said something of this kind-"the woman is (the daughter, or the mother) of the fair one." Similar remarks would serve to show that the article (which is a species of adjective-a qualifying, that is, determinative word) must also agree in form with its noun, seeing that it of necessity agrees in sense, both referring to the same object. As adjectives and substantives which agree in sense must agree in form, so The subject must agree with its verb. If, for instance, I had put before the verb or a plural sub ject, as al yuvaukeç, saying the women is fair, then I should have represented the subject as at the same time plural and singular, intimating that it was plural by the form of the noun and the form of the adjective; and intimating that it was singular by the form of the verb. Similarly erroneous would it have been had I written to (they are) for eori (she is). We now come to case. Take the example ἡ γυνη τυπτει τον υἱον. Here rov viov is in the accusative case, illustrating the fact that runrw is one of those verbs which require their object to be in the accusative case. Other verbs place the object in the genitive case, and others in the dative case. In either the accusative, the genitive, or the dative case must every object be. Consequently a noun found in either one of these cases is known to be an object-an object governed by a preposition if not by a verb. In the sentence given above, then, I know that rov viov is the object, or receives the action implied in TUTTA, because it is in the case of the object, the objective or accusative case. Instead of being rov vior, were it ò vioç, I should not know which of the two, yuvn or ò vios, was the subject. And if ǹ yuvŋ were rηy yuvaika, then ò vioç remaining the same, the sense would be the son struck the mother; for in Greek the sense depends on the form of the words, not their arrangement. Now then suppose that I had written την γυναικα εστι καλη. I should have sundered ran from yuvn, making the subject an object, for it is in one of the cases in which the object appears. Had I written ǹ yuvŋ torɩ kaλŋy, I should have employed an object xaλŋy, without any verb or preposition to govern it. γυνη προςκαλεῖ ΤΟΥ viov By adding another verb we should add that which would make These two sentences may, however, be reduced to a simple sentence by changing one of the verbs into a participle, thus ή γυνη προςκαλοῦσα τυπτει του viov the woman calling (him) strikes her son. Observe, moreover, that can is in the same case as yuvn, though a verb comes between them. That verb is sort. Hence you may infer, as a general rule, that the verb tivat has the same case after it as before it; the reason is found in the fact already mentioned, that elva, as a copula, merely unites the attribute with the subject. Indeed, whether, as here, the You may also expand the other components of the sentence, adjective is an attribute, or whether it is an epithet im-e. g. mediately qualifying the noun, the adjective must agree with the noun in gender, number, and case. The parts of a sentence thus explained may be variously modified. The Subject ή κακη the bad τύπτει γυνη strikes her woman του vios The Verb ή TUTTEL TOV son. υἱον her son. απειθη υἱον disobedient son. 1. The article may be dropped, and then you have youη LOTL Kaλn. The article becomes plural if the noun is plural; it The Object may also pass into the dual number to agree with the noun. 2. The subject may be in either the plural or the dual number. 3. If the subject is changed so as to be in the plural or dual number, the verb must also be changed. 4. The verb may undergo changes, passing into the dual or the plural, in order to correspond to the subject. 6. If the subject is in the dual or the plural number, the attribute is changed into the corresponding number. Also in the second sentence, yuvŋ TuπTEL Tov viov, many similar changes may be made in the subject, the verb, and the object. Besides changes like those just pointed out, the sub ject may be involved in the verb, being indicated by the person-ending, as γυνη the woman δεινως ή A secondary subject may be introduced, as ή γυνή, ή Ασπασια καλουμένη, τύπτει the woman, who is called Aspasia, strikes her takes place when a noun is added to a noun, the second being, This instance illustrates what is called apposition; apposition in the same case as the first, by way of explanation, that is, in order to state who or what is meant. A secondary object may be introduced; e. g. ή γυνη TUTTEL τον υίον ένεκα της απειθειας the woman strikes her son on account of his disobedience, The secondary object may relate to place and so qualify the verb, as I may exhibit these facts to you thus Subject. Primary ἡ γυνη Secondary ή Ασπασία Verb. τυπτει Object. τον υἱον εν τω οικω ένεκα της απειθειας. καλουμένη You will readily see how each of the principal parts may be extended; thus you may prefix an adjective to yvvn; you may qualify the verb by an adverb, and you may qualify the object by an epithet. As the primary, so also the secondary subject and object may be qualified; the verb may also be doubled, or a participle may be introduced instead of a second verb, or together with a second verb; and thus the simple sentence may be expanded into a compound sentence, and give you an instance of what the Grammarians meant when they termed a sentence or the expression of a thought, a period or a circle (repíodus). I here give the sentence in an expanded form, as a period or compound sentence : Η κακη γυνη, ἡ Ασπασια καλουμενη, προςκαλεσασα τον απειθη υἱον, εν τῳ οικῳ, ένεκα τῆς απειθείας, λοιδορεῖ και τύπτει ἰσχυρῶς. This period may be presented in a state of analysis thus: The sentence thus enlarged brings permanently into view what in grammar is called government. One word is said to govern another, when the second is dependent on the first, and undergoes some inflectional change under the influence of the first. Thus the nominative vios is changed into the accusative viov by the verb TUTTE, on which it depends, and by which therefore it is said to be governed. In the same way απειθης becomes απειθη under the operation of the verb τυπτει, and in order to agree with viov. So the prepositiou ev changes Oikos into oiky, and our is said to be governed in the dative case by the preposition εv. For the same reason απείθεια appears in the genitive case, aπuotias, because it depends on iveka, which requires its object to be in the genitive. These reduced to the same index are (x32) and (y2)*. And the quotient is (23)=2x2. Ans. 6. Divide bar by 3x. 7. Divide dhx2 by dx. 8. Divide (a3+ ax)" by a* 1 9. Divide (a3h) by (ax). 10. Divide (ay) by (ay), + A root is divided by another root of the same letter or quantity, by subtracting the index of the divisor from that of the dividend. ¿¿ = a+ = a3. 11. Thus aa Ha For aaa a3 X Χα =a =a 12. In the same manner, ama" am aw 13. Divide (3a) by (3a). H 14. Divide (ax) by (ax)3. m+m 15. Divide a um by am. 2 16. Divide (b+y)^ by (b+y)^. 17. Divide (23) by (ry3). 20. Divide 24x√ ay by 6√ a 1 21. Divide 18dh√ bx by 2h√ x. 25. Divide ab(x) by a(x). These reduced to the same index are ab(x26)* and a(x2)aa . = 17. Required the cube of 2d + √x. EVOLUTION OF RADICAL QUANTITIES The operation for finding the root of a quantity which is already a root, is the same as in other cases of evolution. Hence we derive the following RULF FOR THE EVOLUTION OF RADICALS. Divide the fractional index of the quantity by the number expressing the root to be found. Or, Place the radical sign belonging to the required root over the given quantity. If the quantities have rational co-efficients, the root of these must be extracted and placed before the radical sign or quantity. 1. Thus the square root of a 21. Multiply a(a+c) into b(a — √e). 1 22. Multiply 2(a + b)a into 3(a + b)TM. 23. Divide 654 by 31/2. 3 24. Divide 472 by 23√ 18. 25. Divide 7 by 3√/7. 26. Divide 8 3/512 by 4 3√2. 27. Find the cube of 17 21. 28. Find the square of 5+√2. 29. Find the 4th power of 6. 30. Find the cube of √ √ b. X FRENCH READING S.-No. XXVI. LA MARGUERITE ET L'E'PI DE BLE'. Lorsque les deux enfants repassèrent le soir, la marguerite était fanée sur la tête de Marie, qui n'y songeait déjà plus et s'en revenait en faisant l'école buissonnière.... Louise, chargée d'une récolte d'herbe, éleva sa figure blonde au dessus de la haie,' et jeta un regard d'espoir à son épi florissant. --Souviens-toi de ces petites filles,3 me dit mon père avec gravité. Je soupçonne qu'elles ressemblent l'une et l'autre, aux objets si différents de leurs vœux. Puis il me fit l'histoire de la marguerite et celle du froment. Dans les champs et dans les jardins, la marguerite est la même; jolie, coquette et inutile. Celle qu'on nomme la páquerette, s'établit dans l'herbe courte, pour l'étoiler de son bouton d'or et de son blanc diadème. Celle qui prend le nom de reine des prés, se dresse et se balance sur sa tige au dessus de tout ce lui l'environne. Mais quand la faux du moissonneur vient l'abattre, elle n'offre au sol qu'une graine funeste et à la dent des bestiaux qu'un fourrage détesté. Enfin, celle qui brille dans les parterres, n'a que son éclat d'un jours et ne présente à l'homme ni parfum ni produit. L'histoire du froment, au contraire, est l'histoire de la civilisation même. Il naît avec elle, il en développe et en suit' les progrès, et il ne meurts que sous les latitudes où elle expire.10 Ceci est la plus admirable harmonie de la nature. COLLOQUIAL EXERCISE. 1. Où était la marguerite, lorsque les enfants repassèrent le soir? 2. Que fit Louise alors? 3. Que dit le père de l'auteur ? 4. Que fit-il ensuite ? 5. Où se trouve la pâquerette ? 6. Que fait la reine des prés? 7. Qu'offre-t-elle après la moisson ? 8. Et la marguerite des parterres ? 9. Qu'est-ce que l'histoire du froment ? 10. Que fait le froment? 11. Que continua de faire 12. Que fit Louise quand l'épi Marie, les jours suivants P de blé fut mûr? 13. Que se passait-il au village? 17. Que rappela à son fils, le 18. Où le conduisit-il? 19. Que lui montra-t-il ? 20. Que dit le jeune homme ? 21. Que répondit le pere? 22. Où allèrent-ils de là ? 23. Que virent-ils dans un champ de blé mûr ? 24. Que faisait la jeune fille? 25. Que dit le père? 26. Qu'avait distrait de ses pro27. Par quel souhait finit lo duits la jeune fille? morceau ? -e. from faire l'école buissonnière; this familliar expression may be renNOTES AND REFERENCES.-a. L. part ii., § 49, R. (1).—b. dered in English by: to play the truant, to stay away from school. -c. L.S. 36, R. 2-d. the singular of bestiaux, is betail.naître; L. part ii., p. 96.-f. from suivre; L part ii., p. 106.-g. from mourir; L. part ii., p. 96.--h. L. S. 36, R. 2.-i. from reconnaître ; L. part ii, p. 102.--j. travail is the subject of the verb.-k. distrait, taken.l. from valoir; L. part ii., p. 108. En fuyant la main qui l'attire16 COLLOQUIAL EXERCISE. 9. Le chien suivit-il le convoi etc.; and from the Technological and Scientific Dictionaries of both Languages. By Professor DE LOLME and HENRY BRIDGEMAN, Esq. The following are the distinctive features which render this Work superior to any of the same class now extant. It has been compiled with unusual care from the very best authorities. It contains correct renderings of all the most modern words and phrases-including those of science, art, manufac ture, commerce, law, politics, etc., as well as familiar conversation-which are indispensable to a knowledge of language, but yet are rarely, if ever, to be found properly translated in any Dictionary. The idiomatic usages of the two languages-the constructions of verbs, the force of prepositions, and the changes of meaning caused by different combinations of words-are more copiously and carefully illustrated than elsewhere within the same limits. The meanings are also classified and arranged in such a manner as to prevent the possibility of mistake. To crown all, the Work is as moderate 12. Comment la gloire y jeta-t-in price as it is comprehensive in aim, accurate in detail, and superior in arrangement. The French-English Division, price 4s. paper covers, or 5s. neat cloth; the English-French Division, price 48. paper covers, or 5s. 10. Paraissait-il triste? 11. Où se traîna-t-il avec peine? elle son maître ? 13. Pourquoi ne le connaissait- 14. Que devint alors le fidèle 15. Son chagrin paraissait-il se 16. Etait-il sensible aux caresses 17. Que semblait-il dire avec NOTES AND REFERENCES.-a. que ton front se découvre, let thy brow be bared! uncover thy brow.-b. il, the master of the dog.-c. vint les atteindre, struck them.--d. from survivre; L. part i., p. 108.--e. parent, relation.-f. juillet, the revolution of July, 1830. ANSWERS TO CORRESPONDENTS. In compliance with the urgent request of several correspondents, it is our intention to give a few Lessons in Spanish, commencing in our next number, and to complete our Lessons in Arithmetic. EDMUND LEE may procure the missing numbers of the POPULAR EDUCATOR by ordering them of any bookseller. W. R.: The bookbinder will understand how to bind the maps and engraving. CONVEX had better apply to the Secretary of the Society of Arts. 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