to be 16, and the velocity is represented by the horizontal line drawn through 1, which we call 32. We can thus see at a glance the space passed over in any given second, or the velocity at any given time. In the same way, if we draw a line midway between 4 and 5 to represent 4 seconds, we can find the space passed over and the velocity acquired in that time. The figure, in fact, gives us a good idea of the action of a uniform accelerating force. Suppose, for instance, we drop a stone down a well and find it is 4 seconds before we hear the splash, we know the depth is 324 feet. The stone falls 16, 48, 80, and 112 feet in the first, second, third, and fourth seconds, and 68 in the last half second; these together make 324; or we may take the square of 41, and multiply it by 16, and thus get the same result. Again, suppose we want to know the velocity any body acquires in falling for 6 seconds, we have only to multiply 32 by 6, and we find it to be 192 feet per second. In all these cases the accelerating force we have taken has been that of gravity. Sometimes, however, different forces act; but the following general rules embrace all: 1. The velocity acquired under the action of a uniform accelerating force is equal to the force multiplied by the time. By force here, we mean velocity acquired in one second, and, as we have seen, a similar amount of velocity is produced in each second. The rule, therefore, is clear. 2. The space passed over is equal to half the force multiplied by the square of the time. Both these laws may be verified by comparing with the results obtained by the action of gravity. If we take ƒ to represent the force or velocity generated in one second, s the space in feet, t the time in seconds, and v the velocity, we have the following formula, which express these laws, and are easily remembered: The third of these formula is deduced from the other two. Now if a body be projected upwards with any given velocity, it will rise to the same height that it would have to fall from to gain that velocity, and when it again reaches the earth it will have the same velocity as it started with. The reason of this is that, as a result of the second law of motion, gravity destroys an upward motion in exactly the same degree that it produces a downward one. If, for instance, a stone is projected with a velocity of 48, it would rise that height in one second, but by gravity it falls 16 feet out of this, and thus only rises 32. Hence if a stone be thrown upwards, it takes exactly the same time to rise as it does to fall; and thus, if we know how long it is in the air, we can tell the height to which it has risen. For example: a stone is 6 seconds in the air, how high did it rise? It must have taken half the time, or 3 seconds, in falling; but in that time a body falls 32 x 16, or 144 feet. This, then, is the height to which it rose. Or, again: a body is projected upwards with a velocity of 120, how high will it rise, and how long will it be before it reaches the ground again? We know here the value of v and f, and by the third formula, v2 2 fs, that is, 14,400 = 2 x 32 x s, or 64 s; s therefore is of this, or 225 feet. Again, by the first formula, v=ft, that is 120 = 32 x t; t therefore is 33 seconds, and as it takes the same time to rise as to fall, the time it is in the air is 7 seconds. There is a simpler way in which many of these experiments may be performed, and by which some of these laws were discovered by Galileo. A body is allowed to slide down an incline, and the time of falling noticed. The part of the weight which produces motion bears the same proportion to the weight itself as the height of the plane does to the length. Hence if we, diminish the height we increase the time taken in falling. We find, however, that the velocity is always proportional to the vertical height fallen through, whatever be the length of the incline. W Fig. 99. Galileo experimented by letting small wagons roll down inclines, which were made as smooth as possible so as to remove friction; and he discovered thus the "law of the squares," as it is called, i.e., that a body will fall four times the distance in twice the time, nine times the distance in three times the time, and so on. EXAMPLES. 1. A stone is thrown up with a velocity of 100 feet per second. How high will it rise, and how long will it be before it reaches the ground again? 2. A bullet takes 51 seconds to fall from an elevation to the ground. What is the elevation ? 3. With what velocity will a stone falling from a height of 400 feet strike the ground? 4. How long will a weight take to fall 784 feet, and how far will it move in the last second? 5. What space will a falling body describe in the 17th second? 6. How long will a ball dropped from a height require to attain a velocity of 192, and what space will be described in attaining it? LESSONS IN ENGLISH-XXII. THE GREEK ELEMENT-GREEK STEMS. THE prefixes and suffixes of which I have treated, are connected with certain roots or stems. So far as these stems are of Saxon birth, you need little instruction in them; they belong to your mother tongue, and, in general, are as readily understood by you as the words which denote the members of your body, or the food that you eat. With other stems you are not acquainted. Among the words I gave you for exercise in composition in the last lesson, there are words for the meaning of which you have probably had to resort to a dictionary. Such a word is accessary. Now accessary being made up of the Latin words ad, to, cedo, I go, and the termination ary, would have occasioned you no difficulty had you been familiar with the foreign or exotic stems of our language. In origin those stems are various. Chiefly they are derived from the Latin, as in the word accessary. Some come from the Greek; others are of different parentage. These must all be separately considered. I begin with an example of Now let me explain the process I here intend. Adelphos is found in Philadelphia, but not in its full form. It is found as it appears under "Stems;" for adelphos, passing into Philadelphia, loses os, and takes ia. By this time you know enough of the changes in language to be aware that these changes in the terminations do not affect the root-meaning, or the essential import of the word. Prefixes and suffixes convert verbs into nouns, and adjectives into adverbs; or they may modify the signification; they may even reverse it, but they nevertheless leave the import of the stem still traceable after it has undergone their influence. Philadelphia, then, has clearly something to do with adelphos, a brother. What that something is, you find indicated in the next Greek word and its stem, namely, philos, loving, and phil. Putting the two together, you have Philadelphia, and putting the two meanings together, namely, love and brother, you obtain brotherly-love, as the import of the word under consideration. Remembering that Philadelphia is the name of a town in the United States, you are reminded that the name, brotherly-love, was given to it by its founder Penn, as indicative of the spirit with which he dealt with the original inhabitants of that region. Passing on to the next word, philosophy, I find at the beginning of it the same phil of which I have already spoken. But I find, also, sophy. What am I to do with sophy? First, I know that the y may represent the Greek ia, as is set forth in the remarks on suffixes. Changing the one into the other, I thus get sophia. Now, by referring to the next line in my list of words, I see one which is very like sophia; that is, sophos. I already know enough of the changes which words undergo to find reason for thinking that sophia is connected with sophos in meaning and source as well as in form. The idea is confirmed by my seeing that soph is given as the stem of sophos. Now soph is equiva lent to our wise; here love and wise must be put together, ard so I learn that philosophy is the love of what is wise, or the love of wisdom. Such being the case, a philosopher must be one who loves wisdom. But soph is given as the origin of sophist. Sophist obviously consists of two parts; the part which is given-that is, soph, meaning wise-and ist. What is this ist? Let me think. Have I not had ist before? Oh, yes, I remember, ist is a suffix, a Greek suffix, and denotes a partisan, one who follows a party in an opinion; like Baptist, one who observes baptism. Sophist, then, must be one who pursues wisdom, one who is given to wisdom. Now such is the meaning of the word, and such is the whole meaning of the word as taught by etymology, or the doctrine of tracing out the root-signification of words. And here you have an instance of the shortcomings of etymology. So far as I have yet gone you see no difference between philosopher and sophist, for both are students of wisdom. Yet, if you meet with the two in a narrative or a discussion, you find that their meanings are different; at least, a philosopher is spoken of with respect, a sophist is spoken of slightingly. kind of assistance. The most effectual teaching is that which leads persons to teach themselves. "David's combat (with Goliath) compared with that of Dioxippus the Athenian athlete."-Delaney. "The legislature of the kingdom (of England) is entrusted to three distinct powers, entirely independent of each other: first, the king; secondly, the lords, spiritual and temporal, which is an aristocratical assembly of persons selected for their piety, their birth, their wisdom, their valour, or their property; and thirdly, of the House of Commons (the representatives of the democracy)."-Blackstone, "Commentaries." EXERCISES FOR PARSING. Philadelphia (λadeλpia) is the word employed by the Apostle Paul in his Epistle to the Romans (xii. 10). Philadelphia, as employed by the Apostle to the Gentiles, is rendered in our English version by "brotherly love." A word of the same origin is used by the Apostle Peter, where (1 Pet. iii. 8) he gives the injunction "love as brethren." Sophos (copos) is the Greek term found in that text: "Professing themselves to be wise they became fools." (Rom. i. 22.) The words just cited accurately describe the character of a sophist. A word Whence derived from sophos is the word employed in this question: Our word athletic has hath this man this wisdom?" (Matt. xiii. 54.) a word of the same origin in the words, "Ye endured a great fight (acov) of afflictions." (Heb. x. 32.) The Greek demos (dnuos) is, in the original, used in the passage, "The people gave a shout." (Acts xii. 22.) Kratos (xpatos) is in the New Testament represented by these English words-namely, strength (Luke i. 51), power (Eph. i. 10), and dominion (1 Pet. iv. 11). EXERCISES IN COMPOSITION. I have entered into these details in order to show you that history must be taken as an ally to etymology in the study of languages. In the case before us history supplies the lacking information. From history we learn that the sophists were a set of Greek teachers who, not content to be called philosophers or lovers of wisdom, pretended to be sophoi or wise men, and came to be designated sophistai, sophists, disparagingly. A sophist, then, you thus learn, is a pretender to wisdom; and as all pretenders are obliged to resort to trickery, so a sophist is one who, by unsound and cunning arguments or delusive appeals, aims, for his own purposes, to produce a false impression. Knowing what a sophist is, you easily infer the meaning of sophism, or a means by which the sophist works; Words with their proper prepositions to be formed into sentences. and sophistry, his art. Advanced thus far, you have no difficulty with sophistical, nor with sophistically. Turn your attention for a moment to the English representatives given above, and observe generally that in representatives, whether designated English or foreign, I mean the radical parts of the words, in each case the radical or essential elements of each word. Now, you have above these three combinations of letters-namely, adelph, phil, and soph. These three parts are the parents of all the words of which I have just treated, and connected with them is all the information I have here set forth. When I have added, that what I have said is only a very small part of what I might have said, you will have some idea of the extent and value of etymological studies. Do not suppose that I have chosen these three terms because they were specially prolific. I took adelph because it begins with the first letter of the alphabet. The other words followed of course. So far from the series being very prolific, one member of it, adelph, gives birth to only one word, and that word is etymologically unproductive. My chief object, however, in going into this detail was to lay before you the principle on which the following list of words is drawn out, and the manner in which you are to study them. If you will faithfully, diligently, and perseveringly study these lists, combining with them the knowledge communicated in previous lessons, you will make rapid progress, and acquire a superior familiarity with the English language in all its elements. Having done with this triplet of words, and pursuing the order of the alphabet, I come to other Greek terms found in English: Adjust to, Affinity to, Foreign Representatives. mone, to remind. fici (fac, fec), making. Agree with, to, on, grat, pleasing. Questions: Where is the difference between to agree with and to agree to? also between agree to and agree on? Form illustrative sentences. Where is the difference between admonish and admonish of? Form illustrative sentences. Besides working each term in this list into a simple sentence, work into simple sentences words formed from them; as, admonition, admission, advocacy, agreement, alienation, taking care to employ the proper prepositions. LESSONS IN DRAWING.-XX. IN drawing the human figure a restricted practice of mere imita. tion cannot be considered, for various reasons, otherwise than a failure. We will briefly consider this, and also include the study of animals, wherein we shall perceive that the amount of knowledge requisite for drawing from animal life is as varied as the subject itself. If we begin with the lowest grade and end with the highest, we shall find our knowledge of their characters, habits, and physical development must increase in proportion as we ascend the scale. That feeling for form which is beyond, and independent of, the simple ability of drawing objects of still life only, first shows its influence where life begins; or, in other words, where life-giving power and will control the action of the body; and this feeling, stimulated by the knowledge we have said to be necessary, will expand as it ascends to the study of man. The eye must be prepared to see something beyond the simple line that gives the boundary of the figure. It is true the line must be imitated, but the question is, how to conduct and regulate the imitation, since it must have an expression according to the infinite variety of circumstances under which it may be placed. For as life is in the body, it is the fact of its existence that makes all the difference between drawing it, as we would a piece of furniture, or, in consequence of its freedom of action, as the exponent of a motive having its origin in the will. Therefore it must be evident that there is a graduated scale of ability extending throughout the whole range of art, commencing with objects of the simplest and lowest kind, where it may be only necessary to note the positions of parts and their extent, until as we ascend to life and intelligence, we make the further discoveries that difficulties arise of a fresh nature, and that it will be indispensable to direct our attention to other branches of knowledge to help us in our efforts. It must be admitted that the human figure is the most interesting and sublime study in Nature. Whilst other objects are only represented for the sake of their forms, in this case the forms must be made subservient to, and are employed to represent, the intentions of the mind. Therefore, it is not only the power of imitative drawing that is necessary, but the ability to adapt that power to purposes of a much higher grade than those which relate to form only. Here is the reason why different men profess different branches of art. If the practice of art depended upon the power of imitation only, no one who is sufficiently skilful with his pencil need confine himself to one especial study; but that which makes art valuable, and at the same time difficult, is something which extends beyond the practice of mere imitation. Mark the various expressions so commonly seen in many countenances, betraying more meaning than words can give. A look of sympathy or of anger is read at once, and he who receives it hesitates not a moment in realising its intended meaning, although not a syllable has been uttered. Who has ever yet succeeded in portraying that divine look that Christ which the power of mere imitation can never overcome, and which oblige us to seek farther for assistance in branches of knowledge which do not immediately belong to drawing, but which must have an important influence in our ultimate success. The knowledge necessary to assist us in drawing the human form is derivable from many sources; the first and most important is that of anatomy. We have in the last lesson directed the student where he may conveniently obtain informa tien upon this part of the subject. We propose now to give him some directions how he is to apply it. We advise him to study the skeleton first, and make himself familiar with the names of the bones, and their several protuberances, and the way in which they are connected with each other, either by ball and socket, as in the hip-joint, or in the form of a hinge, s in the elbow and knee. He would do well to make a drawing of the skeleton, and then from the plates and descriptions cover it with the muscles, as in Figs. 122, 123, being very particular to notice their origin, insertion, and their use. Two or three hours of persevering study in this way will do more for him when he comes to draw from casts, or from life, than months of labour from copies without it. In short, if he relies on copies only, it is more than doubtful if he will ever do anything at all satisfactory; and should his ambition lead him to design for cast at Peter, expressive of all that had gone before in their fellowship with each other, of all that related to their sufferings and trials, both past and present, reminding Peter of his professions, and telling him of his weakness? And though not a word was said, Peter understood its meaning so thoroughly, that "he went out and wept bitterly." It is very evident that to be able to represent such a scene as this, a very high standard of that which is comprehended by the power of drawing must be attained. We can see where it extends, but we cannot see its limits. To explain the exact kind of knowledge capable of affording assistance to the draughtsman in every case would indeed be very difficult. To sum it up in a few words, we may say, all is useful that helps us to understand the construction of the object to be drawn; and, in animal life, how the various impulses of the mind and will command the action of the body. It ought to be the desire of every one who wishes to perfect himself in the particular branch of art which he has chosen, whatever it may be, to seek out every kind of information that can assist him in his object. We will instance one case only to illustrate the rest. The flower-painter, to gain any position at all in the art, must know something of botany, which teaches him the construction of flowers and their classification. With such an auxiliary as botany, will not his work be more satisfactory, and will he not be less likely to overlook many facts connected with his pursuit which would be deemed indispensable by a competent judge ? Therefore there are latent difficulties himself, with the intention of employing his work for any art or decorative purpose, he would be totally at a loss without a knowledge of the anatomical construction of the body, and he has no business to feel any surprise if he fails. These remarks must not discourage; on the contrary, we hope they will induce all to seek the readiest and shortest way to attain the requisite qualification. We must bear in mind that this branch of art is a very different matter to that which includes trees, houses, or ornament. The body is subject to such constant changes of position that it is impossible to omit those instructions which relate to and explain its construction and development. The arm in one position is very different when that position is changed. The same limb in repose is completely altered in action, and, in order to overcome the difficulties arising from these changes, the construction of the limb must be understood. There are those whose ambition goes no farther than copying copies for mere amusement. These need not trouble themselves beyond following the system of arrangement, about which we have said so much in our early lessons, applicable to objects of still life; because they have then only to copy straight and curved lines-that is, to treat the subject as composed only of such lines. Now we feel that if we leave our pupils, especially those who have to employ figure-drawing for useful and practical purposes, with no further instructions than those which will enable them to imitate a printed lithograph, we should fail in our duty. Therefore we proceed, with all who are disposed to accompany us, regardless of difficulties and discouragements, In and with a feeling of determination on their part to obtain as LESSONS IN FRENCH.-XXXV. SECTION LXVII.-IDIOMS RELATING TO DIMENSION, WEIGHT, ETC. RÉSUMÉ OF EXAMPLES. La canelle se vend.deux francs la livre. Cette soie vaut six francs le mètre. hauteur. deur. Une chambre de quinze pieds de pouces. Notre ami est-il grand ou petit? Votre maison est plus haute que la Je vais à l'école deux fois par jour. Cinnamon is sold [at] two francs pa That silk is worth six francs per metre. A room fifteen feet long by eighteen Is our friend tall or short? Loyer, m., rent. EXERCISE 129. Pouce, m., inch. 1. Votre maison est-elle grande? 2. Elle a cinquante pieds de longueur et vingt-cinq de largeur. 3. Combien de longueur votre jardin a-t-il ? 4. Il a vingt-cinq verges de longueur et douze de largeur. 5. De quelle grandeur est ce livre? 6. Il a dixhuit pouces de longueur, treize de largeur et trois d'épaisseur. 7. Votre maison est-elle plus longue que celle-ci ? 8. Elle est plus longue de deux pieds. 9. Quelle profondeur a ce puits? 10. De quelle hauteur est ce clocher? 11. Il a trois cent cinquante trois pieds de hauteur. 12. De quelle taille est cet officier ? 13. Il est de haute taille. 14. De combien cet Écos. sais est-il plus grand que son frère ? 15. Il est plus grand de toute la tête. 16. N'êtes-vous pas de beaucoup plus grand que 17. Je suis plus grand que vous de trois pouces. 18. Combien cette étoffe se vend-elle la verge? 19. Elle se vend trois francs le mètre. 20. La cassonade ne se vend-elle pas cher ? 21. Elle se vend à bon marché. 22. Combien de lettres écrivez-vous par semaine? 23. Je n'en écris que six par semaine. 34. Combien payez-vous par semaine pour votre loyer? 25. Je ne paie que dix francs par semaine. moi ? EXERCISE 130. 1. How large is your father's garden? 2. It is twenty-five yards long and ten broad. 3. Is your cousin's house large ? 4. It is fifty-six feet long and forty broad. 5. Is your house larger than mine? 6. It is larger than yours by ten feet. 7. Do you know how deep that well is? 8. It is twenty-five feet deep and six feet broad. 9. How is that cloth sold per mètre? 10. It 1. THE verb avoir is used in expressing the size of an object. is sold [at] forty-five francs per mètre. 11. How much do you The preposition de precedes the noun of dimension. When receive a week for your work? 12. I receive fifty francs a week there is no verb in the sentence, the preposition must be placed for my work. 13. How much does your friend pay a month before the number, and again before the noun of dimension. for his board (pension, f.) ? 14. He pays seventy francs a Cette muraille a dix pieds de That wall is ten feet high. month. 15. Are you taller than your cousin? 16. I am taller hauteur, than he by the whole head. 17. Is not your nephew taller than your son? 18. He is taller than my son by three inches. 19. How large is this room? 20. It is sixty feet long by forty. 21. What size is your brother? 22. He is tall, he is taller than I. 23. How many books do you read a week? 24. I read ten volumes a week. 25. How is butter sold per pound? 26. Butter is sold [at] two francs per pound. 27. Do you know how much your son earns a day? 28. He earns as much as yours, he earns ten francs a day. 29. How much is that silk worth per mètre ? 30. It is worth six francs per mètre. 31. Our friend's stature is middling. 32. Do you go to church twice a day? 33. I go to church once a day. 34. Does your son go to the post-office every day? 35. He goes thither six times a day. Ce puits a cent pieds de profondeur, gueur, That well is one hundred feet deep. 2. In sentences where sizes are compared, and the verb être is used, the preposition de is placed before the number expressing the excess. Vous êtes plus grand que moi de You are taller than I by two inches. deux pouces, 3. When the price of an article is mentioned, the article le is used before the noun expressing the measure, weight, etc. When the remuneration, or rent, etc., for a definite space of time is mentioned, the preposition par (per) is used. Le beurre se vend un franc la livre, Il gagne six francs par jour, Butter is sold [at] a franc per pound. 4. The same preposition is used when we speak of the number of times any occurrence takes place in a given space of time. Je vais à la poste deux fois par I go to the post-office twice a day. jour, SECTION LXVIII.-IDIOMS RELATING TO METTRE, ETC. 1. Mettre (4, ir.) forms, in French, many idiomatic expressiora. Mettre à même de, to enable; mettre pied à terre, to aligh', to land; mettre le pied, to set one's foot; mettre à la porte, to form out of doors; mettre au fait de, to acquaint with; mettre à |