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PLURAL FOR ALL GENDERS.

Nom. Unsere schöneren, our fairer.

Gen. Unserer schöneren, of our fairer.
Dat. Unseren schöneren, to our fairer.
Acc. Unsere schöneren, our fairer.

Sometimes the e in the endings of pronouns and comparatives is omitted, or transposed; thus, instead of unser es schöner en, we may say unsers schönern, or unsres schönern.

(2.) In the superlative of the old form, the vocative case only is used; a case which has not been set down in the paradigms or examples, because it is always like the nominative in form.

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(1.) In place of the regular form of the superlative, preceded by the article and agreeing with the noun in gender, number, and case, we often find a circumlocution employed; which consists in the dative case singular of the new form preceded by the particle am: thus, die Tage sind im Winter am kürzesten, the days are shortest in the winter. The explanation is easy: am, compounded of an (at) and bem, the dative of ter (the), signifies at the. Translated literally, therefore, the sentence above will be: The days in winter are at the shortest; that is, at the shortest (limit): where, in the German, kürzesten agrees with some noun in the dative understood, which is governed by an. But the phrase is used and treated just as any regular superlative form would be under the same circumstances. In like manner, auf (upon) and zu (to) combined respectively with the

article (auf das and zu dem), and producing the forms aufs and jum, are employed with adjectives in the superlative: thus, aufs schönste eingerichtet, arranged upon the finest (plan); zum schönsten, to, or according to the finest (manner). These latter forms, however, are chiefly employed to denote eminence, rather than Freely rendered, therefore, aufs schönste to express comparison. and zum schönsten will be: very finely, most beautifully, or the like. (2.) Sometimes aller (of all) is found prefixed to superlatives to give intensity of meaning; as :-Der allerbeste, the best of all, i.e., the very best; die allerschönste, the handsomest of all, i.e., the very handsomest.

(3.) When mere eminence, and not comparison, is to be expressed, the words äußerst (extremely) and höchft (highest) are employed; as :-Dies ist eine äußerst schöne Blume, this is a very

beautiful flower.

KEY TO EXERCISES IN LESSONS IN GERMAN.
EXERCISE 150 (Vol. III., page 138).

1. My little brother has a cold; he caught a violent cold on the ice. 2. He who is overheated and cools himself too quickly may soon catch cold. 3. We ought not to trouble ourselves about things which do not concern us. 4. As far as this affair concerns me, I have taken the necessary steps. 5. This does not concern you. 6. At this intelligence he stood as if struck with the palsy. 7. The palsy has struck the old man. 8. The man has been struck with the palsy. 9. She sank down as if struck with the palsy. 10. These goods sell well. 11. When does the next steamer leave? 12. I do not see that this man stints himself in anything. 13. Has the session passed off

quietly? 14. No, it has not passed off quietly; the debate was very stormy. 15. This book had a great sale. 16. The young merchant fancy takes me, I shall start from here. told me that the sale had considerably increased. 17. Just as the 18. According as he is disposed, he can be the most pleasant, but also the most quarrelsome man. 19. According as he manages, will be his success. 20. As far as I can be useful to you, I will do it with all my heart. 21. He will assist me with his advice, as far as it is possible to him, 22. His father promised me to advance the matter, as far as it lay in his power. 23. Such a thing never occurred to my mind. 24. The concert commences at half-past six o'clock. 25. My friend had a bright idea. 26. With the merry German, one idea is more humorous than the other. 27. To the question what an idea was, some one answered, "When a house falls in."

EXERCISE 151 (Vol. III., page 138).

1. Meine Schwester hat den Schnupfen; sie hat sich an einem nassen Abende erkältet. 2. Jene Sache geht mich nichts an, und deßhalb werde ich mich nicht darum bekümmern. 3. Ist der Zug schon abgegangen? 4. Nein, er ist noch nicht abgegangen. 5. Ist der Zug nach Orford abgegangen? 6. Es sind schon zwei Züge nach Orford diesen Morgen abgegangen. 7. Ist die Debatte ruhig abgegangen? 8. Nein, es war eine sehr stürmische. 9. Englische Waare geht in jedem Lande gut ab. 10. Diese Grammatik geht gut ab. 11. Nach euren Kenntnissen werdet ihr belohnt werden. Seitdem er vom Schlage gerührt worden ist, ist er nicht im Stande gewesen sein Geschäft zu versehen. 13. Er wurde vom Schlage gerührt während unseres Besuches in Ihrem Hause. 14. In so fern es mich angeht, werde ich jede Vorsicht gebrauchen. 15. Troß ihrer Armuth lassen sich diese Leute nichts abgehen. 16. Den Menschen ist nichts besser, als eine gute Erziehung. 17 3ch weiß nicht, ob er meine Bitte gewähren wird.

GEOMETRICAL PERSPECTIVE.-XX.

12.

SHADOWS OF CURVILINEAR OBJECTS, PROBLEM LVI. (Fig. 94).—A globe casts its shadow upon the ground; the sun's rays parallel with the picture at an angle of 45 with the horizon.

This problem may be done upon the principle of drawing a circle in perspective; thus the shadow produced would be of an elliptical form. From c, with c a as a radius, draw the semicircle a db; the chord a b to be equal to the diameter of the globe. From PS arrange the distance points DE1 and DE2. Refer to Problem XII., Fig. 31, Vol. III., page 9, for the method of drawing the remaining lines, preparatory to drawing a circle in perspective. For the inclination of the sun's rays, draw A B according to the given angle anywhere, either on the HL or the base of the picture. dicularly projected plan of the globe would be a circle, and as the line i k is the perspective diameter of the circle, and h the centre, make ho equal to hi; and from o, the centre of the globe, with the radius o h, draw the circle s hn. Tangential to the circle s hn at s and n, and parallel to A B, draw the rays r,r, also

The perpen

the line ro through o to k. Produce ik and its parallels from s, z, a indefinitely; through the point m, where ik produced intersects the ray rn, draw u v in the direction of PS, also through p draw the line tw to PS. Draw the diagonals u w and t v, through their intersection k draw the line e f towards Ps; we shall then have the rectangle in perspective, within which is to be drawn by hand the elliptical form of the shadow as in Fig. 31. For observe, in proportion as the sun's rays are inclined to the plane on which the shadow falls, so will the diameter h m become longer than the diameter of the circle.

PROBLEM LVII. (Fig. 95). -An archway parallel to the picture. The sun's inclination 40° and elevation 30°.

Because the arch is parallel to the picture, draw a line A from VPSE to PS; this represents a plane perpendicular to the picture and passing through the sun. Draw the line ab tangential to the arch and parallel to the line A, also any number of normals anywhere at pleasure, c c, d d, e e, etc. Commencing at the tangent, the point where the shadow begins, draw lines from it and c, d, e, f, etc., to Ps, and from the opposite corresponding points in the arch draw lines to VPSE; the intersections of these last with the former will give the points through which to draw the form of the shadow. The shadow appears to be convex, it really is not so; it is only the effect produced from having a front view of it as it lies upon the interior of the arch. If we had a side view of this shadow, we should then see it

was concave.

cylinder. If the rays and the base of the horizontal cylinder had been parallel, then both would have retired to the same vanishing point, and then the shadow of the base would have been a straight line, but their not being parallel causes the shadow of the base on the ground to be slightly curved. To draw this curve, the shadow of the base a b c d e, lines must be ruled from a, the part of the cylinder that is upon the ground, from b, the projection of the point f, and c, the projection of the point g, each to VPSI. Rays drawn from ƒ and g towards VPSE

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proportions, angles of sight, etc., at pleasure. It will be noticed that we have drawn the semicircle of distance from the PS through E (the position of the eye) below the HL; hitherto we have drawn it above. It is of no importance on which side of the HL it may be drawn; the process of working is the same in both cases. Our present reason for placing it where we have is for the sake of economising space, and it gives us the opportunity of introducing this convenient arrangement to our pupils. As the bases of both cylinders retire, it will be necessary to construct them according to the rule given in Lesson V., Vol. III., page 9, already referred to in Problem LVI. The principle upon which the shadow of the upright cylinder crosses the horizontal one is, that in perspective projection its form takes that of the object receiving it, and is in this case almost the repetition of a section of the cylinder parallel to the base. We say almost, because the rays of the sun's inclination are not quite parallel with the base of the

to intersect those lines respectively in d and e will determine the points through which the curve is to be drawn by hand; the remaining portion of the edge of the shadow from e is straight and directed towards the vanishing point of the cylinder VP2. In the same way the curve of the shadow across cylinder B is not parallel to the curve of the base: therefore, to obtain it, produce the tangent in h at the base of cylinder A to the base of the picture in o, draw the perpendicular, and make the distances oo', 002, etc., equal vv, vv2, etc.; rule from each point o, o to VPSI, to intersect lines drawn from i, k, m, n towards the VP2; through the intersections at xxl, etc., draw the curve of the shadow by hand. The shadow which falls on the ground beyond the cylinder B will not need an explanation. The mode of construction has been al ready given in Lesson XVII.

PROBLEM LIX. (Fig. 97).-A column supporting a horizontal square slab at right angles with the picture plane. A pole leans against the wall behind, and casts its shadow

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on the column. Sun's inclination

DE1 40°, elevation 35°. Shadows

on curved surfaces are for the most part produced by projecting lines. Let A be the pole; mark any number of points in the pole, at any distance apart, and draw perpendicular lines from these points to intersect the horizontal projection of the pole, a VPl. From the points of intersection draw lines towards VPSI as far as the base of the column; afterwards they must be taken perpendicularly to meet the rays drawn from the points in the pole to VPSE. Where these rays intersect the perpendiculars will be found the points of the shadow of the pole projected on the column, and through which the curve of the shadow must be drawn by hand. The same principle obtains with regard to the shadow of the slab on the column of which b is the shadow of the corner c. Draw a line from c to VPSI to the edge of the column beneath the slab, from which draw perpendicular line to cut the sun's rays from c to VPSE. The intersection of these two lines will give the shadow of c at b. The same process from d will give the shadow of date; any other point in the course of the shadow may be thus projected; through these projected points draw by hand the curve of the

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For Amount of Sales of Coffee, per the Wellington, as per Account
Sales Book, fol. 2:

To Insurance (for Premium and Policy on £700 and Com. on Do.)
To Brokerage (per W. Knight & Co.) .

To Charges (Freight £42 15s., Duties and Fees £3 4s. 6d., Dock
Dues, etc., £12 11s. 1d., Public Sale Charges £1 7s. 6d.).
To Commission (2 per cent. on £676)

To J. Henderson, for Net Proceeds

Insurance Dr. to Sundries*

To N. Herschell

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December 31st.

Interest Dr. to Schofield, Halse, & Co.

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For Interest due to them, less postage, as per Account Current
Book, fol. 1

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This entry is rendered necessary because both the parties whose names appear were debited with the Insurance in July, and they are again charged for the same in the account of the sales in the preceding entries. They must, however, be only once charged in the Ledger, and this entry effects the required purpose.

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THOSE verbs are called impersonal, that is, without persons, which have not the ordinary persons. When I say, pater amat, father loves, I use a personal verb, of which pater, in the third personal singular, is the subject. When I say, ego rideo, sed tu fles, I laugh, but thou weepest, I use personal verbs, having respectively the persons ego and tu, I and thou for their subjects. If, however, I say, gelat, it freezes, I employ a verb which has none of the ordinary persons for its subject. Yet is the form of the verb gelat that of the third person singular. Hence it appears that impersonal verbs are found in the third person singular. In some sense then, they have one person, namely, the third. They may therefore be called uni-personal verbs. Uni-personal is a less inaccurate designation for these verbs than impersonal.

From these remarks we may define impersonal verbs as those which express an action without reference to any defined subject. Such are

IMPERSONAL VERBS RELATING TO ATMOSPHERIC PHENOMENA. Diluculat, it dawns. Pluit, it rains. Tonat, it thunders. Vesperascit, it grows dark, or, evening comes on.

Fulgurat, it lightens.
Fulminat, it strikes
with lightning.
Gelat, it freezes.

Grandinat, it hails. Lucescit, the day breaks. Ningit, it snows. Noctescit, the night approaches.

Connections are rare in which these verbs have a definite subject: for example, Jupiter tonat, Jupiter fulgurat; dies vesperascit, cœlum vesperascit; lapides pluunt: we find, however, lapidibus pluit, and sanguinem fluit. Besides vesperascit, there is the form advesperascit, and the perfect vesperavit.

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The person who is the subject of the feeling, or liable to the duty, is put in the accusative case; as, te oportet in literas in cumbere, you ought to apply to literature, or to study. Besides an accusative of the person, these verbs, in general, may have a genitive of the thing; for example, miseret me tuæ calamitatis, I am sorry for thy calamity. We may exhibit their construction thus :

Pudet me ignaviæ, I am ashamed of Pudet nos ignaviæ, we are ashamed idleness. of idleness. Pudet te ignaviæ, thou art ashamed Pudet vos ignaviæ, ye are ashamed of idleness. of idleness. Pudet illum ignaviæ, he is ashamed Pudet illos ignaviæ, they are of idleness. ashamed of idleness.

Oportet, however, has for its subject two accusatives, thus: oportet te hoc facere, you ought to do this. Libet and licet require a dative of the person: for example, libet mihi, I am allowed; licet vobis, you are allowed. Of licet there is the imperative form liceto, otherwise the subjunctive present is used for the imperative: for example, pudeat te, shame upon thee. For the most part these verbs are without participles. Yet we find the following:-Decens, libens, licens, pœnitens, liciturus, puditurus, and pigendus, pudendus, pœnitendus; also the gerunds, pœnitendi, pudendo, and pigendum.

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