48 expressed by points, or by inverting the fraction which expresses Any set of numbers are said to be respectively proportional to the direct ratio. any other set containing the same number when the one set can A ratio is said to be compounded of two other ratios when it be obtained from the other by multiplying or dividing all the is equal to the product of the two ratios. Thus, %is a ratio numbers of that set by the same number. Thus, 3, 4, 5 are compounded of the ratios į and 1. proportional respectively to 9, 12, 15, or to ļ, 4, . 3. Proportion. 7. To divide a given number into parts which shall be proporDifferent pairs of numbers may have the same ratio. Thus, tional to any given numbers. the ratios , 13, 3, are all equal. Add the given numbers together, and then, dividing the given When two pairs of numbers have the same ratio, the four number into a number of parts equal to this sum, take as many numbers involved are said to form a proportion; and they them of these parts as are equal to the given numbers respectively. selves, in reference to this relation subsisting among them, are EXAMPLE.—Divide 420 in proportion to the numbers 7, 5, called proportionals. Thus, 3, 4, 12, 16, are proportionals, and 3. because the ratio 1, or 3 : 4 = the ratio lá, or 12 : 16. 7 + 5 + 3 = 15; A proportion is expressed either by writing the sign of equality And therefore the respective parts are-(=) between the two equal ratios, or by placing four dots in the o X 420 = 196. form of a square, thus, :: between them. * 420 = 140. Thus, the proportionality of 3, 4, 12, 16, might be expressed it X 420 = 84. in any one of the three following ways : These parts are evidently in the proportion of 7, 5, and 3, = 18; 3:4 = 12 : 16; 3:4:: 12:16. and their sum, 196 + 140 + 84 = 420. The last expression would be read, 3 is to 4 as 12 is to 16. 8. The same method will apply if the given number or The first and fourth terms of a proportion are called the quantity is to be divided proportionally to given fractions. extremes ; the middle two, the means. EXAMPLE.--Divide 266 into parts which shall be respectively 4. If jour numbers be proportional, the product of the extremes proportional to , and . is equal to the product of the means. Following exactly the same method as before, the answer, Take any proportion, 3: 4:: 9:12, for instance. Expressing without reduction, would bethis in the fractional form, we have Po, and reducing these x 266, and X 266. fractions to a common denominator 12 x 4, we get 3 + + 4 3 + + 3 Or we may proceed thus :- Reducing the fractions to their least common denominator, Now, 12 and 3 are the extremes, and 4 and 9 are the means, which is 60, we get 40, 45, and 18. of the given proportion. Conversely, if the product of two numbers is equal to the pro- Now these fractions are proportional respectively to 40, 45, 48. duct of any other two numbers, the four numbers will form a Hence we have to divide 266 in the proportion of 40, 45, and proportion. Thus, since 48, to which the required answer is, since 40 + 45 + 48 = 133, 8 X 3 = 6 x 4 8, 4, 6, 3 form a proportion; !" 266, it's x 206, and is * 266, or 80, 90, and 96. Or we may write it thus, 8:6:: 4:3; EXERCISE 41. 3:6:: 4:8; Find in their simplest form: 1. The ratio of 14 to 7, 36 to 9, 8 to 32, 54 to 6. Thus we see that either product may be separated to form 2. The ratio of 324 to 81, 802 to 99. the extremes, and that, the order of either the means or the 3. The inverse ratio of 4 to 12, and of 42 to 6. extremes being interchanged, the numbers still form a pro 4 Find the fourth term of the proportions, 3:5::6: -; 4:8::9:-; portion. 1:::$:5. If three numbers be given, a fourth can always be found 4:8::- : 9; 1:1::-:%. 5. Insert the third term in the following proportions-3:5:: - :6; which will form a proportion with them. 6. Insert the second term in the following proportions-3:-::5:6; This is the same thing as saying that if three terms of a pro- 4:-::8:9; $ :-:: 1:8 portion be given, the fourth can be found. 7. Insert the first term in the following proportions- -:3:: 5:6; Take any three numbers—3, 4, 5, for instance. Then we have - : 4::8:9; -;}:::. 8. Find a fourth proportional to 2-13, •579, and 3:14159, correct to 3:4:: 5: fourth term, 5 places of decimals. Thereforo 9. Divide 100 in the ratio of 3 to 7. 10. Two numbers are in the ratio of 15 to 34, and the smaller is 75; 3 x fourth term = 5 x 4 (since the products of the means and find the other. extremes are equal). 11. What two numbers are to each other as 5 to 6, the greater of Therefore, dividing both of these equalities by 3— them being 240 ? As tests by which the correctness of the processes of 5 X 4 Fourth the required number. addition, subtraction, multiplication, and division may be Here we have found the fourth term, but we could in the has not been thonght requisite to give answers to the Exercises ascertained, were given in Lessons in Arithmetic, II. to V., it same way find a number which would form a proportion with already given in abstract Arithmetic. The answers will, howthe three given numbers when standing in any of the terms. ever, be supplied to future examples in concrete Arithmetic. For instance, for the second term we should have 3 : second term :: 4:5, and therefore MECHANICS.-IX. 4 X second term = 5 * 3. THE STEELYARD. Hence, dividing both of these equalities by 4 ANOTHER weighing instrument is the steelyard, which (Fig. 54) second term = is a lever of the first order, to the short arm of which is attached at b a hook from which the substance, w, to be weighed is and similarly for the other two terms. suspended, while on the long arm slides the movable counter. The most important application of proportion is the solution poise P. The object aimed at in this instrument being that a of examples of this kind, where three terms of a proportion are small weight, P, should balance a large one, w, on the hook, it riven to find a fourth. This is what is usually called Rule of | is clear that there must be a corresponding disproportion in the Three, which will be dealt with in a future lesson. arms—the fulcrum, a, must be near one of the ends of the beam. 6. It is evident that if the two terms of a ratio be multiplied Further, since it is necessary that the steelyard should take an or divided by the same quantity, the ratio is unaltered. horizontal position, both when loaded and unloaded at its hook, or, 3 5 x 3 soane , onu minta ha un timon The genrinie sf fis instziment. 3 pes Ie sin ina m4 woman sina for which won glitrans, su se rugang ettes may be miestaisins Maon #nha net te perband mething, schor, sonompaatang 5 5. Om saright cand siis , arab ming Set, sny amount of sonundo niny mhr an. *9.of much c is the senten Beruni < dan *** in ne now, when the final 2 4907, mal sent. but in the igne presenti == mina My, a mi man lantai, wa nane » math :ama at ngat sçies to each otáz tie sa BA : 5134 Manon ita ring fan Tha faerm a wnal *** aig sé email weight, being lightiy sosteutel. še Bourbbegato Avram, "Saya na uhrading musnart sowata, trgother (* nazilet the index azn* is heavily regtei si *** bin winnen, ne man bet, muitas ng he distance end, the centze af gravity of the whole lere has being zeszly I'** terity that som frent, i4 email the ment the bean, st some point. s. ist Ax sirang gun, Shaina totoons Chat Multiplied by ita On sme substance to be Aventura Tren the worly Arvinium ja w to w mnltipliert brg ah, weighed, being suspende! Minn, in with the gradovala, la, na mapene me pond and w from 2, the index mure tres 'nun w* hann in notkua waven times a b anal ones its zero point, op ste quad. tha thamaill then hamturidae freno (1, which telle on the exact mnt until the weight of the primento la genunda in the book, namely, that you find it by lever seting at & balances w #marting ipinih li to the left serven paras sanh bai to ab. at 2, that is until the mo 1m w lv 19 prona 1 % pomode, then in like manner you ments of these forces are menava 14 pessoa eeprial to ab. It thus appears that the equal, which will be when w viabma fer the knew alve painda are smal to ench other, maltiplied by B = is equal to and we thay wheredige lag dwn the following role for gruinating the weight of the lever mal Pig. 56. tiplied by GL The divisions Wind put the vert nulliviaia by Iringing the unloaded in of the quadrant corresponding "btnment Inte non liriumtal pemilien by the counterpoine. Put to the several weights 1, 2, 3, 4, etc., suspended from B are, then * the bike it in the pun, much in number of even pounda however, best determined by experiment for each weight. wa will priah the funntorpening to the greatest distance it onn go im ile iron for even prindia, and divide the distance between this THE LEVER WHEN THE FORCES ARE NOT PARALLEL Inel primitive and the were peamt foto nn many equal parts as In all the cases of levers and weighing instruments we have there are then penanda on the hook. The points of divinion ko ho far considered, the forces were supposed parallel-in weighing ablaknad are the position of the counterpoise for the noveral instruments necessarily so. The treatment of the subject is , prwia wple that number. however, not complete until the condition of equilibrium is de pie limit and quarter pounds those divisions must be sub- termined for lovers the forces acting on which are not parallel . divideid, and fur arouter weights than one pound will balance This is the most general Cése that can occur, and indeed it w the love arm, the cominterpolne must be doubled or troblod, includes all the others. To Cearly understand it, let a lever be b. If He stoolyard be intonded for wolghing small objects, defined a mass of matter of ary shape which has one fixed point a letters, the counterpolso may be onnoon, or tonths in it. It may be a bar straicht, or simply bent, or bent and of all ownes, to even omaller wolght, an ooonston requiron. twistod, or it may be a solid lock. So long as there is a 10 Heappear thut the construotion of a stoolyard is very point fived, wo may treat it as, lever, that point being the simple, and that any handy poreon of a moohanionl turn fulcrum. may make one of stool or iron, Moreover, the two forces whichact on it are supposed to be or ovon of a piece of hard such that their directions when rodaced meet, and that their wood, without much trouble. plano passes through the fuloru. In cases where the two foroon do not moot, or their play does not pass through the TIN DANIH NALANCE. fulorum, there cannot be equilibum. For example, the ont The le a species of stool | wtrotohed right arm of a man is a of which the fulcram is yard, in which (Fig. 65) tho in the right shoulder. Suppose, ane stretches it before him in Culorum in movable, and tho a horizontal position, one force is plied to the hand obliquely counterpolne in the weight of from him towards the left to th ground, while another acts the beam moting at its centro horizontally at his elbow towards e right and at right sngles of variera f the autistance to be weighed being responded to the arm; those foroes cannot set, and therefore would not #honde o placed in pan, at the extremity, , on under any circumstances keep th Pure in equilibrium; further, the whoy sila call the lorum. The question is, how may you even were they to meet, they wou at se keep it sless their To do this, let us suppose plane passed through the fuloru in the shoulder soeket Sup thu hwm te www pound, wd that I out of como substance posing the forces, therefore, the is essere assis, that I Wawel in the evalo, thou i la prilont that the hulorum, their dirvotions meet and their we passes thrvegà se fulcram, yer, M A E what is the condition of equilibrium ? In order that you may the perpendicular from o on A P. So likewise is the moment clearly understand this, the knowledge of the following goo- of Ag in reference to o equal to A Q multiplied into o y, the metrical principles is necessary. corresponding perpendicular. What I have then to prove is FURTHER PROPERTIES OF A PARALLELOGRAM AND TRIANGLE. that these products are equal. But they are equal; for, from 1. The area of a triangle is half that of any parallelogram which the second geometrical has its base for one side, and a line drawn through its vertex parallel principle above, the to that base for the side opposite.—This areas of the triangles C appears from Fig. 57, where A V B is the A OP, AOQ, are half triangle, and A B C D any parallelogram these products; and, on A B formed by drawing from A and B by the third, since х any two parallel lines AD, BC to meet the these triangles stand parallel D C to A B through v. For, draw Fig. 60. on the common base VE parallel to AD, and therefore parallel AO, and the line PQ to BC, to meet A B in E. Then the triangle joining their verticos, being a diagonal, is bisected by a R, that is, AV B is made up of the two triangles Ave by that base, their areas are equal. The moments of AP and a Q, and B V E. But since A E v D is a parallelo- therefore, in reference to o are equal, as I undertook to prove. gram, the triangle A V E (Lesson III.) is Now, to apply this to the lever, using the same figure, let us Fig. 57. equal to ADV, and is therefore half the suppose the two forces to be a P, AQ, meeting, as I have stated parallelogram Á EVD. So likewise is BVE to bo necessary, at some point a. Then it is evident, since there half BEVC; and therefore the triangle A VB half A B C D. is but one point fixed in the body, that there cannot be equi. 2. The area of a triangle is, in numbers, half the product of its librium unless the resultant of AP and a Q passes through that base and the perpendicular from its vertex on that base. This point, and is there resisted by the supports that fix it. The follows from the previous principle. Let the number of inches fulcrum, therefore, you see, must be on the resultant, and thereor feet, say inches, in A B (Fig. 58) be 6, and in the perpen- fore taking o to be the fulcrum, we must have a p multiplied into dicular, v E, be 7, and construct on A B a parallelogram, o x equal to 1 Q multiplied into o y, that is, the moments of the forces in reference to ABCD, whose sides are parallel to this perpendicular. Such a parallelogram is termed a "rectangle,” on account of its angles thus at the two following modes of stating the fulcrum must be equal. We arrive being all right angles. Mark out the inches on A B and V E, and draw the dotted lines in D the condition of equilibrium in a lever, the figure parallel to A B and v E, cutting either of which may be selected for use as this rectangle into the smaller ones the sides the occasion requires :of which are all equal to one inch, and which 1. In a lever, the forces not being parallel, are therefore so many square inches. Now the power multiplied by the perpendicular there are seven rows of these squares, one row from the fulorum on its direction is equal above the other, and there are six squares in to the resistance multiplied by the perpen Fig. 61. dicular on its direction. each row; and therefore there are altogether 7 times 6, or 42, square inches in the rectangle. 2. The power and resistance are to each other inversely as the But the triangle being half the rectangle, is perpendiculars dropped from the fulcrum on their respective half of 42 square inches, that is, it is, in num Fig. 58. directions. bers, half the product of the base and perpendicular. Were the numbers 13 and 9, or any other pair whatever, Figs. 61, 62, and 63, is a kind of lever, or succession of lovers, This useful mechanism, of which several forms are given in the reasoning would be the same. 3. If two triangles stand on opposite sides of a common base, revolving round an axis, from which they project at right angles. and the line joining their vertices is bisected by that base, the Corresponding to this central axle triangles have equal areas.-In Fig. 59, the triangles A B C, ABD line is a cylindrical axle of some stand on the common base, A B, at opposite sides, and Dc join , thickness, round which winds the ing their vertices is supposed to be bisected at m; I have to rope which bears the resistance, or prove that the areas of the triangles are equal. Draw E F and weight, to be raised. In Fig. 61 is HG through A and B parallel the simplest form of the instrument, to DC, and also through D and consisting of an horizontal axle and c draw H E and G F parallel four levers, which are worked in to AB. Then we have a succession by the power. In the large parallelogram E F G H, ship's capstan for raising the anchor which is divided into four Fig. 62, (Fig. 62), the resistance acts horizonsmaller ones by A B and D c. tally, a man pushing also horizontally But since D C is bisected at the end of each lever, the power being multiplied in the proF We have in Fig. 63 at M, making mc equal to portion of the number of levers and men. Fig. 59. MD, and therefore A E equal another form, where the levers are the spokes of a wheel, and the to a F, the parallelograms power a works in succession on them along APGB and AE H B are equal to each other. But, as proved the tire as they come round. above, the triangles A B C and A B D are half of these parallelo The principle in all is the same, whether tams, and therefore are also equal to each other, as was the resistance and power be parallel or not, required to be proved. and may be understood from Fig. 64, which We now return to our Mechanics, applying these geometrical represents a transverse section, the outer principles to determine circle being the wheel and the inner the axle. The central line of the axle, which THE MOMENTS IN THE LEVER OF FORCES NOT PARALLEL. you must conceive perpendicular to the Two such forces, A P, A Q (Fig. 60), being supposed to meet at paper at the centre of these circles, is the kome point, A, to which they are transferred, and there com- fulcrum, represented by the point o. The pounded into a resultant A R, represented by the diagonal of the line A B thus is seen to be the lever, at the parallelogram, A P B Q, and o being a point taken at random on ends of which the power, P, and resistance, A that diagonal, we can prove the following proposition :- w, act; and, as already proved, these forces Fig. 63. The moments of two intersecting forces in reference to any point must be inversely as o A to o B, which lines op their resultont are equal to each other.—Now the moment of a are the radii of the wheel and axle respectively. When the power force in reference to a point, as has been already explained, is and resistance act parallel to each other this is evident; but the the product of the force by the perpendicular dropped on it from same holds good were they not so to act, as in the capstan, where that point. In Fig. 60, therefore, the moment of A p in refe- the power is continually changing direction as the sailors go round; 1c22e to o, a point on the resultant, is a P multiplied into ox, for, referring again to Fig. 64, if the power were to act not in the THE WHEEL AND AXLE. B A is all gone. line A P, but along any other tangent to the large circle, the per LESSONS IN GERMAN.-XXI. pendicular from the fulcrum o on its direction would still be the radius of the wheel ; and, by the general principle of the lever SECTION XL.-PECULIAR IDIOMS—(continued). established in this lesson, the power and Was für ein (66.5), literally, what for a, answers to the English resistance would be still inversely as the "what kind of,” or simply "what;" as :-Was für ein Buch haben radii of wheel and axle. Sie? what kind of a book have you ? Was für ein Messer ist tas? A treadmill, used for punishment in prisons, what kind of a knife is that? Für, in this connection, loses its B is another instrument of this kind, the power prepositional character, and may precede any case, as :-Was für being the weight of the prisoners ascending Bücher fint ries? what kind of books are these? Was für Bücher the steps placed on the outside of the wheel, haben Sie? what kind of books have you ? Mit was für einem and the resistance the weight of the water Buche sind Sie beschäftigt? with what kind of (a) book are you em. pumped, the corn ground, or other work done. ployed ? P The windlass is another, turned generally by 1. Was für is likewise used in the way of exclamation, correFig. 64. a winch handle, and used to raise water from sponding to " what,” as :-Was für Thorheit! what folly! Was wells, or lift goods into stores. In Fig. 21 Für ein Mann: what a man! Welch, abbreviated from welcher , is (page 188) the reader will find an example of the utility of the used in the same manner, as:-Weld ein Mann! what a man! wheel and axle as a mechanical power in the crane, by which two 2. Jeter and jeglicher are often preceded by the indefinite article, men, by turning the winch-handle attached to the axle, are able and are then, accordingly, inflected after the Mixed Declension. to lift a horse out of the steamer alongside of the quay. (Sect. X.) They are never used in the plural, as:- Der Tod jetes A particular form of the windlass, which was first invented in Menschen, or eines jeden Menschen ist gewis, the death of every man is China, and which may therefore be called the “Chinese windlass," certain. Gin Jeder mus sterben, every one must die. is given in Fig. 65, where only the axle is represented, consisting 3. Aller, onlike the English "all,” is joined directly to its of two parts, one thicker than the other, but both forming one noun without any article intervening, as:- :- Aller Wein, all the solid piece. The winch handle, wine. Alles Wasser, all the water, etc. or wheel, is to the right con Our word “all," when connected with the names of conntries, nected with the larger axle. The towns, etc., as also in such phrases as “all day, all the time, weight to be raised is suspended all my life," etc., is not expressed in German by all, but by from a hook attached to a pul. ganz, as :—Wanz Guropa, all Europe. Banz Böhmen, all Bohemia. ley, round which the lifting rope Die ganze Shneiz, all Switzerland. Den ganzen Tag, all the day, or passes, one part winding round the whole day. Die ganze Zeit, mein ganzes Leben, etc. the thick axle while the other Alle or all, in some elliptical phrases, is equivalent to our "all unwinds from the thin. The gone," " no more," and the like, as :- -Sein Geld ist alle, his money weight with each turn of the wheel ascends by the difference 4. Mancher answers to “many a," as :-Mancher Reiche ist uns between the length of the rope glüdlich, many a rich man is unhappy. that winds and unwinds, that 5. šolcher is often preceded by the indefinite article, as also is, by the difference between by fein, and is then, like jeter and jeglicher, inflected after the the circumferences of the Mixed Declension, as :-- Er ist eines solchen Lebens nicht würdig, he is two axles. Moreover, since not worthy of such a (a such) life. Ich habe fein solches Buch, I the weight is equally divided have no such book. between the two ropes which ascend from the pulley, the Fig. 65. 6. Aller, mancher, solcher (and welder, see R. 1) often drop the last syllable, and are then undeclined. Thus, aller, when it preforce acting at the circumference of each axle is half the weight. cedes a pronoun, is often abbreviated to all; mancher, when it It is evident, moreover, that the power applied to the winch precedes an adjective, often becomes manch; solcher (as also handle has to balance the difference of the actions of these welcher) is always thus abbreviated when it precedes the indefiforces at the axle, or the moment of the power must be equal to nite article, as also, sometimes, when it precedes an adjective, the difference of the moments of these forces. But each force as:-3ch habe all mein Geld verloren, I have lost all my money. being half the weight, its moment is half the weight multiplied Ich habe all diese Bücher gekauft, I have bought all these books. by the radius of the axle at which it acts; and therefore their Manch ehrlicher Mann ist arm, many an honest man is poor. difference is equal to half the weight multiplied by the difference Solch ein Tag ist angenehm, such a day is agreeable. Solo of the radii of the axles, or, which comes to the same thing, schönes Papier ist thcuer, such beautiful paper is dear, etc. It to the weight into half the difference of these radi. But the should however be noted, that, as in the above examples, when moment of the power being that force into the radius of the the abbreviated form is followed by an adjective, this latter, inwheel, we immediately learn that, stead of being inflected after the New Declension (Sect. IX. 2), In the Chinese windlass the power multiplied follows that of the Old ($ 29). by the radius of the wheel is equal to the resist- 7. Giniger and etlicher are regularly declined. They are ance multiplied by the difference of the radii nearly synonymous, and answer to our words “ some, a few;" of the axles. etc., as :--Er sprach nur einige Worte, he spoke only a few words, THE COMPOUND WHEEL AND AXLE. Er hat noch etliche Freunde in Deutschland, he has still some friends in Germany. Gr wohnt in einiger Entfernung von der Start, he reThis is a combination of wheels and axles, of sides at some, or a little distance from the city. Nad einiger Zeit the kind already explained, made for the same fam er, after some time he came. Ich habe noch etliches Mehl, I still purpose as the similar combination of levers in have got some flour. Gtliches fiel an den Weg, some fell by the way. Lesson VIII., namely, the mechanical advan- side (Mark iv. 4). tage of a multiplication of the effect of the 8. Etwas, besides the signification noticed in Sect. XIV. 2, has power. The wheel and axle being once clearly also an adverbial use, and answers to “ somewhat,” as :-GT ijt understood to be a lever, there can be no etwas älter, als ichy, he is somewhat (or something) older than I. difficulty in extending the rule which holds Gs ist etwas fälter, als vorgestern, it is somewhat colder than the day Fig. 63. good of the compound lever to this combina- before yesterday. VOCABULARY. cogged teeth the axle of each wheel works on the circumference of the next succeeding, the power, P, being applied by a rope to Ablegen, to lay aside. Beschwer'te, f. hard- Blind, blind. the circumference of the first wheel, which does not require teeth. Anblick, m. aspect. ship. Darüber, about it It is evident that, as explained of the compound lever, the condi- An-näherung, f. ap- Vefig'en, to possess. thereon. tion of equilibrium must be that proach. Bewunderung, f. ad. Davon', of it, thereIn the compound wheel and axle, the power is to the resistance Vege'hen, to commit. miration. of. as the product of the radii of the axles is to the product of the Beschäftigen, to em- Bilten, to form, con. Dennoch, still, not- dii of the wheels. withstanding ploy. stitute. W one an ntc ence. agree, accord. em you? Eigen, own, particu- Gesell'schaft, f. society. Seefisch, m. sea-fish. 24. Unter den Einwohnern sind manche sehr wohlhabend. 25. Haben Sie lar. Gewäh'ren, to grant, Seltsam, strange. nicht auch schon manches Seltsame erlebt? 26. O ja, ich habe schon Ginander, allow. Solcher, such. manches Merkwürdige erfahren. 27. Manch tapferer Soldat mußte in der other. Gewiß', certain, cer- Stählen, to steel, Schlacht sein Leben lassen. 28. Hat dieser Schriftsteller nicht viele gute Cinmal, once. tainly. harden. Bücher geschrieben? 29. Gewiß, mande davon sind vortrefflich. 30. Gin'wehner, m. inha- Größe, f. size, magni. Sturm, m. storm. Haben sich die beiden Freunde über diese Sache verstanrigt ? 31. Ja, in bitant. tude. Theils, partly. einigen Punkten sind sie miteinander übereingekommen. 32. Einige eng Grfahren, to experi- Hantlung, f. action, Thorheit, f. folly. lische Schiffe gingen bei diesem Sturme 33. Etliche fluge Männer procedure. Uebercin'kommen, to sogen fich aus der Versammlung zurück. 34. Alle Einwohner der Stadt Grle-ben, to live to see. Hegen, to cherish. flüchteten sich bei der Annäherung der Feinde. 35. Manche Menschen brinErstau'nenswürdig, as- Herrlich, glorious. Bersamm'lung, f. meet- gen ihr ganzes Leben mit Nichtsthun zu. 36. War das Ihr Bruder, der tonishing. Hervor'rufen, to call ing. gestern den ganzen Tag in Ihrer Gesellschaft war? 37. Nein, es war mein Gt'licherseveral, forth. Verständigen, to agree, Neffe, ter mich alle Jahre einmal besucht. 38. Welch eine Größe hat die some, a few. Knochen, m. bone. to come to an ex. Erde, und wie viel kleiner ist sie dennoch, als die Sonne ! 39. Welche VorFeinheit, f. delicacy. Macht, f. power. planation. züge hat der Mensch vor den Thieren? 40. Was für eines Vogels Feder Firmament“, n. firma. Mancher, many a. Verwen'den, to ist dies? 41. Ist der Schüler fleißig, so lernt er etwas. ment. Meinung, f. opinion. ploy, apply. EXERCISE 77. Vorzug,m. advantage. 1. Many a learned man has been misunderstood. 2. Oh, what Gefühl', n. touch, feel. Musit', f. music. Was für,what kind of. folly does man commit in his life! 3. With what kind of ing. Nachwelt, f.posterity. Werf, n. work. society have you associated ? 4. Many an industrious mer. Gemüth' , n. mind. Nichtstiyun, n. inac- Wvýl'habend, opulent. chant has been ruined by an imprudent speculation. 5. Full Genuß. m. enjoy. tion. Zu'vringen, to spend, many a flower is born to blush unseen [blühet im Verborgenen). 6. ment. Noth'wendigkeit, f. ne- pass. Every leaf, every twig, and every drop of water, testifies infinite Geffent', n. present, cessity. Zurüđóziehen, to retire, wisdom and power. 7. Every one must give an account of himgift. Punft, m. point. withdraw. self. 8. The whole environs of Coblentz are romantic. 9. All RÉSUMÉ OF EXAMPLES. are well (wohl] at home. 10. The conversation with such per sons is instructive. 11. I have never heard of such an accident. Was für einen Camera'ten hast What kind of a companion have 12. It is beautiful weather to-day, but somewhat colder than yesterday. 13. I have had already many a pleasure. 14. I Was für ein Lantsmann bist Du? What countryman are you? wish to have some lemons. 15. He came somewhat too late. Welt ein Niesc: What a giant ! LESSONS IN BOTANY.-XI. nicht. not. Ginen solchen Sturm ßabe ich noch Such a storm I have not yet SECTION XXI.-ON THE NATURAL ORDER OF FLOWERING PLANTS. nicht erlebt'. experienced. Selch ein Saiser fonnte sich To Such an emperor could thus In these papers we shall not enter on the consideration of crypte'müthigen! humble himself. togamic plants until we have noted the peculiarities that distinSolch schönes Wetter kommt selten. Such beautiful weather comes guish the different natural orders of flowering plants. Those seldom. which possess flowers are far more likely to arouse the young Er sprachy so leise, daß ich ihn nicht He spoke so softly, that I could botanist's attention; they are far more useful, moreover, and barste'ben fonnte. not understand him. are those members of the vegetable world which botanists know Mander Traum der Jugend schwin. Many a dream of youth disap- most about. kt mit den Jahren. pears with the years. We shall select the Crow-Foot tribe, termed by botanists Manch schönes Buch habe ich schon Many a beautiful book have I Ranunculacec, as the one first to be considered. Let us see, gele'sen. already read. then, in how few words & botanist defines the characters of Nach einigen Minu'ten Echrte er After some minutes he re- Ranunculacea RANUNCULACEAE. jurid'. turned. Te Elephant' ist etwas ftirfer, als The elephant is somewhat Characteristics.-Calyx, polysepalous; petals, hypogynous, in tas Nashorn. stronger than the rhinoceros. form various, sometimes absent; stamens, ordinarily numerous ; Ter un'erfahrene Raufmann fann The inexperienced merchant anthers, usually adnatant; ovule, reflexed; plumule, dicotyleleicht all sein Vermö'gen verlieren. may easily lose all his for. donous, small, at the base of a horny albumen. fruit, apocarpous. tune. A very pretty collection of hard names, is it not ? and suffi. Gr war das ganze Jahr franf. He was sick all the year. ciently unintelligible. Nevertheless, the reader, we are sure, In großen Städten sieht man alle In large cities one sees some- will admit that if the characters of the Ranunculus, or CrowTage etwas Neues. thing new every day. Foot tribe, admit of description in so few words, it is worth while to learn the meaning of these words. Well, then, let us EXERCISE 76. set about it; let us analyse the definition clause by clause. 1. Was für Wetter ist es hcute? 2. Es ist heute schönes Wetter, aber First, then: calyx polysepalous; what is the meaning of that? etwas kälter, als gestern. 3. Was für eine Meinung hegt er von dieser The reader, by this time, knows the meaning of calyx; it is the Sache? 4. Seine Meinung darüber ist nicht die beste (Sect. XXXV. 3). outside greenish-yellow whorl of which the buttercup flower is 5. Meine Gesellschaft ist ihm die angenehmste von der Welt. 6. Wað für composed, and being made up of several parts (sepals, and the gücke sind dies? (Sect. XXXV. 3.) 7. Es sind Scefische. 8. Mit was Greek word, tolus (pol-use], signifying many), the calyx is denofür Arbeiten beschäftigt er sich ? 9. Er beschäftigt sich theils mit Schreiben, minated polysepalous, a somewhat important characteristic thus theils mit lesen. 10. Welch eine Macht hat die Musit über das Gemüth easily conveyed in few words. Now for the second clause, de Meniden! 11. Welch ein hoher Genuß ist es, die Welt zu sehen : petals hypogynous. As for the word petal, the reader knows its 12. Helth einen herrlichen Anblick gewährt das Firmament mit seinen un- meaning already; but hypogynous, what is the meaning of that jåkligen Sternen! 13. Jeter Stern am Himmel biltet eine eigene Welt. term ? Complex words, like complex plants and complex ani14. Der wahre Tugendhafte verwentet jeden Tag seines Lebens varauf, seine mals, require dissection. Hypogynous being dissected into hypo fehler immer mehr abzulegen. 15. Hat nicht jeter Ihrer Freunre einen and gynous, we shall soon arrive at its meaning. In the first solchen Ext? 16. Nein, ein Ieter hat einen andern. 17. Solche Männer place, hypo is the almost literal rendering of the Greek word UTO find nothwendig, um das Waterland zu retten. 18. Saben Sie jenen (hu'-po), under ; and gynous is evidently a derivation from another Plinten gesehen, der eine Feinheit des Gefühles besißt, die erstaunens, Greek word, guvn (gu'-ne), signifying woman. When, therefore, mwärtig ist ? 19. Ja, ich babe ihn geschen. 20. Der Geber eines folchen it is said that the petals are hypogynous, the sense meant to be eihenfes ist zu loben.' 21. Die Bestwerden einer solchen Reise ställen conveyed is, that they spring from underneath the carpels or ten Korter. 22. Solche Handlungen werden die Bewunderung der Nacha female parts of the flower. A very slight examination of a distwelt hervorrufen. 23. So angenehme Stunden habe ich lange nicht gehabt. sected buttercup will show that the arrangement of petals is as |