student has trembled when, in an examination, a temporal bone has been placed in his hand. These bones are no doubt composed of many elements which are distinct in reptiles, birds, and fish: but, to make confusion worse confounded, the student of comparative anatomy finds on the one hand that Professor Owen divides the bone into at least nine elements, and gives them names according to his theory; on the other Professor Huxley transposes all the relations, and christens them by new names. SECTION L-FRENCH PRONUNCIATION (continued). EU.-Name, uh; sound, like the e mute or unaccented, which has been already explained, except when it is a verb, or comminees a verb, in which latter case it has the sound of French u, which also has been explained. Sometimes the u of this combination is under a circumflex ant, thus, eû, in which case the sound of the compound vowel is prolonged. The correct cound of this compound vowel is no more difficult to be acquired than is the correct sound of e mute or unaccented. But it often happens that the letter, or combination of letters, which immediately follows it, adds vastly to the difficulty of pronouncing it. Bring the lips nearly together, ovally, in speaking this compound vowel. Practise patiently and thoroughly upon the above and other examples, until you are satisfied you Lave mastered the difficulty. OI.-Name, och, or wah; sound, like the letters oah of the proper name Noah. Do not give this compound vowel the sound of wor, or co-are, as is too commonly done. nees. Pondre Poodr Poder. Toucher Too-shay To touch. VI.--DIPHTHONGS. Rottenness. A magpie. This combination is a very common ending of words in the French language. The e, however, often bears the acute accent, thus, ie. These vowels also appear very often in the body of a word, with the e accented. In such cases they do not constitute a diphthong, and cannot be illustrated by the sound of ee in the English word bee, but each preserves its own distinct vowel sound. IO.-Name, eo; sound, like the letters io in the last syllable of the Latin word cur-cu-lio. 1. There are in French, as in other languages, verbs which are called irregular, because they are not conjugated according to the rule, or model verb of the conjugation to which they belong [§ 62]. 2. Many irregular verbs have tenses which are conjugated regularly. 3. The singular of the present of the indicative of the irregular verbs is almost always irregular. 4. In verbs ending in yer, the y is changed into i before an e mute [§ 49]. VENIR, 2, to come. Je vicus, I come, do 5. PRESENT OF THE INDICATIVE OF THE IRREGULAR VERBS. Il va. P. Nous allons. Vous allez. Ils vont. ENVOYER, 1, to send. Nous envoyons. [ing. Vous envoyez. come, or an comika, Tu viens, Il vient. Nous venons. Vous venez. Ils viennent. 6. All verbs ending in enir are conjugated like venir. 7. The student will find in § 62 the irregular verbs alphabetically arranged. He should always consult that table when 68. There are six diphthongs, namely:-ic, ie, io, ua, ue, ui, he meets with an irregular verb. whose sounds we now proceed to illustrate. But do not suppose that these combinations of vowels are always diphthongs, in whatever place they are situated. If followed by two consonants, the first of which is m or n, the lest vowel forms with the m or n a nasal, unless the m or n be doabled. 9. The preposition chez, placed before a noun or pronoun, answers to the English at the house of, with (meaning at the Sometimes, again, these vowels which now appear as diph-residence of), among, etc. [§ 142 (3)]. thongs are but parts of syllables of a word, and must be pro- Chez moi, chez lui, chez elle, nounced only as distinct vowels. 11. The word y means to it, at it, at that place, there. It is generally placed before the verb, and refers always to some IE-Name, ce; sound, like the letters ee in the English thing mentioned [§ 39, § 103, § 104]. there; I have some. The words oui or non, without a verb, maker's? 32. It (elle) is there. 33. Have you two gold would, however, suffice. Where is the colonel? Où est le colonel? Il est chez son frère aîné. N'est-il pas chez nous? Non, Monsieur, il n'y est pas. He is at his eldest brother's. Malame votre mère est-elle à la Is your mother at home? No, Madam, she is not. watches? 34. I have only one gold watch. 35. Who intends to go to my father's this morning? 36. Nobody intends to go there. OUR HOLIDAY. HOCKEY. WHEN the frosts of winter have hardened the ground, and the air is keen and bracing, out-door amusements, to be at once enjoyable and beneficial, must be active and exhilarating in their nature. Hence the popularity in the winter season of such games as Football and Hockey, with their new competitor La Crosse, which, since we wrote about it in No. 1 of the POPULAR Do you go to our house, or to his EDUCATOR, we are glad to find is advancing in favour, more house? We go to the captain's. Is he not at your brother's? Do you not send your clothes to your I send them to their house. VOCABULARY. Hollandais, -e, Dutch. EXERCISE 41. Relieur, m.,bookbinder. Russe, Russian, Ven-ir, 2, ir., to come. 1. Où allez-vous mon ami? 2. Je vais chez Monsieur votre père; est-il à la maison? 3. Il y est ce matin. 4. D'où venezVons? 5. Nous venons de chez vous et de chez votre sœur. 6. Qui est chez nous? 7. Mon voisin y est aujourd'hui. 8. Où avez-vous l'intention de porter ces livres ? 9. J'ai l'intentien de les porter chez le fils du médecin. 10. Avez-vous tort de rester chez vous? 11. Je n'ai pas tort de rester à la maison. 12. L'horloger a-t-il de bonnes montres chez lui? 13. Il n'a pas de montres chez lui, il en a dans son magasin. 14. Chez qui portez-vous vos livres? 15. Je les porte chez le relieur. 16. Allez-vous chez le capitaine hollandais? 17. Nous n'allons pas chez le capitaine hollandais, nous allons chez le major russe. 18. Est-il chez vous ou chez votre frère? 19. Il demeure chez 20. Ne demeurons-nous pas chez votre tailleur? 21. Vous y demeurez. 22. Votre peintre d'où vient-il? 23. Il vient de chez son associé. 24. Où portez-vous mes souliers et mon gilet? 25. Je porte vos souliers chez le cordonnier et votre get chez le tailleur. 1. Where does your friend go? 2. He is going [Sest. XXII., 6 to your house or to your brother's. 3. Does he not intend to, go to your partner's? 4. He intends to go there, but he has no time to-day. 5. What do you want to-day? 6. I want my waistcoat, which (qui) is at the tailor's. 7. Are your clothes at the painter's? 8. They are not there, they are at the tailor's. 9. Where do you live, my friend? 10. I live at your sister-inlaw's? 11. Is your father at home? 12. No, Sir, he is not. 13. Where does your servant carry the wood: 14. He carries it to the Russian captain's. 15. Does the gentleman who (qui) is with your father live at his house? 16. No, Sir, he lives 17. Is he wrong to live with you? 18. No, Sir, he is right to live with me. 19. Whence (d'où) comes the carpenter? 20. He comes from his partner's house. 21. Has he two partners? 22. No, Sir, he has only one, who lives here (ici). 23. Have you time to go to our house this morning? 24. We have time to go there. 25. We intend to go there, and to speak to your sister. 26. Is she at your house? 27. She is at her (own) house. 28. Have you bread, butter. and cheese at home?! 29. We have bread and butter there. 30. We have no cheese there, we do not like cheese. 31. Is your watch at the watch with me. The French, in speaking to a person whom they respect, prefix the word Monsieur, Madame, or Mademoiselle, to the word represent ing their interlocutor's relations or friends. than one club having been established for its systematic practice during the winter months. A new game is a new source of harmless pleasure to hundreds, and perhaps to thousands or tens of thousands. The great and almost sudden popularity of Croquet shows how welcome is a suitable addition to the list of popular amusements, and we therefore spare a passing word to comment upon the reception given to the Indian game which was the subject of our first paper. Of Football we have also treated; and we have now to describe the game of Hockey, which, under the names of Shinty in Scotland and Hurling in Ireland, is popular throughout the United Kingdom. Hockey consists in driving a ball from one point to another by means of a hooked stick, and is believed to derive its nam› from the shape of the latter implement, sometimes called a hookey. No precise rule is laid down as to the form this stick should take. It is simply a weapon with a bent knob or hook at the end, large or small, thick or thin, according to the option of the player, and used for the purpose of striking the ball, or perhaps of catching it up on the point for a throw towards the goal. Hockey-sticks, therefore, are of all shapes, sometimes simply in the form of a stout walking-stick with a crook at the end. The Hockey ball must be one fitted to receive hard and frequent blows. Anything in the nature of a cricket-ball is found to be ill-adapted for this peculiar game, as the leather soon bursts, through the effects of the knocks received from all kinds of rugged-pointed sticks. A large bung, strongly tied and quilted over with string, is a favourite and an inexpensive ball for the purpose; and the best of all is perhaps a solid indiarubber one, or the larger part of a thick india-rubber bottle, firmly closed at the end from which the neck has been cut. Now for the game itself, which in its principle bears a great resemblance to Football, and contains at least the germ of the Canadian La Crosse. The players are divided into two parties, each of which has its goal, the goals being fixed towards either end of a tolerably spacious ground. They consist, as at Football, of two upright posts, about six feet apart, but the cross. pole is almost invariably employed at Hockey, and is usually placed at a height of about four feet from the ground. Through these goals the ball has to be driven; and the space through which it has to pass at either end, before the game is won, is therefore a space of about six feet by four. The In commencing, the two parties meet midway between the goals, and are arranged in line, their left hands towards the opponents' goal, and their right directed to their own. ball is thrown up into the air by one of the party winning the toss, by which toss also the choice of position for the goal is determined. As the ball falls, it is the object of both sides to strike it towards the goal of the enemy, or at least to prevent it from being struck in the direction of their own. goal-keepers are stationed at each end to beat back the ball if it approaches dangerously near; and, if the party playing be large enough, it is usual to place two of the opposite side near the respective goal-keepers, in order that their defensive efforts may be rendered unavailing. Two It may well be imagined that on the fall of the ball an exciting scene ensues. In the attempt to strike it, the hockeysticks are crossed in mimic warfare, and as it reaches the ground both sides surround it in a general "scrimmage," while it is pushed, thrust, or struck by the hockey-sticks, according to the chance which the various players may get of aiming at it. The hockey-stick properly should never be raised much higher than the ground, for a dexterous shove at the ball may sometimes be quite as effective in serving the purpose of your side at a critical moment as a swinging blow, the opportunity for which may, indeed, very rarely occur. If the ball receives a good hit, and flies forward to the goal, a general rush is made in pursuit, one side aiming to follow up the advantage, and the other to overtake the ball first and restore the balance of the game. It will be apparent that in a rush and struggle of this description a fall or a hard knock is exceedingly likely to occur, and that Hockey is therefore not a game suited to weakly or timid players. But there are rules by which it is sought to avoid, even in the heat of the conflict, any chance of more than a comparatively slight injury to the players, and to confine that result purely to the effects of accident. It is forbidden, in the first place, to raise the head of the stick higher than the shoulder, under the penalty of a blow on the shins from the hockey-stick of one of the opposite side; and thus a check is given to the reckless and promiscuous flourishing about of the player's stick, to the imminent hazard both of his friends and opponents. Moreover, any player proved wilfully to have struck another is at once excluded from the play. Besides these rules, the following are generally accepted: 1. A player must not cross to the side of his opponents before a rush or scrimmage has commenced. 2. The ball must be fairly struck through the goal, and not thrown or kicked. 3. It is forbidden to kick or throw the ball during the general game, but the ball may be stopped by any part of the person of a player who may intervene between it and the go:l. 4. If the ball be struck beyond, but not through the goal, and if it be passed through the goal otherwise than by a fair hit, the youngest player of the side owning that goal shall return it by a gentle throw towards the centre of the ground. These, with the two rules given before, comprise all that it is necessary to observe in playing the game of Hockey, except the general rules of good temper and forbearance, which are required in all games alike. The Scottish form of the game, known as Shinty, calls for no special remark, more than that the goals are called "hails," and that the game itself may owe its name either to the frequent danger to the player's shins, or to the shindy which characterises the culminating struggle. "Hurley," the Irish variation of the game, also differs but little from that here described; but in Ireland the game has been, perhaps, a more general favourite, and played occasionally on a larger scale, than in either of the sister kingdoms. We borrow from Mr. and Mrs. S. C. Hall's "Ireland" an amusing anecdote in illustration of this fact. "About half a century ago," we are told, "there was a great match played in the Phoenix Park, Dublin, between the Munster men and the men of Leinster. It was got up by the then lordlieutenant and other sporting noblemen, and was attended by all the nobility and gentry belonging to the vice-regal court, and the beauty and fashion of the Irish capital and its vicinity. The victory was contended for a long time with varied success; and at last it was decided in favour of the Munster men, by one of that party running with the ball on the point of his hurley and striking it through the open window of the viceregal carriage, and by that manoeuvre baffling the vigilance of the Leinster goalmen, and driving it in triumph through the goal." There is no record of matches on quite so extensive a scale having been played in the sister kingdoms; but we learn on the authority just quoted that, in the last generation, several good matches at hurley were played on Kennington Common between the Irish residents of St. Giles's and those of the eastern portions of the metropolis, the affair being got up by some of the sporting noblemen of the day. Besides Kennington Common, several of the other open spaces around London were once noted as favourite spots for the exhibition in perfection of the game of hockey, and especially, in the last century, the extensive fields which then lay at the back of the British Museum. The amusement is not so frequently seen now, having yielded somewhat before the rival attractions of football and cricket, but it is a favourite still in many parts of the country. LESSONS IN GEOMETRY.-VII. PROBLEM XIV.-To find a third proportional to two given straight lines. E -A Let A and B be the two given straight lines to which it is required to find a third proportional. Draw two straight lines c P, c Q, forming with each other a small angle PCQ. On CP set off C D equal to A, and DF equal to B, and on CQ set off c E equal to B. Join D E, and through the point F draw F G parallel to D E, and cutting co in G; the straight line E G is a third proportional to A and B; that is, A is to в as B is to E G. If we know the length of A and B, we can find the third proportional to them by dividing the square of the length B by the length of A. Thus, if A be three feet, and в be six feet, the third proportional to A and B measures twelve feet, for the square of 6 divided by 3, or 36 ÷ 3 = 12. Fig. 21. PROBLEM XV.-To find a fourth proportional to three given straight lines. A I would be represented numerically by 9, I K by 33 inches, etc., and lines involving fractions of inches such as, which are not to be found on an ordinary scale, would be very difficult to mark out without making a special scale for the purpose, or resorting to the plan given above. PROBLEM XVII.-To draw an equilateral triangle on any given straight line. Let A B be the given straight line on which it is required to draw an equilateral triangle. From the point A as a centre, with A B as a radius, describe the arc BC; and from the point B as a centre, with B A as a radius, describe the arc A C, cutting the arc B C in the point c. Join A C, BC; the triangle ABC is equilateral or equal-sided (see Definition 19, page 53), and it is drawn on the given straight line A B. Fig. 24. B If the arcs CA, C B be extended to cut each other in the point D below the straight line A B, by joining D A, D B, we get another equilateral triangle A B D, which is equal to the equilateral triangle A B C, and which is also drawn on the given straight line Let A, B, and c be the three given straight lines to which it is A B. By taking any straight line as a required to find a fourth pro-radius, and from each of its extremities as A portional. Draw two straight centres striking arcs intersecting or cutting B lines DP, DQ, forming with each other on opposite sides of it, we get, by drawing straight each other a small angle, PDQ. lines from the points in which the arcs cut each other to the On D P set off DE equal to A, extremities of the straight line used as a radius, a regularlyand E F equal to c, and on formed diamond-shaped figure, whose four sides and shortest DQ set off D G equal to B. diagonal or diameter, are all of equal length, such as A C B D in Join E G, and through F draw the above figure. This figure with four equal sides is called a FH parallel to E G, and cutting Do in H. The straight line rhombus. (See Definition 30, page 53.) He is a fourth proportional to A, B, and C; that is, A is to B as c is to H G. Fig. 22. C If we know the length of A, B, and C, we can find the fourth proportional to them by multiplying the length of B and c together, and dividing the product by the length of A. Thus, if A be four feet, B six feet, and c two feet, the fourth proportional to A, B, and c measures three feet; for 6 x 2 = 12, and 12÷ 4 = 3. Fig. 23. PROBLEM XVI.-To divide a given straight line into any number of parts which shall be to one another in a given proportion. Let A B be the given straight line, which it is required to divide into five parts, which are to one another in the following proportions-namely, 5, 2, 3, 1, 4. First draw the straight line A c of indefinite length, making a small angle B A C with the given straight line A B. Along A C, from a scale of equal parts, set off in regular succession A D equal to 5 of these equal parts, DE equal to 2, E F equal to 3, F G equal to 1, and G H equal to 4. Join H B, and through the points D, E, F, G, draw the straight lines D I, E K, F L, GM, cutting the straight line A B in the points I, K, L, M. The given straight line A B is now divided into five parts, A I, I K, K L, L M, M B, which are to one another in the required proportions, namely, 5, 2, 3, 1, and 4. This method of dividing a straight line into any number of parts, which shall be to one another in a given proportion, is based on Problem XII. (page 192). Supposing it had been required to divide A B into 15 equal parts, it is manifestly only requisite to set off along A c 15 equal parts, denoted by the dots on the line ▲ c, from A to H, and then draw straight lines in succession through each dot on H A, from H to A, parallel to H B. The process that has been described in this Problem, ensures an accurate division in cases where the different parts would be represented by fractions or mixed numbers (see Lessons on Arithmetic, page 160), if we endeavoured to arrive at them by an arithmetical process. For example, had the line A B in Fig. 23 measured 30 inches, we can see at once that, as the sum of the numbers which show the proportion of the lines into which it is required to divide it is equal to 15, the half of 30, we have only to multiply each number by 2, and mark off A I equal to 10 (or 5 x 2) inches, I K equal to 4 (or 2 x 2) inches, and so on. But supposing A B had measured 29 inches, instead of 30, then VOL. I. The learner should construct Fig. 24 on a large scale by the aid of his compasses and ruler. On applying a parallel ruler to the opposite sides of the figure A C B D, he will find that they are parallel to each other, namely, A C to B D, and B C to A D; A CBD is therefore a parallelogram, and A B, C D are its diagonals. (See Definition 26, page 53.) From Theorem 5 (page 156) the student learnt that the greatest side of every triangle is opposite the greatest angle, and that the greater the opening of the angle the greater must be the line that subtends or is opposite to it. Now in the triangle A B C, or in any other equilateral triangle, the three straight lines or sides by which it is contained are all equal to one another, and as equal sides must necessarily subtend equal angles, the three angles of the triangle A B C—namely, A B C, B C A, C A B—are also all equal to one another. Again, from Theorem 7 (page 156) we have learnt that the three interior angles of any triangle are equal to two right angles. A right angle contains 90 degrees, and as two right angles contain just twice as many, or 180 degrees, each of the equal angles A B C, B CA, CA B, in the interior of the equilateral triangle A B C, contains 1803, or 60 degrees. Continuing our investigations a little further, we find that each of the angles ACE, BCE is half of the angle A C B, and is therefore an angle of 30 degrees. The angles A DE, BDE are also angles of 30 degrees, because each of them is half of the angle A D B, which, like the angle A C B, is an angle of 60 degrees. The angle CAD is equal to the angles CAB, DAB, and as each of these equal angles contains 60 degrees, the angle CAD contains 120 degrees. In the same way the angle CBD also contains 120 degrees. The diagonals of the rhombus A C B D intersect each other at right angles, therefore it will be seen that each of the angles CEA CE B, D E A, D E B is a right angle.. Fig. 24 teaches us how to draw an angle of 45 degrees without the aid of the protractor, as we will proceed to show. ACE is an angle of 30 degrees, and so is its adjacent angle ERRATA. In a few of the earlier impressions of our last Lesson in Geometry, some typographical errors occurred, which we must request the reader to correct, as follows:-Page 191, Problem VII. At the Problem IX. At the extremity opposite to "B" of the line E F insert apex of the triangle whose base is "A c," insert "B." - Page 192, ""; at the other end of the diagonal from "E" insert "A".-Page 192, Problem XI., line 3. For "the centre D," read "the centre A.”— Page 192, Problem XIII., line 9. For "DE equal to F," read "DE equal to B." 14 |