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I. THE CHIEF STATES OF EUROPE-THEIR CAPITALS, AREA, POPULATION, ETC.

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The remaining states of Europe which as yet preserve a semblance of independence, though the rulers of all of them may be considered as being virtually subordinate to the will of Prussia, are included within the limits of the great central territorial division of Europe called Germany. The new German Empire was constituted by the treaties made at Versailles in 1871, after the close of the Franco-German War, under the Presidentship of the King of Prussia, who bears the title of Emperor of Germany.

We give herewith a list of the states that make up the German Empire, and in every case the names of the states given in II. THE CHIEF STATES OF EUROPE-THEIR

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Tables I. and II. are printed in italics to distinguish them from the small states that are not included in these tables.

THE GERMAN EMPIRE. -The Kingdoms of Prussia, Saxony, Bavaria, and Wurtemberg; the grand-duchies of Oldenburg, Mecklenburg-Schwerin, Baden, Hesse-Darmstadt, MecklenburgStrelitz, and Saxe-Weimar; the duchies of Anhalt, Brunswick, Saxe-Altenburg, Saxe-Meiningen, and Saxe-Coburg-Gotha; the principalities of Schwartzburg-Sondershausen, SchwartzburgRudolstadt, Waldeck, Reuss-Schleiz, Reuss-Greiz, SchaumburgLippe, and Lippe-Detmold; the free cities of Lubeck, Bremen, and Hamburg, and the provinces of Alsace and Lorraine. RULERS, REVENUE, NATIONAl Debt, etc.

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in pounds sterling.

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To give the reader an accurate idea of the extent of Germany and its territorial limits, it should be said that Prussia Proper, comprising the two provinces marked East and West Prussia in our map, and Posen, or Prussian Poland, are without the boundaries of Germany. The eastern portions of the duchies of Limburg and Luxemburg, however, are within its limits, and nine provinces of Austria-namely, Bohemia (1), Silesia (2), Moravia (3), Upper Austria (4), Lower Austria (5), Salzburg (6), Styria (7), Illyria (8), and the Tyrol (9). The duchies of Limburg and Luxemburg, mentioned above, belong to Holland or the Netherlands, as Holland is frequently called. The area of the whole of Germany, including the whole of Prussia except the parts which have been named, the nine Austrian states, the Dutch portions of the duchies of Limburg and Luxemburg, and the other states named in the lists of the North and South German States, is estimated at 243,375 square miles.

The Emperor of Germany, as president or head of the several states or kingdoms previously enumerated, represents the empire in all cases of international law, and in respect of declaring war, making peace, treaties, &c. Notwithstanding, before any declaration of war can be made by him, he must obtain the consent of the Bundesrath, a council of delegates of all the confederate governments. The Emperor is also the commanderin-chief of the whole army and navy in time of war, as he is also in time of peace, except in the cases of the kingdoms of Bavaria and Wurtemburg.

LESSONS IN ARITHMETIC.-XXXIII. RULE OF THREE-SINGLE AND DOUBLE (continued). 8. IN Simple or Single Rule of Three, the method of performing which was explained in the last lesson, it will be found that questions of the following kind often occur:

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EXAMPLE 4.-How long will 20 men take to build a wall 10

EXAMPLE 1.—If 8 men can reap 32 acres in 6 days, how feet high, if 11 men require 17 days to build one of the same

many acres can 12 men reap in 15 days?

Such questions can always be solved in a manner similar to the following:

Since 8 men can reap

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1 man 99

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6 days, 6 days,

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length, but only 7 feet high?

This we will work by the rule.

Here the amount of wall built increases if the number of men is increased, and if the time they work is increased. If a be the time required, we have therefore

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I 20
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71 17 11

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And 12 x 15 x

EXAMPLE 2.-If the carriage of 6 cwt. 3 qrs. for 124 miles costs £3 4s. 8d., what weight would be carried 93 miles for £1 4s. 3d. ?

Since 6 cwt. 3 qrs. is carried 124 miles for £3 4s. 8d., or £335, Therefore, 6 cwt. 1 mile for £335,

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124

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The answer therefore is 3 cwt., or 3 cwt. 1 qr. 14 lbs.

9. Questions of this kind can always be solved by the method given above-i.e., by finding what quantity of one kind corresponds to one unit of each of the other kinds. Thus we have found, in the first example, how many acres can be reaped by one man in one day. In the second example we have found what is the cost of carrying one cwt. one mile. After this has been done, the process is easy.

The result, can, however, be always arrived at more simply by means of the following rule, which depends, however, upon an algebraical principle which we cannot explain here.

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EXERCISE 52.-EXAMPLES IN DOUBLE RULE OF THREE. 1. If 12 horses can plough 11 acres in 5 days, how many horses can plough 33 acres in 10 days?

2. If 40 gallons of water last 20 persons 5 days, how many gallous will 9 persons drink in a year?

will earn £35 2s. in 24 days?
3. If 16 labourers earn £15 12s. in 18 days, how many labourers

4. If 24 men can saw 90 loads of wood in 6 days of 9 hours each, how many loads can 8 men saw in 36 days of 12 hours each?

5. If 6 men can make 120 pairs of boots in 20 days of 8 hours each, how many days will it take 12 men to make 360 pairs, working 10 hours a day?

6. If 12 men can build a wall 30 feet long, 6 feet high, and 4 feet thick in 18 days, how long will it take 36 men to build a wall 360 fest long, 8 feet high, and 6 feet thick ?

7. If £250 gain £30 in 2 years, how much will £750 gain in 5 years? 8. What will £500 gain in 4 years, if £600 gain £42 in 1 year?

9. If 8 persons spend £200 in 9 months, how much will 18 persons spend in 12 months ?

10. If 15 men working 12 hours a day can hoe 60 acres in 20 days, how long will it take 30 boys working 10 hours a day to hoe 96 acres, 3 men being equivalent to 5 boys?

11. If the 8d. loaf weighs 48 oz. when wheat is 54s. a quarter, what is the price of wheat when the Gd. loaf weighs 32 oz. 8 dwt.P

12. If 35 barrels of water last 950 men 7 months, how many m would 1464 barrels last for 1 month?

long will 425 men consume 175 barrels ?
13. If 13908 men consume 732 barrels of flour in 2 months, in how

14. If 3 men with 4 boys earn £5 16s. in 8 days, and 2 men with
earn 20 guineas?
3 boys earn £4 in the same time, in what time will 6 men and 7 bogs

15. If 5 men with 7 women earn £7 138. in 6 days, and 2 men with 3 women earn £3 3s. in the same time, in what time will 6 men with 12 women earn £60?

should be the weight of the shilling loaf when wheat is 78. 6d, a bush
16. If the penny loaf weigh 6 oz. when wheat is 5s. a bushel, what
men will perform a piece of work half as large again in a fifth part
17. If 20 men can perform a piece of work in 12 days, how mat

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CHARACTERS that lack the element of perseverance seldom reach any goal worth attaining. There is very little of what is called luck in the world, and a careful analysis of many seemingly easy successes would discover, not a chance success, but a strenuous persistence in the path which has led to victory. The humblest plodder often outstrips the cleverest genius so far as ultimate attainment is concerned. The old fable of the hare and the tortoise has a lesson for us all, as it often happens that mediocrity wins the day, whilst superiority tires and wearies in the long course of pursuit. Constitutional temperament has doubtless something to do with perseverance, both in a physical and moral sense. Some are by nature endowed with powers of endurance which their less-famed compeers do not enjoy; they seldom suffer from headache or ailment, whilst others have to bind the wet towel round the hot brain, and to humour in many ways the weakness of the flesh. There is, too, in a moral sense, some inherent tendency to laziness that has to be fought against with unremitting energy; whilst to others early rising and perennial activity are fraught with no difficulty at all. There is an air of vigour about them, so to speak, as to "the manner born." It cannot, however, be questioned that the differences of natural temperament are not so influential as the influences of habit; and that perseverance is one of those moral virtues which may be attained and cultured even by those who are by nature inclined to ease and averse to difficulties. There can be no necessity to hide from any of the racers in the great arena of life that there are hedges and obstacles in any path, whichever they may choose. The attainment of success results from a succession of obstacles overcome. If one of these difficulties daunts us, we lose that prestige which is one of the great secrets of victory. An army accustomed to defeat is soon demoralised, and a man who finds himself thwarted by early difficulties, loses that moral tone which is of such supreme importance in the oncoming struggles of life. In highly civilised nations like our own, every path becomes more and more hedged about with preparations and conditions. The Civil Service, the Army, the Navy, the Church in all its sections, the law, the department of medicine, even to the pharmaceutical examination for which the chemist has earnestly to prepare all these and other departments of duty have their standard of necessary qualification raised from year to year; and he must give up the race as hopeless who is not prepared in the engagements of commerce, as well as in the practice of the professions, to exercise that persevering energy which will sustain him in the conflicts of the course. All this is well. Perseverance is not only a virtue in itself-it educes, sustains, and strengthens all other virtues, for these are indebted to perseverance for the opportunities they have for healthful exercise. Memorable are the instances in which judges and bishops have risen from lowly ranks to wear the ermine or the lawn, and wonderful are the cases in which, amidst pain and weakness, the seeker after truth has plodded on his way. When pained with incurable heart-disease, the celebrated Robert Hall lay on his back to learn a continental language that he might be the better acquainted with its literature; and when deserted by the Johanna men, the adventurous Livingstone pursued his onward way through the desert wilds of Africa. These men teach us, in the study and in the field, what it is indeed to persevere! Obstacles, however, are not the greatest difficulties in our path-disappointments are

far heavier to bear. An obstacle is something in the traveller's path; a disappointment is something in himself-a wounded spirit or a chagrined heart. Well, let him still press on, for the noblest heroism is to endure, and, like all emotions, the smart of wounds caused by disappointment gets dulled in time, and the aching nerve is at ease again. It is very trying to have to fight the battle with a sore heart, but there is a needs-be: we have to conquer ourselves as well as the great outside world, and the hour of victory will bring compensation for all the hard struggle and toil.

Perseverance becomes, however, in time a pleasant thing. Even digging up Greek roots is an enjoyable mental agriculture to the learned professor, and pursuit of all kinds has in it the power to stir our energies, quicken our pulses, and by filling all the channels of our being with life, to produce that healthy state of energetic existence which is happiness in and of itself. Persevering people must be content to lose many passing advantages of a pleasing kind, and in seeking the higher end to lose many nearer ambitions. After all, it is the ideal to which the pursuer aspires which regulates all his energies; and he who is content to be complimented as the painter of a sign-post will feel no pang of disappointment that his productions are excluded from the Academy walls. All earnest students should aim high, and in doing so they must remember that if the path be toilsome and wearisome, yet the end is worth more than all the energy of their will, and all the investment of their time-for the pursuit itself invigorates their own nature as well as secures for them the triumph they sought. Perseverance will have its sphere also in the conquests of temper and in the regulation of common life. It is not easy to tame the propensities and passions which are inherent in us; and in the use we make of those instrumentalities which a kind Providence has placed within our reach, there will be ample scope for the arduous exercise of perseverance. No more difficult work can be assigned to us than the introspective care which is necessary in the sphere of our own inner life; but without this all other rewards of perseverance will be shorn of their sweetest joy; for unless we have persevered in self-conquest, the world-conquest without us will only bring successes to hearts which have not learnt the first lesson of how to enjoy them. Perseverance is the stern duty of all who would be victors; even in the humblest ambition it is quite true that the persevering will not always win the race; but for the most part they will, and they will have the felicity of feeling that they deserved to do so. Checks and defeats, however, sometimes serve higher ends than success would do, and it is alike the duty and the privilege of dependent beings to believe and trust in the wisdom of a Superior Will. In the main, let it be remembered that in the records of history and in the experience of common life we have abundant evidence that, amongst all races, and in all ages, the persevering, even when mediocre in their talents, have been honoured with triumph over the most brilliant geniuses and over many much more highly favoured with opportunities for securing the coveted end. Therefore, let it be well understood that the grand element of success is within the reach of most, and that the voice of all time keeps whispering in the ear of the earnest plodder"Persevere."

LESSONS IN DRAWING.-XXI. THERE are a few more observations to make upon the proportions of the entire figure, before we introduce those relating to the face and head. We consider this to be necessary, because, when practically employed in drawing the figure, we must determine upon its action and proportions before the details are entered upon. Then the head and face claim our first attention. Some artists design their groups in the nude, and clothe them afterwards, by which means they obtain a more life-like representation than when they proceed by drawing drapery only in conjunction with the extremities-the head, hands, and feet. By this process not only are the proportions better maintained, but the contour of the body and limbs is established also; and, especially when the costumes fit closely, we know of no course of practice more favourable than this for giving expression and character to the whole design.

The unit of proportion employed to regulate the height of the figure is the head, and various have been the opinions and practice of artists as to the number of lengths of the head to

Fig. 128.

be used. Some have drawn their figures as low as seven heads, others as high as eight and a-half and nine, and occasionally, even more; the heroic cannot be less than eight. But certainly, whichever of these units of measurement we may choose, if the one employed represents the head large in proportion to the body, it is not a distinctive mark of beauty; this defect may be noticed amongst Laplanders, Tartars, and some other nations. Consequently, if we desire to give dignity and beauty to the figure, we must endeavour to avoid littleness of style, which unavoidably belongs to lowness of stature, unless, of course, the character of the subject demands it. The Apollo Belvedere, a celebrated ancient Greek statue, is eight heads and a half high. Rubens, a painter who flourished in the reign of Charles I., occasionally drew his figures eight heads high; but there is generally an appearance of heaviness in most, of his figures, which may be partly attributed to their being only seven heads high. Michael Angelo, the Florentine painter and sculptor, who was born in 1474, did not restrict himself to any fixed proportion, but would employ that which he deemed the best for his purpose. Eight heads might have been his lowest standard, but Professor Camper says, "C. Vander Mander has proved that in some of the figures of Michael Angelo, the size is equal to nine, ten, nay twelve heads, in order to communicate more grace to a stooping attitude." It is generally allowed that eight heads is the better proportion for a figure than one of a less number. Men above six feet high, for the most part, reach that standard, some a little more. The reason of lowness of stature in men is, in most cases, attributable to the shortness of their

legs; and this leads us to another proportion proper to be observed, namely, that the distance from the top of the head to the pubis should be equal to that from the pubis to the feet; the face to be one-tenth, and the foot one-sixth of the figure. Therefore, adopting the above standards of proportion, the heights of the figures we draw are determined by the number of the repeated measurements of the head; two figures may be drawn, each on a separate piece of paper, and although the one may not occupy a larger space than the other, yet it is according to the size of the head that we decide which is the tall man, and which the short.

The next consideration connected with this part of our subject relates to the head and face alone, and the proportions of their parts relative to each other; a knowledge of these is as important as those of the body, but there is a difference in the use and application which must not be overlooked. No part

of the whole frame is subject to such a variety of change and expression as the face. We look into it for a reflex of the mind; it is stronger than the arm in its power of repelling or attract ing those who seek to approach us; and the whole state of the mind, whether as friend or foe, is revealed in the countenance. In short, so keen are our detective powers when reading the signs depicted in the human face, that dissimulation must be practised art before it can be thoroughly successful. The smile of some men is repulsive because it is not genuine, and we see that it is not; there is a raising of the upper lip and exposure of the teeth along with it, which betrays envy or malice. The kind. hearted man can frown only with his brows, and in spite of himself the generous feelings of his heart will linger about

the corners of the mouth, slightly raised by the swelling muscles of the cheeks. Thus, in either case, the cha racter of the indivi dual, which is one of the most difficult things to conceal, will show itself; the most trifling acci dental circumstance will serve to reveal it, and he will be es teemed or disliked accordingly. When we reflect that the same features are capable of expressing opposite pas sions, such as jo and sorrow, love and hatred, compassia and revenge, we have to make the estar blished rules of proportion subservient

to the end sought for. There are occa sions when these received regulations must be set aside when some particu lar passion or emotion is to be ex pressed. According to the scale of depar ture from true proportion, in like man ner does the ratio of deformity increase. 1 Deformity in the countenance ought only to be employed to express deformity of mind; and therefore, in order to be able to represent the bad passions, the rules of proportion must be learnt, that we may know when and how to break them.

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When animal expression is associated with the human face, it degenerates into caricature, and although there are brutal passions found amongst men, and they are deeply imprinted on their countenances, yet those countenances must be humanised; for, notwithstanding the similarity of character which exists between the most degraded of mankind and the brute creation, we cannot go so far as to transgress the laws which regulate the human face as a whole, so entirely as to divest it of the higher nature belonging to man, and substitute that of the animal. We select an example from Lavater's "Essays on Physiognomy" to illustrate our observations, "The head of Judas, after Hol bein" (Fig. 128). It is the personification of selfishness, deceit, and hypocrisy, combined with other latent and bad qualities that nurture them and contribute to their development. It

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of the nose; the third at the base of the nose; and the last ending with the chin: thus making the whole head four noses in length. The width of the head is equal to three-fourths

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was necessary to employ these features to represent the man, for, however revolting they may be, the painter is justified in the extremity of the means by the intensity of the character to be portrayed. Lavater says of it: "Who can persuade himself that an apostle of Jesus Christ ever had an aspect like this, or that the Saviour could have called such a countenance to the apostleship? And whose feelings will be offended when we pronounce a visage like this base and wicked? Who could place confidence in such a man?" Mr. Charles Bell, in his "Essays on the Anatomy of Expression in Painting," says:— "To brutify a human countenance, we have only to diminish the forehead, bring the eyes nearer, lengthen the jaws, shorten the nose, and depress the mouth. If this be done, no expression of individual features will give elevation to the character. A breadth and squareness in the lower part of the face is quite consistent in a vulgar head with a certain representation of strength and manliness; but if the eyes be diminished and the space between them contracted, the expanse of the human countenance is lost, and there can remain no dignity of expression." We have gone thus far into our subject to show that when the proportions of the figure and face are properly understood and practised, the draughtsman must not rest there; he has only acquired the means of proceeding; afterwards, we repeat, he has to employ them for purposes of a higher kind than those which

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of the length. Bisect the second division in E, and with the distance EA describe the circle A D F C, and draw CD through E at right angles to A B. On the third division, with F as centre and F B as radius, describe another circle; then, by drawing the curve upon which the ears are placed between 2 and 3, the oval will be made. Divide the line C D into five equal parts; the eyes will be placed under the second and the fourth divisions. Divide the lowest division from 3 to 4 into two equal parts; the 2 line G will mark the position of

1

3

the under lip. The distance from line G to the division of the mouth is one-third of the line from 3 to G; the width of the upper lip somewhat smaller; the ears equal to the length of the nose (between the divisions 2 and 3). These proportions may, no doubt, assist us in drawing the head; where nature deviates, we must make the necessary alteration, otherwise we shall fail in representing individual character. The most remark4 able point of difference in the shape of the head amongst nations especially, and frequently between individuals of the same nation, is in the facial angle (the inclination of the face from the base-line of the skull, rejecting the lower jaw). In the profile of the negro (Fig. 130) we find this angle,. ABC, much more acute than that of the European (Fig. 131). In the former it is about 50°, and in the latter about 70°. We give but these two examples as representing the extremes of the human family, between which the various degrees of intellectual capacity exist. We have already remarked that where this

B

Fig. 129.

A

Α

A

Fig. 130.

Fig. 131.

belong to mere imitation: these refer to the mind, and how he can best express its intentions, knowing the influence it has in controlling the actions of the body. If we examine the practice of the ancient Greeks, we shall find that their proportions were generally arbitrary. They considered the oval to be the most perfect form of the human head; this proportion may be adopted in some cases where the ideal is intended, but it is not the rule in nature; such a standard would make the crown of the head too high, and they, in order to relieve this, reduced the length from the front to the back. We will give these proportions, although to employ them invariably would produce a mannerism that

B

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would be extremely objectionable, and in portrait painting they | would be altogether useless. (See Fig. 129.) Draw a perpendicular line, A B, of the required length of the whole head, and divide it into four equal parts. The first of the several divisions will be seen at the root of the hair; the second at the bridge

Fig. 132.

angle becomes still more acute, we leave the hu

man and take up the brute creation; on the other hand, where the angle increases, then we approach the ideal conceived and practised by the ancients (Fig. 132). It is very

evident that they avoided everything that was deemed characteristic of the brute when they represented their gods or heroes; thus, by enlarging the mean angle common amongst men, they felt that they had increased

those distinguishing attributes which marked the difference between the intellectual and the brutal; and then again, when the subject was a satyr or a faun, the sensual was indicated by a decreased angle. No one will question the truth of these prin ciples, since they are founded upon nature.

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