divide it without a remainder; then divide the quotient in the same way, and thus continue the operation till a quotient is obtained which can be divided by no number greater than 1. The several divisors with the last quotient will be the prime factors required. Every division of a number, it is plain, resolves it into two factors, -viz., the divisor and dividend. But according to the rule, the divisors, in every case, are the smallest numbers that will divide the given number and the successive quotients without a remainder; consequently they are all prime numbers. And since the division is continued till a quotient is obtained, which cannot be divided by any number greater than 1, it follows that the last quotient must also be a prime number; for, a prime number is one which cannot be exactly divided by any whole number except a unit and itself. Since the least divisor of every number is a prime number, it is evident that a composite number may be resolved into its prime factors, by dividing it continually by any prime number that will divide the given number and the quotients without a remainder. A composite number, therefore, can be divided by any of its prime factors without a remainder, and by the product of any two or more of them, but by no other number. Thus, the prime factors of 42 are 2, 3, and 7. Now 42 can be divided by 2, 3, and 7 ; also by 2×3, 2X7, 3×7, and 2×3×7; but it can be divided by no other number. EXAMPLE 1.-Resolve 4 and 6 into their prime factors. 8=2X2X2. Ans. EXERCISES. Here, 1. Resolve all the composite numbers from 9 to 108 into their prime factors. 2. Relsove 120 and 144 into their prime factors. A common divisor of two or more numbers, is a number which will divide each of them without a remainder. Thus 2 is a com mon divisor of 6, 8, 12, 16, 18, &c. The greatest common divisor of two or more numbers, is the greatest number which will divide them without a remainder. Thus 6 is the greatest common divisor of 12, 18, 24, and 30. It A common divisor is sometimes called a common measure. will be seen that a common divisor of two or more numbers is simply a factor which is common to those numbers, and the greatest common divisor is the greatest factor common to them. Rule: To find a common divisor of two or more numbers. Resolve each number into two or more factors, one of which shall be common to all the given numbers. Or, resolve the given numbers into their prime factors, then if the same factor is found in cach, it will be a common divisor. If the given numbers have not a common factor, they cannot have a divisor greater than a unit; consequently they are either prime numbers, or are prime to each other. The following theorems will assist the learner in finding factors or divisors: 1. The number 2 is a factor of every even number, that is, a number whose right-hand figure is divisible by 2. The number 4 is a factor of every number whose two right-hand figures are divisible by 4. The number 8 is a factor of every number whose three right-hand figures are divisible by 8. The number 16 is a factor of every number whose four right-hand figures are divisible by 16; and so on. 2. The number 5 is a factor of every number whose right-hand figure is divisible by 5. The number 25 is a factor of every number whose two right-hand figures are divisible by 25. The number 125 is a factor of every number whose three right-hand figures are divisible by 125; and so on. 3. The number 3 is a factor of every number, the sum of whose digits is divisible by 3. The number 9 is a factor of every number, the sum of whose digits is divisible by 9. The number 6 is a factor of every even number, the sum of whose digits is divisible by 3. The number 18 is a factor of every even number, the sum of whose digits is divisible by 9. By divisible in these theorems, is understood divisible without a remainder. EXAMPLE. Find a common divisor of 6, 15, and 21. SOLUTION.-Here 6=3×2; 15—3×5; and 21=3X7. The factor 3 is common to each of the given numbers, and is therefore a common divisor of each of them. EXERCISES. 1. Find a common divisor of 15, 18, 24, and 36. 5. Find a common divisor of 42 and 66. Ans. 2, 3, or 6. more than one common divisor. In many cases it is highly important to find the greatest common measure or divisor of two or each of them without a remainder. more given numbers, that is, the greatest divisor that will divide EXAMPLE.-What is the greatest common divisor of 35 and 50 ? Operation. 35)50(1 Explanation. Dividing 50 by 35, the remainder is 15, then dividing 33, (the preceding divisor) by 15 (the las remainder) the remainder is 5; finally, dividing 15 (the preceding divisor) by 5 (the last remainder) nothing remains; consequently 5, the last divisor, is the greatest common divisor. 35 15)35(2 30 5)15(3 15 ANALYSIS. Since 5 is a measure of the last dividend 15, in the preceding solution, it must therefore be a measure of the preceding dividend 35; because 35-2×15+5; and 35 is one of the given numbers. Now, since 5 measures 15 and 35, it must also measure their sum, viz., 35+15, or 50, which is the other given number. In a similar manner it may be shown that the last divisor will, in all cases, be the greatest common divisor. I. To find the greatest common divisor of two numbers. Rule :Divide the greater number by the less; then divide the preceding divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor. II. To find the greatest common divisor of a series of numbers. Rule: : then find that of the common divisor thus obtained and of another First find the greatest common divisor of any two of them ; given number, and so on through all the given numbers. The last common divisor found, will be the one required. Numbers which have no common measure greater than 1, are said to be incommensurable. Thus 17 and 29 are incommensurable numbers. EXERCISES. 1. What is the greatest common divisor of 285 and 465? 2. What is the greatest common divisor of 532 and 1274? 3. What is the greatest common divisor of 888 and 2775 ? 4. What is the greatest common divisor of 2145 and 3471? 5. What is the greatest common divisor of 1879 and 2426? 6. What is the greatest common divisor of 75, 125, and 160? 7. What is the greatest common divisor of 183, 3996, and 108? 8. What is the greatest common divisor of 672, 1440, and 3472? EXAMPLE.-What is the greatest common divisor of 30, 42, and 66? Analysis. Operation. 30=2X3X5 42=2×3×7 66=2×3×11 Now 2×3 6. Ans. By resolving the given numbers into their prime factors, we find that the factors 2 and 3 are both common divisors of them. But we have seen that a composite number can be divided by the product of any two or more of its prime factors; consequently 30, 42, and 66 can all be divided by 2×3; for 2x3 is the product of two prime factors common to each. And since they are the only factors common to the given numbers, their product must be the greatest common divisor of them. Second Method of finding the greatest common divisor of two or more numbers. Rule: Resolve the given numbers into their prime factors, and the cop tinued product of those factors which are common to cach, will be the greatest common divisor. If the given numbers have but one common factor, that factor itself is the greatest common divisor. EXERCISES. 1. What is the greatest common divisor of 105 and 165 ? One number is said to be a multiple of another, when the former can be divided by the latter without a remainder. A common multiple of two or more numbers, is a number which can be divided by each of them without a remainder. Thus, 12 is a common multiple of 2, 3, and 4; 15 is a common multiple of 3 and 5, &c. A common multiple is always a composite number, of which each of the given numbers must be a factor; otherwise it could not be divided by them. The continued product of two or more given numbers will always form a common multiple of those numbers. The same numbers may have an unlimited number of common multiples; for, multiplying their continued product by any number, will form a new common multiple. The least common multiple of two or more numbers, is the least number which can be divided by each of them without a remainder. Thus, 12 is the least common multiple of 4 and 6, for it is the least number which can be exactly divided by them. The least common multiple of two or more numbers, is evidently composed of all the prime factors of each of the given numbers repeated once and only once. For, if it did not contain all the prime factors of any one of the given numbers, it could not be divided by that number. On the other hand, if any prime factor is employed more times than it is repeated as a factor in some one of the given numbers, then it would not be the least common multiple. EXAMPLE. What is the least common multiple of 10 and 15.? ANALYSIS.-10=2X5, and 15-3X5. The prime factors of the given numbers are 2, 5, 3, and 5. Now, since the factor 5 occurs once in each number, we may therefore cancel it in one instance, and the continued product of the remaining factors 2×3×5, or 30, will be the least common multiple. Explanation. Operation. 5)10 15 We first divide both the numbers by 5 in order to resolve them into prime factors. Thus, all the different factors of which the given numbers are composed, are found in the divisor and quotients once, and only once. fore the product of the divisor and quotients 5X2X3, is the least common multiple required. Hence, :- 5×2×3=30 Ans. To find the least common multiple of two or more numbers. Rule:Write the given numbers in a line, but distinct from each other. Divide by the smallest number which will divide any two or more of them without a remainder, and set the quotients and the undivided numbers in a line below. Divide this line and set down the results as before; thus continue the operation till there are no two numbers which can be divided by any number greater than 1. The continued product of the divisors into the numbers in the last line, will be the least common multiple required. We have seen that the least divisor of every number is a prime number, hence, dividing by the smallest number which will divide two or more of the given numbers, is dividing them by a prime number. The result will evidently be the same, if, instead of dividing the smallest number, we divide the given numbers by any prime number, that will divide two or more of them, without a remainder. The preceding operation, it will be seen, resolves the given numbers into their prime factors, then multiplies all the different factors together, taking each factor as many times in the product, as are equal to the greatest number of times it is found in either of the given numbers. If the given numbers are prime numbers, or are prime to each other, the continued product of the numbers themselves will be their least common multiple. Thus, the least common multiple of 5 and 7 is 35; and of 8 and 9 is 72. EXAMPLE.-What is the least common multiple of 6, 8, and12? 2×2×3×3=36 Ans. "Dividing by any number, which will divide two or more of the given numbers without a remainder," according to the rule given by some authors, does not always give the least common multiple of the numbers. The reason of the preceding rule depends upon the principle that the least common multiple of any two or more numbers, is composed of all the prime factors of the given numbers, each taken as many times, as are equal to the greatest number of times it is found in either of the given numbers. The reason for dividing by the smallest number, is because the divisor may otherwise be a composite number, and have a factor common to it and one of the quotients, or undivided numbers in the last line; consequently the continued product of them would be too large for the least common multiple. EXERCISES. 1. Find the least common multiple of 6, 9, and 15. 2. Find the least common multiple of 8, 16, 18, and 24. 3. Find the least common multiple of 9, 15, 12, 6, and 5. 4. Find the least common multiple of 5, 10, 8, 18, and 15. 5. Find the least common multiple of 24, 16, 18, and 20. 6. Find the least common multiple of 36, 25, 60, 72, and 35 7. Find the least common multiple of 42, 12, 84, and 72. 8. Find the least common multiple of 27, 54, 81, 14, and 63. 9. Find the least common multiple of 7, 11, 13, 3, and 5. The process of finding the least common multiple may often be shortened, by cancelling every number which will divide any other given number, without a remainder, and also those which will divide any other number in the same line. The least common multiple of the numbers that remain, will be the answer required. By attention and practice, the student will be able to discover, by inspection, the least common multiple of numbers, when they are not large. EXAMPLE. Find the least common multiple of 4, 6, 10, 8, 12, 1. Find the least common multiple of 9, 12, 72, 36, and 144. 6. Find the least common multiple of 72, 120, 180, 24, and 36. First find the greatest common divisor of two of the given num bers; by this divide one of these two numbers, and multiply the quotient by the other. Then perform a similar operation on the product and another of the given numbers; thus continue the process until all of the given numbers have been employed, and the final result will be the least common multiple required. EXAMPLE.-What is the least common multiple of 24, 16, and 12? SOLUTION.-By inspection, we find the greatest common divisor of 21 and 16, is 8. Now, 24-3; and 3X16=48. Again, the greatest common divisor of 48 and 12, is 12. Now, 48-12 #4; and 4X12=13. Ans. PROOF.-Resolving the given numbers into their prime factors, 24=2×2×2×3; 16=2x2x2x2; and 12=2X2X3; con sequently, 2×2×2×2×3=48, the least common multiple. The reason of this rule depends upon the principle, that if the product of any two numbers be divided by any factor which is common to both, the quotient will be a common multiple of the two numbers. Thus, if 48, the product of 6 and 8, be divided by 2, a factor of both, the quotient 21, will be a multiple of each, since it may be regarded either as 8 multiplied by the quotient of 6 by the factor 2, or as 6 multiplied by the quotient of 8 by the same factor. Hence, it is obvious, that the greater the common measure is, the less will be the multiple; and, consequently, the greatest common measure will produce the least common multiple. When the common multiple of the first two numbers is found, it is evident, that any number which is a common multiple of it and the third number, will be a multiple of the first, second, and third numbers. EXERCISES. 1. What is the least common multiple of 75, 120, and 300 ? LESSONS IN GERMAN.--No. XIX. SECTION XXXIII. Beite (plural) is declined like an adjective, and, unlike its equivalent, (both) comes after the article, or pronoun with which it is used. Ex.: Die beiten Site; both the hands: meine beiten Sinte; both my hands. Atte (all) is sometimes, for the sake of emphasis, placed before beite, and, may together be transated, both of them," or simply, "both" as, alle beite; both of them; both. I. Veites, (neuter singular) is frequently employed to couple two things different in kind, whether designated by nouns alike or different in gender. Ex.: Wem ift ($ 129. 2.) dieses Messer und riefes Schwert? Beites gehört meinem Freuate; b belong to my friend. Hat Ihnen ter Uhrmacee nur die Uhr ett, auch ticha Ring gemacht? Er hat Beites gemacht; or, Vei e gema. Sind Sie mit ter Uhr und dem Ring zufrieden? Nein ich bin mit item unzustieten, benn Beites ist nicht nach mlaem Wunsde; no, I am dissatisfied with both, for both are not according to my wish. II. For the pronoun "neither" the phrase feines or feins von feiten" is used. Ex.: Haben Sie tas neue eter das alte Buch? Ich habe keine von Beiten; I have neither (of the two). III. Recht and Unrecht like the words "right" and "wrong' are nouns, adjectives, and adverbs. The phrases, however, "to be right, to be wrong," are expressed in German by the noun, with the transitive verb haben. Ex.: Er hat Recht; he (has) is right. Sie haben nicht Unrecht; you (have) are not wrong. IV. Gbense, before an adjective, signifies, "just as." Ex.: Dieses Kind ist eben so alt wie jenes; this child is just as old as that. Dieser Mann hat eben so viel Klugheit wie Verstand; this man has just as much prudence as understanding. ,, V. Ganz wie," with a verb, signifies "precisely" or "just as or like." Ex.: Gr ist ganz wie ich; he is just as I (am), he is just like me. Sie tenkt ganz wie er; she thinks precisely as he (thinks), she thinks precisely like him. VIII. Anter, with a noun denoting time, may be employed to designate as well a future as a past period; but never, like the word "other," as in the phrase "the other day," to denote indefinite past time. Ex. Den antern Tag nach seiner Zukunft verlæ er feinen Vater; the "next" day after his arrival, he lost his father. Mergen gebe ich nach Rem, und den andern Tag nach Nearel; to-morrow I go to Rome, and the "nert" day to Naples. As in the above examples, anter, when similarly employed, is rendered by "next." IX. The neuter anteret, preceded by etwas," (în conversation usually contracted to was) is rendered by the phrase "another thing" Das ist etwas Anteres, or, das ist was Anteris; that is "another thing." X. The adverb anters is readily distinguished by its form, and is rendered by "otherwise, differently," &c. Ex.: Or spricht anters als er tenft; he speaks ofheririse than he thinks. Absegeln, to set sail; Beite, both; G'benso, just as (IV.); Geleert, vacant, empty; Er hat zwei Söhne, aber beide sind Der Riese faste die Keule mit bei. Hat ter Kaufmann ein Pierd eter Er hat Beires. nen. Ein aufʼrichtiger Mann verabscheut Fast jeder Mensch hat e'ben so viel He has two sons, but both are deaf and dumb The giant seized the club with both hands. Has this merchant a horse or He has both? An upright man abhors a lie. Nearly every human being has quite as much sorrow as joy Ich will feines von beiden haben. 3. Wir geben ihm einen Trauer für jeten der beiden Männer. 4. Trinken Sie Wein eter Vier? 5. Ich Sommerrode? 10. Er braucht ebensoviel, wie zu einem Winterrede. 11. Der Staat Pennsylvanien liefert ebensoviel Kohlen, als ganz England. 12. Arbeitet Guftav nicht ebensoviel, wie sein Bruder Hermann? 13. ie VI. Nech, besides its signification as disjunction, (Sect. 12.) kleine Elife gab ihrer Schwester Pauline ebensoviel Pflaumen, wie ihrer is variously rendered by "still, some or yet more, another, Freundin Emma. 14. Haben unsere Nachbarn noch keinen Garten? 15 besides," &c. Ex.: Gr schläft ned; he sleeps still. (ich dem Kinte noch Bred; give the child some more bread. Mann hat er Nein, fie haben noch keinen. 16. Bleiben sie noch lange auf rem Lante? noch ein Pferd getauft? when did he buy another horse? Einen 17. Ich bleibe noch eine kurze Zeit da, und auch meine Freunde 18. Geben Apfel hat das Kind gegessen, aber es hat noch einen; the child has eaten one apple, but it has one besėles (or another). VII. Wicht, connected with a negative word, is used like its equivalent "more." Ex.: Ich habe keins mehr; I have no more. Ich habe nicht viel mehr; I have not much more. Used with a noun the adverb follows, while in English, it precedes the noun Cie heute noch spazieren? (Sect. 65. 1) 19. Nein, denn ich muß noch arbeiten. 20. Die Freutenthränen ter lang getrennten Breunte rührten tie Herzen aller Zuschauer. 21. Können sie die Waaren nicht billiger ver kaufen? 22. Es ist rein unmöglich. 23. Sie müssen dieses anders mechta 28 Was kann ich anters thun? 24. Du kannst anders reden und Handeln. 25. Ich weite Sie besuchen, wenn Sie es erlauben. 25. Er | noch zu überret:n. 15. Sein Betragen ist gar nicht zu verzeihen. 16. erzählte die Sache ganz auters. 26. Es ist etwas anderes, ob ich schreibe: Wie heißt Ihr Freund? 17. Er heißt Jakob. 18. 2ie heißt das auf er in „gelehrt," eter „geleert." 1. Has the teacher taken away the paper or the book? 2. He has taken away both; then both belong to him. 3. Both towns are situated on navigable rivers. 4. They may take either way, as they have proceeded so far. 5. A great part of the land in America is still uncultivated. 6. He who wants the purpose. must will the means. 7. The Rhine steamboat has just set sail for Holland. 8. You err altogether when you say that you have quite surmounted every difficulty, otherwise all that you have stated would be correct. 9. Which of us is right, I or he? 10. You are both wrong. 11. It is quite another thing to say that he was not well, and could not come in consequence of it. 12. I shall speak no more about it; because I have found upon closer investigation, that he is neither covetous, nor prodigal. 13. They do not think themselves better than others. 14. Emma is just as intelligent as Elisa. SECTION XXXIV. VERBS ACTIVE IN FORM WITH PASSIVE SIGNIFICATION. Deutsch? 19. Es heißt eine Brille. 20. Ein Kunstwerk ist desto schöner, je vollkommener es ist, das heißt, je mehr Theile es hat und je mehr alte diese Theile zum Zwecke beitragen. 1. The pronunciation of foreign words is only to be acquired through practice. 2 Nothing is to be learned without pains. 3. Perfect felicity is not to be found in this world. 4. You speak so quick, that you are not to be understood. 5. Health is not to be bought with money. 6. The peace of the town was not to be restored through severe orders. 7. How do you call these flowers? 8. They are called tulips. 9. The intelligent scholar is to be praised. 10. The difference between to buy and to sell, must, by this time, be known to the scholar. This book is to be had of the bookseller C. in London. LESSONS IN ENGLISH.-No. XX. 11. 1. The infinitive of the active voice, in certain phrases, is, THERE is nothing that will more help to form an English heart especially after the verb in, often employed in a passive sig-We could scarcely receive a single lesson on the growth of our English in ourselves and in others than the study of the English language. nification. Ex.: Er ist 3: chren; he is to be honored. Gr ift 3 tongue, we could scarcely follow up one of its significant words, leben; he is to be praised. Bay ihn rufen; let him be called. This use of the infinitive prevails to some extent in English without having unawares a lesson in English history as well; with Thus, we may translate literally the following examples out not merely falling on some curious fact illustrative of our Dieses Haus ist zu vermiethen; this house is to let. Sind diese erfel national life, but learning also how the great heart which is beating zu effen? are these apples to eat? Dieses Waffer ist zu trinken; this should thus grow, too, in our feeling of counexion with the past, at the centre of that life was gradually shaped and moulded. We water is to drink. Dieser Knabe ist zu tateln; this boy is to blame of gratitude and reverence to it; we should estimate more truly, II. Heißen, signifies, to name, to call; also sometimes to command. In the sense of naming or calling, it is most gene-bequeathed us, all that it has made ready to our hands. and therefore more highly, what it has done for us, all that it has rally used in a passive signification. Ex.: Wie heißen Sie? How something for the children of Israel when they came into Canaan, are you called? or, what is your name? Ich heiße Rutelph; my to enter upon the wells which they digged not, and vineyards which name is Ralph. they had not planted, fields which they had not sowed, and houses EXERCISE 38. which they had not built; but how much greater a boon, how much more glorious a prerogative, for any one generation to enter upon the inheritance of a language which other generations by their truth and toil have made already a receptacle of choicest treasures, a storehouse of so much unconscious wisdom, a fit organ for exover-pressing the most subtle distinctions, the most tender sentiments, the largest thoughts, and the loftiest imaginations, which at any time the heart of man can conceive.* Aussprache, f. pronun- Heißen, to name (See llebung, f. practice, use; to per Beitragen, to contri- Herstellen, to restore, leberve'ten, Jafob, m. James; con bute; city; art; ly; Ein beses Gewis'sen ist nicht zu be. ru'higen. Ein Gelehrter ist leichter zu über. Die Rose heißt die Königin der Der Löwe heißt der König der excuse; 1. Diese greßen schönen Häuser find alle zu vermiethen. 2. Das eine Haus ist zu vermiethen, das audere zu verkaufen. 3. Es ist nicht zu glau ben, daß er uns verlassen hat. 4. Dieses Buch ist bei Herru Westermann in Braunschweig zu haben. 5. Kein einziger Stern war am ganzen Him mel zu sehen. 6. Wie ist dieses lange Wort auszusprechen? 7. Wo sind die besten Stiefel, Schuhe und Ueberschuhe zu finden? 8. Die beften, die ich gesehen habe, sind bei meinem alten Nachbar N. zu finden. 9. Das Feuer brannte so schnell, daß nichts im Schlosse zu retten war. 10. Nichts❘ Werthrelles ist ohne Mühe zu gewinnen. 11. Dieser hohe Felsen ist nicht zu erklimmen. 12. Dieses alte Haus ist nicht mehr herzustellen. 13. Durch diesen Walt ist nicht zu kommen. 14. Er ist weter zu überzeugen, It was Ette, of French origin, is found in words taken from the French; as, coquette, etiquette. Coquette is, with us, applied to a female who employs her personal attractions to gain attentions from males. In French, there is the word coquet, a male coquette. Coquet seems to come from cog, a cock, a showy and uxorius animal; and accordingly, it signifies a man who resembles a cock in his attention to woman. By a natural step, in the progress of language, the term was applied to females. the short inscriptions, or tickets put on packages of goods to point Etiquette is the same word as our ticket, and originally denoted out what they contained. But similar etiquetts or tickets were employed to declare certain observances required in a public assembly; and so the word came to signify forms and formalities, a strict regard to custom, and in general, social conventionalism, particularly in relation to deportment. "Coquet and coy at once her air, Both study'd, though both seem neglected; Congreve. Eur, a French termination, from the Latin or; thus vendeur from Latin proditor. It is similar in import to our ending er, (a seller), is from the Latin venditor; proditeur, a betrayer, and denotes an actor; e. g., producteur, Fr. a producer. Of old many English words, now terminating in or, terminated in cur ; as autheur for author. The termination is still retained in certain nouns denoting abstract qualities; for instance, grandeur (Lat. grandis, great); hauteur (Fr. haut, high), derived immediately from the French. The notion of the actor is retained in the French douceur (from doux, sweet), a sweetener; a fee, or bribe. Ever, connected in origin with the Latin aevum, age; and the Greek aion, age, come to us directly from the Anglo-Saxon aefre, French "On the Study of Words,” p. 25-6, and signifies always, an enduring reality, either in time past (Ps. xxv.6; xc. 2), time present (Ps. cxix. 98), or time to come (Ps. cxi. 5). Ever, as a suffix, strengthens the word to which it is appended, thus: "whatever you do " has more force than "what you do." Ever is found in other compounds; e. g., whoever, however, wherever, whenever. Additional force is given by the insertion of the particle so; as, whosoever, whencesoever, whithersoever. This so used to stand where ever is now placed; as, whoso, howso, whatso. Spenser, "Faerie Queene." "Her cursed tongue (full sharp and short) Appeared like aspis' sting, that closely kills, Or cruelly does wound whomso she wills," Full, of Saxon origin, obviously the same as the adjective full, gives an instance of the origin of these particles in words which originally had a definite form and signification. According to its root-meaning, full (now in combination written ful) denotes a large portion of the quality indicated by the word to which it is affixed; as, hate, hateful; thank, thankful; grateful, delightful. Full has for its opposite less; e. g., merciful, merciless. In the employment of words, you cannot follow analogy alone, but must consult authority, thus: you may say penniless, but cannot say penniful; yet pitiful is as good as pitiless. "How oft, my slice of pocket store consum'd Still hungering, pennyless, and far from home, I fed on scarlet hips and stony haws." Cowper, “Task." Fy, is from the Latin facio, I make. Facio, in combination, becomes ficio; as in efficio. The fi in this word, written fy, is the particle under consideration. It is seen in fructify, literally, to make fruit; that is, to make fruitful. ANSWERS TO CORRESPONDENTS. LATIN.-J. R.: In Lesson IX., "norse" qualifies “nothing,” and must Your statement under therefore agree with gender, number, and case. 2nd" is incorrect; consult the Lesson, and do not make unnecessary inquiries; your letter has other proofs of haste or want of care. The specimen of your Latin is pretty well; consult the Key.-VINCIO will act foolishly if he quits the Latin so soon as our present series of lessons is completed. By running from one thing to another, he will become master of nothing. Every aid that marks of accentuation can give, is given in the Lessons; only from a living tongue can complete accuracy be obtained. T. R. N.: We do not remember receiving his communications, and we have a tolerably good memory. Can he kindly suppose, not to say charitably believe, that wE, THE EDITOR, never received them?-W. O. M. (London): We are not aware that there is at present any professed teachers of artificial memory going about town or country.-J. M. In the sentence alluded to that is used for the relative which, the antecedent being years, and is therefore the nominative to the verb have.-AMICUS: See the regulations for the degree of M.A. in the "London University Almanac." Your solution of the snail query is wrong.-W. MOORE (Chelsea): If he will send a list of words requiring explanation it will be given.-J. J. (Aberdeen) must send us a correct copy of the inscription; there is an error in it.-Correct answers to the snail query have been received from J. S. (Woodhall Colliery); A YOUTH TEN YEARS OF AGE (Easington-lane), beautifully done; ISAK (Leicester), still more beautifully done; S. M. P. (Shores wood); EUPHEMIA SMEATON (Portobello); and others.-A SUBSCRIBER (Piccadilly) should by all means study the Lessons in English first.-CONSTANT READRR (Dartmouth), and J. O. N. (Liverpool) have not come up to the requirements of the nine-digitsquare query.-INQUIRER (Wakefield): The Lessons will ultimately be published as he wishes; in the meantime, we recommend the P. E. or Dr. Beard's "Latin Made Easy," see note, col. 2, page 72, vol. I. P. E.-B. A. S. S.: Apply to the Rev. J. Curwen, Plaistow, by letter.-HENRICUS: Go on and prosper; study the Lessons in Penmanship in the P. E. and Cassell's Arithmetic and Euclid, with the Lessons on the same in the P.E., and then apply to the Normal school nearest to your residence.-J. GOUGH (Liverpool): Thanks for his suggestion; as to eyes, ours are not the best, but we advise him to let doctoring them alone; the improvement of the general health will do all that is required. You know "if one member suffer all the members suffer with it," so, if all the members improve by health so will the eyes.-R. the same for the Spanish when they come out.-J. THURLOW (Minories): We stated repeatedly that this office supplies covers for the P. E. only at the prices Is for the common edition, and 1s. 61, for the fine edition. If it is wanted to be bound in any other style, application must be made to regular bookbinders.-J. G. jun. (Kelso): As his answer to the snail query is wrong, we do not insert his proposed query; besides we cannot read the word of whose spelling he is doubtful. In the German words the f and the are pronounced, and not the p.-G. A. jun. (Liverpool): It is now too late to alter our plan; but the two volumes can still be bound together, and the title-pages and indexes retained. There is an Illustrated Edition of UnciTom's Cabin, issued by Mr. Cassell, price Is., in boards; and George Cruikshank, Esq., has undertaken to illustrate this surprising tale by 27 drawings from his inimitable pencil, to be published in Weekly Numbers, price 2d. each, the first of which is issued this day. "Calling drunkenness, good-fellowship; pride, comeliness; rage, TUCKER (Cheapside): The P. E. Lessons, of course, for the German; and valour; bribery, gratification.”—Bishop Morton. Head or hood, from the Saxon had, head, in composition, denotes the essence of any person or thing; its essential condition, viewed as a whole; thus, in Anglo-Saxon and English, manhad, manhood; wifhad, wifehood, or womanhood; cildhad, childhood; brotherhad, brotherhood; preosthad, priesthood. "Can'st thou, by reason, more of godhead know, Than Plutarch, Seneca, or Cicero." Dryden, "Religio Laici." Head is sometimes employed with a more direct reference to the meaning which it has in current use; as in wronghead and wrongheaded. "Much do I suffer, much to keep in peace, Pope. This jealous, waspish, wronghead, rhyming race." "Whether we [the Irish] can propose to thrive so long as we entertain a wrongheaded distrust of England?"-Bishop Berkeley. After a similar manner we use both heart and head, in fainthearted, lighthearted, hotheaded, lightheaded, &c. Ible, see able formerly explained under suffixes. Ic, ick, ich, have counterparts in the Latin termination icus, and the German ich, isch; as soporificus (sopor, Lat. sleepiness), soporific, rusticus (rus, Lat. the country), rustic, cildise in AngloSaxon, childish in English; bookish. "The sweet showers of heaven that fall into the sea are turned into its brackish taste."-Bates. Ile, from the Latin adjective termination ilis, to be seen in docilis (doceo, Lat. I teach), docile, teachable; fragilis (frango, Lat. I break), fragile, easily broken. Some Latin adjectives in ilis are represented by adjectives in ful in our tongue, as utilis, useful. In, ine is from the Latin termination inus, which denotes sometimes a name, as Tarentine, an inhabitant of Tarentum, but in English more often a quality, as genuinus (genus, Lat. a kind or race), genuine; that is, that which possesses the qualities belonging to its kind, in opposition to spurious, which, in its Latin meaning, signified a bastard. "We use AMICUS (Liverpool): Whateley's.-M. J. (Belfast) surprises us; here we have FOUR important languages, carrying on from week to week in our penny numbers, besides other important, useful, and varied information, and yet he wants a FIFTH language put in, and all for a penny! Greek SHALL be given; but WE MUST take our own time; reason's reason. Be cause HE FINDS a difficulty in learning Greek nouns, probably in some bad Grammar, this is no reason why we should throw al! our numerous students And he is not alone; of other subjects overboard, in order to serve him! we have numerous correspondents like him every day; to satisfy all of whom, would require a book as large as the Bible to be given to them every week for a penny. We hope some of our readers will take this friendly hint, and be more considerate in future. We shall do all in our power to please he can Matriculate at the London University, without going under the wing all; but we cannot do impossibilities.-W. M. R. W.: We are doubtful af of some tutor, but we advise him to try; we have sometimes seen attached to the name of one who passed the Matriculation examination successfully, pronounced exactly as they are spelt. the words private tuition—A. S. W.: The words Russia and Prussia, are Price Sixpence, THE ILLUSTRATED EXHIBITOR ALMANACK for 1853, containing upwards of Thirty beautiful Engravings. Price Twopence, THE POPULAR EDUCATOR ALMANACK for 1853, containing Forty-eight Pages of most interesting and valuable Educational Essays on the Leading Sciences; Brief Notices of Eminent Scholars; ExStatistics; including a Comparative View of Education at Home and Abroad; position of Technical Terms ; &c. &c. Price Twopence, THE TEMPERANCE ALMANACK for 1853, much improved and enlarged, and in which will be inserted a Tale of thrilling interest, from Tom's Cabin," entitled, "THE PLEDGE TAKEN; or, The Husband Saved, the inimitable pen of Mrs. Harriet Beecher Stowe, authoress of "Uncle and a Family made Happy;" with valuable details of the great Temperance Movement, Statistics, &c. With several Engravings. Price Sixpence, THE PROTESTANT DISSENTERS' ALMANACK, for 1853, with 12 beautiful Designs, by Gilbert, of striking Events in the History of Nonconformity. Printed and Published by JOHN CASSELL, La Belle Sauvage Yard, Ludgatehill, London.-October 23, 1852. |