LESSONS IN GERMAN.—XV. SECTION XXVII.—SEPARABLE PARTICLES—(continued). o refers to the place where anything may be supposed to exist or transpire, as :-Wo ist mein Messer? Where is my knife? Wo laufen die Kinder? Where (in what place) are the children running? Da is used in answer to wo; that is, to designate some particular place, as:-Da ist es, here it is. Da laufen fie, they are running here. şin denotes direction, or motion from the speaker, as:-Warum laufen die Kinder hin? Why are the children running thither? her is the opposite, in signification, to hin; denoting motion or direction toward the speaker, as :-Warum laufen die Kinder her? Why are the children running hither? Hier signifies "in this place," as :-Warum bleiben die Kinder hier? Why do the children remain here? These words are frequently compounded, one with the other; thus, from we and hin, we have the compound wohin; from wo and her, woher; from da and hin, dahin; from da and her, daher; from hier and hin, hierhin; and from hier and her, hierher (sometimes contracted to hicher). (§ 103. 3.) Examples of the use of wo, da, Wo reisen unsere Freunde hin? ober, Wohin reisen unsere Freunde ? Be kommen diese Zugvögel her? eber, Woher kommen diese Zugvögel? hin, her, and hier compounded. Whither do our friends travel? Where do these birds of pas- Sie kommen daher, wo es jest zu They come from (there) where kalt für sie ist. it is now too cold for them. RÉSUMÉ OF EXAMPLES. Wo ist das größte Glück: an dem Morgen reitet er mit seinen Schaaren In ter Hoffnung finden die Un'glück lichen Troft. Der Vater ist da, aber der Bruder ist in der Statt. Ich gebe heute dahin, wohin ich schon gestern gehen wollte. auf ten Berg. 13. Wo geht unser alter Nachbar hin? oder, Wohin geht unser alter Nachbar? (§ 89. 1.) 14. Er ist jezt in dem kleinen Garten, aber er geht bald in den großen Garten. 15. Seine Frau ist in diesem Hause, aber sein Vetter geht in jene Bildergallerie. 16. 3ch stehe an dem (am) Fenster, und sie kommen ans (§ 4. 2) Fenster. 17. Der Ritter sigt schon auf seinem guten Pferde, und der Knecht springt auch so eben auf sein gutes Pferd. 18. Der Mann fißt am (§ 4. 2) Tische, und das Buch liegt auf dem Tische. 19. Ich habe keinen Hut auf dem Kopfe. 20. Wo geht der Solvat hin? 21. Die Soldaten gehen aufs (§ 4. 2) Feld; sie sind schon auf dem Felve. 22. Der Frosch springt in den Fluß und schwimmt in rem Flusse, und die Gans schwimmt auf dem Teiche. 23. Ich habe diese Worte irgendwo gelesen. 24. Ich kann meine Mühe nirgends finden, obgleich sie irgendwo in diesem Zimmer sein muß. EXERCISE 45. 1. Where is the picture-gallery of this town? 2. Where was that gentleman born [geboren]? 3. He was born in Bohemia. 4. Where does your friend, the actor, reside? 5. He resides in the city. 6. Whither do these emigrants go? 7. Whence do these immigrants come? 8. They come from France. 9. Where much is given, much is required. 10. Here the revenge [Rache] and whetted dagger [geweste Dolch] of a traitor enter not [tringt nicht];-beneath [unter] the shade of this tree comes no king. 11. He threw down the book before me. 12. Whither art thou going? 13. I am going to my brother-in-law. 14. Will these emigrants go to America? 15. No, they will stop here. 16. There is water in the pond. 17. Where does she come from? 18. She comes from Germany. tance. Löhmen, n. Bohemia. VOCABULARY. Italie'nisch, adj. Ita- Aus'wanderer, m. emi- | Dahin'ziehen, to pro-Italie'ner, m. Italian. thither. Dahin'reisen, to travel thither. Dahin'schicken, to send thither. to Nie, never. how many? Wohl, well. Schwimmen, to swim. Where is the greatest happi- The father is here, but the I go to-day (thither) where I EXERCISE 44. 1. Wo ist der Schwager? 2. Er sizt an dem (am) Tische. 3. Wo geht der Zuckerbäcker hin? 4. Er geht in die Backstube. 5. Wo ist sein Freund, te Schauspieler? 6. Er ist in dem Opernhause. 7. Wo geht sein Freund, ta Seiler, hin? 8. Er geht in seine Werkstatt. 9. Wo ist der Hirte? 10. Er ist auf tem Berge. 11. Wo geht der Hirte hin? 12. Er geht 19. 1. When did he live? 2. He lived in the fourteenth century [im vierzehnten Jahrhundert]. 3. My friend told me he would never go there again [wieter]. 4. Do you go to Spain ? 5. No, I shall not go thither. 6. The commander-in-chief has sent his troops where the danger was most [die meiste Gefahr]. 7. Is this ship from Spain or from Havre ? 8. No, it is neither [weber] from Spain nor [nech] from Havre; it comes from Hamburg. 9. These immigrants are going to Milwaukee, and are emigrants from Bohemia and Venice. 10. Can you leap over that gate [Thor] ? LESSONS IN PENMANSHIP.-XVI. turned in an easy and flowing stroke. To show the necessity of this, the learner has only to turn the loop before reaching the line h h, when he will find that this imparts a stunted appearance to the stroke, or to any letter into whose composition it enters, which is far from satisfactory. In our last lesson, in Copy-slip No. 52, we gave an example of the elementary looped stroke which enters into the composition of the letters j, y, and g, and, with a little modification, into the formation of the letter z. To make this new elementary To form the letter j, it is only necessary to place a dot above stroke, a thick down-stroke must be commenced at the line a a, the elementary looped stroke that has just been described, on as in Copy-slip No. 57, for example, and carried downwards in a the line d d, which is, as it has been stated in a previous lesson slanting direction towards the left. As the stroke approaches (page 61), three-sixteenths of an inch above the line a a. In the line bb, the pressure on the pen must be lessened and Copy-slip No. 54 the elementary strokes entering into the comgradually reduced until the thick stroke narrows into a hair-position of the letters y and g are shown, the first of these line, which is turned at the line hh, and brought upwards over the line bb, in a direction slanting upwards towards the right, crossing the down-stroke in a graceful curve a little below the last-named line. The distance between the lines bb and h h should be exactly nine-sixteenths of an inch. The learner, on referring to Copy-slips No. 30 (page 133) and No. 39 (page 173) will see that letters carried below the line b b terminate on a line at the distance of seven-sixteenths of an inch below it, when the stroke below b b is of uniform thickness throughout, as in the letter p, or has a bottom-turn to the right, as in the letter q. In the formation, however, of looped letters, an eighth of an inch more is required to give space enough to admit of the loop being letters consisting of the top-and-bottom-turn and the elementary looped stroke, while the second is formed by a combination of this stroke and the letter o. In Copy-slips No. 55 and 56, the letters y and g are given, showing how the elementary strokes of which they are composed are joined together, while in Copyslip No. 57 an example is given of the method in which the letter j is joined to any letter that follows it, and the letter y to a letter that precedes it. The learner has now been taught how to make nineteen out of the twenty-six letters of the writing alphabet, and these we shall bring under his notice in a single lesson, after giving a few more examples for practice in writing letters looped below the line bb, and combining them with others. LESSONS IN GERMAN.—XV. SECTION XXVII.—SEPARABLE PARTICLES—(continued). Be refers to the place where anything may be supposed to exist or transpire, as :-Wo ist mein Messer? Where is my knife? Wo laufen die Kinder? Where (in what place) are the children running? Da is used in answer to wo; that is, to designate some particular place, as-Da ist es, here it is. Da laufen fie, they are running here. Sin denotes direction, or motion from the speaker, as:-Warum laufen die Kinder hin? Why are the children running thither? her is the opposite, in signification, to hin; denoting motion or direction toward the speaker, as:-Warum laufen die Kinder her? Why are the children running hither ? Hier signifies "in this place," as :-Warum bleiben die Kinder hier? Why do the children remain here? These words are frequently compounded, one with the other; thus, from we and hin, we have the compound wohin; from wo and her, woher; from da and hin, dahin; from da and her, daher; from hier and hin, hierhin; and from hier and her, hierher (sometimes contracted to bicher). (§ 103. 3.) Examples of the use of wo, da, We reisen unsere Freunde hin? ober, Wohin reisen unsere Freunde ? Sie reisen rahin, wo ihre Verwandten wohnen. Wo kommen diese Zugvögel her? eber, Woher kommen diese Zugvögel? hin, her, and hier compounded. Where do our friends travel Sie kommen daher, wo es jezt zu They come from (there) where kalt für sie ist. it is now too cold for them. Wo ist das größte Glück: an dem Hofe eines tyran'nischen Königs, eter in der Hütte eines zufrie'denen Tag'löhners ? Wo gehen Sie hin? an den Hof oder in die Hütte ? Der Feltherr fizt auf dem Pferte und reitet ruhig längs den Reihen ter Solda'ten hin und her. Morgen reitet er mit seinen Schaaren auf das Schlachtfeld. In ter Hoffnung finden die Un'glück. lichen Trost. Der Vater ist da, aber der Bruder ist in der Statt. Ich gehe heute dahin, wohin ich schon gestern gehen wollte. Schwimmen, to swim. Seiler,m. rope-maker. Sigen, to sit. Springen, to spring, leap. Stehen, to stand. Teich, m. pond. Werkstatt, f. workshop. Wohin'? whither? what way? 3ud'erbäcker, m. confectioner. Where is the greatest happiness: at the court of a tyrannical king, or in the cottage of a contented day-labourer? | Whither do you go? to the court or into the cottage? The commander-in-chief upon the horse rides tranquilly along the ranks of the soldiers to and fro. To-morrow he rides with his troops to the battle-field. The unfortunate find consolation in hope. The father is here, but the brother is in the city. I go to-day (thither) where I wished (already) to go yesterday. EXERCISE 44. 1. Wo ist der Schwager? 2. Er fißt an dem (am) Tische. 3. Wo geht der Zuckerbäcker hin? 4. Er geht in die Backstube. 5. Wo ist sein Freunt, ter Schauspieler? 6. Er ist in dem Opernhause. 7. Wo geht sein Freund, ter Seiler, hin? 8. Er geht in seine Werkstatt. 9. Wo ist der Hirte? 10. Er ist auf dem Berge. 11. Wo geht der Hirte hin? 12. Er geht auf ten Berg. 13. Wo geht unser alter Nachbar hin? oder, Wohin geht unser alter Nachbar? (§ 89. 1.) 14. Er ist jezt in dem kleinen Garten, aber er geht bald in den großen Garten. 15. Seine Frau ist in diesem Hause, aber sein Vetter geht in jene Bildergallerie. 16. Ich stehe an dem (am) Fenster, und sie kommen ans (§ 4. 2) Fenster. 17. Der Ritter sigt schon auf seinem guten Pferte, und der Knecht springt auch so eben auf sein gutes Pferd. 18. Der Mann fizt am (§ 4. 2) Tische, und das Buch liegt auf dem Tische. 19. Ich habe keinen Hut auf dem Kopfe. 20. Wo geht der Solvat hin? 21. Die Soldaten gehen aufs (§ 4. 2) Feld; sie sind schon auf dem Felde. 22. Der Frosch springt in den Fluß und schwimmt in rem Flusse, und die Gans schwimmt auf dem Teiche. 23. Ich habe diese Worte irgendwo gelesen. 24. Ich kann meine Müze nirgends finden, obgleich sie irgendwo in diesem Zimmer sein muß. EXERCISE 45. 1. Where is the picture-gallery of this town? 2. Where was that gentleman born [geboren]? 3. He was born in Bohemia. 4. Where does your friend, the actor, reside? 5. He resides in the city. 6. Whither do these emigrants go? 7. Whence do these immigrants come? 8. They come from France. 9. Where much is given, much is required. 10. Here the revenge [Rache] and whetted dagger [geweßte Dolch] of a traitor enter not [bringt nicht];-beneath [unter] the shade of this tree comes no king. 11. He threw down the book before me. 12. Whither art thou going? 13. I am going to my brother-in-law. 14. Will these emigrants go to America ? 15. No, they will stop here. 16. There is water in the pond. 17. Where does she come from? 18. She comes from Germany. Aus'wanderer, m. emi-| Dahin'ziehen, to pro- Italieʻner, m. Italian. grant. ceed thither. Bediente, m. servant. Gin'wanderer, m. imBefann'te, m. acquain- migrant. Englisch, English. Euro'pa, n. Europe. Feldherr, m. commander-in-chief. Französisch, French. Frembe, m. stranger. Havre, n. Havre. Hierher kommen, come hither. Pöhmen, n. Bohemia. Bremen, n. Bremen. Dahin'gehen, to go thither. Dahin'reisen, to travel thither. Dahin'schicken, to send thither. EXERCISE 46. to how many? Wohl, well. 1. Die Soldaten sind hier, und der Feldherr kommt auch hierher. 2. Der Feind ist schon da, und unsere tapfern Brüder müssen dahin zichen. 3. Wann gehen sie nach Spanien? 4. Ich will gar (Sect. XIV. 3) nicht tahin gehen, aber mein Vater will in nächster Woche dahin reisen. 5. Sind Sie schon da gewesen? 6. Nein, aber einer meiner Bekannten war ta und will nie wieder dahin gehen. 7. Wir gehen auf den Verg, wollen Sie mit uns gehen? 8. Will der Russe seinen Bedienten in die Stadt schicken? 9. Er hat ihn schon tahin geschickt. 10. Werten die Truppen hierher kommen? 11. Sie werden nicht hierher kommen. 12. Wo kommen diese Fremden her? 13. Sie sind Einwanderer und kommen aus Böhmen. 14. Ist dieses Schiff von Bremen over Havre ? 15. Es ist weder von Bremen, noch von Havre, es ist von Venedig. 16. Gehen diese französischen Einwanderer nach Milwaukee? 17. Ein Theil von ihnen geht dahin, die antern bleiben in New York. 18. Die Einwanderer in Amerika sind Auswanderer aus Europa und aus andern Theilen der alten Welt. 19. Wann wollen Sie auf das Feld gehen? 20. Ich bin schon auf dem Felde gewesen, und kann nicht wieder dahin gehen, aber ich muß jezt bald in den Garten gehen, denn mein Lehrer ist da und will mich sehen. 21. Warum will dieser Italiener nicht englisch sprechen? 22. Er möchte es wohl (Sect. XLIII. 4) sprechen, aber er kann es noch nicht; er spricht nur italienisch und spanisch. 23. Wie viel Sprachen können Sie sprechen? 24. Ich spreche nur zwei, aber ich will noch andere lernen. EXERCISE 47. 1. When did he live? 2. He lived in the fourteenth century [im vierzehnten Jahrhundert]. 3. My friend told me he would never go there again [wieter]. 4. Do you go to Spain? 5. No, I shall not go thither. 6. The commander-in-chief has sent his troops where the danger was most [die meiste Gefahr]. 7. Is this ship from Spain or from Havre ? 8. No, it is neither [weber] from Spain nor [noch] from Havre; it comes from Hamburg. 9. These immigrants are going to Milwaukee, and are emigrants from Bohemia and Venice. 10. Can you leap over that gate [Thor] ? 11. I could when I was young. 12. He bade [bat] me go thither, ab, hinauf geht unser Lauf. that he might speak to me about it. 8. Das Reh sprang den Berg hinab, während der Hase den Hügel hinauflief. 9. Die Soldaten stürzten aus der Caserne heraus, als der Feind in die Stadt hineinstürmte. 10. Als die Nachtwache SECTION XXVIII.-SEPARABLE PARTICLES-(continued). in das Haus trat, eilte der erschrockene Dieb die Treppe herunter. 11. Ich Wo, da, hin, etc., besides being compounded one with another kann nicht aus den Kreuzwegen dieses Gartens hinauskommen. 12. Wissen (Sect. XXVII.) are also united with prepositions; thus pre- Sie nicht, wie dieser Vogel hereingekommen ist? 13. Ja, aber er weiß ducing a separate class of adverbs, as :-Wovon sprechen Sie? Of nicht, wo er wieder hinauskommen kann. 14. Der junge Schweizer schaute 15. Kommen Sie what (whereof) are you speaking? Ich spreche von meinen Büchern; hinüber nach den blauen Bergen seines Vaterlantes. wollen Sie eins davon haben? I am speaking of my books; will you heute nicht herunter? 16. Ja, wenn der Oheim heraufkommt, werde ich have one of them? (one thereof ?) Ich bin auf dem Dache; kom hinabgehen. 17. Haben Sie diesen Mann schon gesehen? 18. Ja, er kam men Sie herauf! I am on the roof; come up! Ich kann nicht zur Thüre herein, als ich hinausging. 19. Der Freund fuhr in einer Stunte hinauf gehen; kommen Sie herab! I cannot go up; you come den Fluß hinüber und herüber. 20. Der Strom stürzt mit großem Geräusch den Felsen herab. down! Hinab, hinauf, hinaus, herab, etc., when used with nouns, are translated by prepositions; and the adverb, unlike its English equivalent, is placed after the noun, as-Ich gehe den Berg hinauf, I go up the mountain. Kommen Sie den Berg herab, come down the mountain. 1. The verb fommen frequently answers to our get," as:Wie ist er in diesen Garten gekommen? How did he "get" into this garden? Er weiß nicht, wie er heraus kommen soll, he does not know how to "get" out. Ich komme mit tiefem Manne sehr gut fort, I "get" along with this man very well. RÉSUMÉ OF EXAMPLES. EXERCISE 49. 1. The son hastened down to receive his father. 2. His speech lasted over two hours. 3. The roe sprang out from his hiding place. 4. Will you go over to Frankfort to-day by the steamboat? 5. No, I shall go over by the railroad and return by the steamboat. 6. Do not go beyond the crossway. 7. I saw your friend come in as your uncle went out. 8. These men who go over that bridge are in danger of their lives. 9. Will you go out to-day with your friend? 10. From this hill we can look over our country. 11. How did the thief get into your house? 12. Edward precipitated himself from the rock. 13. I shall pass your house this morning, and shall come in, without your asking me to do so. LESSONS IN ARITHMETIC.-XVI. 15. Terminating and Circulating Decimals. Reducing Fractions It is evident, from what has been said, that vulgar fractions can be reduced to decimals by the process of the division of decimals. For we have only to write down the dividend with a decimal point, followed by a series of ciphers, and then divide by the divisor, according to the rule already given for the division of decimals. Thus, may be reduced to a decimal as follows: 40) 7.000 (175 40 300 280 200 200 Therefore = 175 Decimals which, after continuing the division of the fractions Sie sehen hinab' in das wilde Meer. They look down into the wild from which they arise far enough, at last give a result without a remainder, are called terminating decimals. 16. To determine whether a Fraction will produce a Terminat ing Decimal or not. Since a decimal is a fraction with 10 or power of 10 for its denominator, it is evident that if a given fraction will produce a terminating decimal, it must be capable of being expressed in the form of an equivalent fraction, which shall have a power of 10 for its denominator. Now 10 is composed of the prime factors 2 and 5. Hence, if the denominator of the given fraction, when in its lowest terms, contains any factor besides 2 and 5, it cannot produce a terBut if the denominator contains only 2's and minating decimal. 5's as its factors, then, by multiplying numerator and denominator of the fraction by a factor, we can always transform the fraction into an equivalent one, having a power of 10 for its denominator-that is, into a terminating decimal. For example: will produce a terminating decimal, because 250 is com. posed only of factors 2 and 5. 17. We see from the preceding remarks the truth of the following Rule for determining whether a given Vulgar Fraction will produce a Terminating Decimal. Reduce the given fraction to its lowest terms, and split the denominator into its prime factors. If the denominator have for its factors 2's or 5's, or both, and no other factors, the fraction will give a terminating decimal, but not otherwise. 18. To determine in this case the Decimal without actually dividing. If one of the factors 2 and 5 occur fewer times than the other, multiply numerator and denominator of the fraction by that power of the factor which occurs the fewest times in the denominator, which will make the number of times it occurs equal to the number of times the other occurs. Thus, in the instance already given, 250 is made up of three 5's and one 2 as factors. We therefore multiply numerator and denominator by the second power of 2. Similarly, in, 8 being the third power of 2, we multiply numerator and denominator by the third power of 5. Obs. It will be perceived that the number of decimal places in the terminating decimal which is equivalent to a vulgar fraction, will be the same as the greatest number of times that either of the factors 2 or 5 is repeated in its denominator, when the fraction is reduced to its lowest terms. 1750° EXAMPLE.-Determine the decimal which is equal to 348. 382 382 Reduced to its lowest terms this is or Multiplying 125 53. numerator and denominator by 23, or 8, the fraction becomes 3056, or 3.056. 1000 Decimals in which the period commences immediately after the decimal point, are sometimes called pure circulating or recurring decimals; others being entitled mixed circulating decimals. Thus above 6 is a pure, while the other two are mixed circulating decimals. 20. Fractions producing Circulating Decimals. We have seen that all vulgar fractions in their lowest terms, which have any other factors besides 2 and 5 in their denominators, will not produce terminating decimals; that is to say, in performing the division we shall never arrive at a remainder which is zero. We shall, however, arrive at a remainder which is the same as one of the remainders which has already occurred. This is evident from the following considerations : The largest possible remainder in any division is the divisor diminished by unity, and therefore there cannot possibly be more than this number of different remainders. Hence, at the very farthest, after this number of remainders have occurred, a remainder will occur which is the same as one of the preceding remainders. Now it is plain that when this is the case, the whole of the operation which has been performed since that remainder last occurred will be repeated, and that the same remainder will occur again after exactly the same interval, and so on ad infinitum. Now to every remainder there will correspond a figure in the quotient, and therefore the figures in the quotient corresponding to the interval between two remainders which are the same will continually recur. Here it will be seen that at the point indicated by the star the remainder 2 occurs, and therefore the division will, after this point, be identical in every respect with that already performed. Hence the figures in the quotient, 285714, will continually recur, or the quotient is the pure circulating decimal, 285714. It will be observed that the period here is as large as it could possibly be, for the greatest possible remainder is 6, and all the remainders from 1 up to 6 inclusive occur. [The process has been exhibited in the form of Long Division, to allow of the remainders appearing in the operation.] 22. Reduce to a decimal. We see at once that the quotient will be a circulating decimal, since being in its lowest terms, 3 is a factor of the denominator. Here the remainder 20 is at once repeated, and therefore the quotient after the first figure 5 will consist of 6 continually repeated, or it will be the mixed circulating ⚫56. 23. Reduce to a decimal. 55) 129.00 (2·345 Answer. 110 190 165 250 220 300 275 * 25 |