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The remaining states of Europe which as yet preserve a sem- Tables I. and II. are printed in italics to distinguish them from blance of independence, though the rulers of all of them may the small states that are not included in these tables. be considered as being virtually subordinate to the will of THE GERMAN EMPIRE. —The Kingdoms of Prussia, Saxony, Prussia, are included within the limits of the great central | Bavaria, and Wurtemberg; the grand-duchies of Oldenburg, territorial division of Europe called Germany. The new German | Mecklenburg-Schwerin, Baden, Hesse-Darmstadt, MecklenburgEmpire was constituted by the treaties made at Versailles in Strelitz, and Saxe-Weimar; the duchies of Anhalt, Brunswick, 1871, after the close of the Franco-German War, under the Saxe-Altenburg, Saxe-Meiningen, and Saxe-Coburg-Gotha ; the Presidentship of the King of Prussia, who bears the title of principalities of Schwartzburg-Sondershausen, Schwartzburg. Emperor of Germany.

Rudolstadt, Waldeck, Reuss-Schleiz, Reuss-Greiz, SchaumburgWe give herewith a list of the states that make up the Ger- Lippe, and Lippe-Detmold; the free cities of Lubeck, Bremen, man Empire, and in every case the names of the states given in and Hamburg, and the provinces of Alsace and Lorraine.


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To give the reader an accurate idea of the extent of Germany both the other kinds. Then the ratio of the two quantities of and its territorial limits, it should be said that Prussia Proper, this kind will be equal to the ratio (See Lesson XX., Art. 2 comprising the two provinces marked East and West Prussia in Vol. I., page 342) compounded of the ratios of the others. our map, and Posen, or Prussian Poland, are without the boun. 11. We will work out the previous examples by this rule. daries of Germany. The eastern portions of the duchies of EXAMPLE 1.-Here the acres increase if the men increase, Limburg and Luxemburg, however, are within its limits, and and if the days increase. nine provinces of Austria-namely, Bohemia (1), Silesia (2), Hence, the sixth quantity, æ, being days, we have Moravia (3), Upper Austria (4), Lower Austria (5), Salzburg (6),

12 x 15 Styria (7), Illyria (8), and the Tyrol (9). The duchies of Limburg

32 8 x 6

'12 x 15 and Luxemburg, mentioned above, belong to Holland or the

Therefore x =

120 days. Netherlands, as Holland is frequently called. The area of the

8 x 6 whole of Germany, including the whole of Prussia except EXAMPLE 2.—Here the price increases if the weight increases, the parts which have been named, the nine Austrian states, the and if the distance increases. Dutch portions of tho duchies of Limburg and Luxemburg, and Hence, the sixth quantity, a, being weight, we havethe other states named in the lists of the North and South

93 German States, is estimated at 243,375 square miles.


124 The Emperor of Germany, as president or head of the several

Or states or kingdoms previously enumerated, represents the em

Therefore x = V cwt. = 3 cwt. 1 qr, 14 lbs. piro in all cases of international law, and in respect of declaring

EXAMPLE 3.-If 27 men can do a piece of work in 14 days war, making peace, treaties, &c. Notwithstanding, before any declaration of war can be made by him, he must obtain the of 10 hours each, how many hours a day must 24 boys work, in consent of the Bundesrath, a council of delegates of all the order to complete the same in 45 days, the work of a boy being confederate governments. The Emperor is also the commander- half that of a man? in-chief of the whole army and navy in time of war, as he is

27 men do the work in 140 hours;
1 man

27 x 140 hours; also in time of peace, except in the cases of the kingdoms of Bavaria and Wurtemburg.

24 boys or 12 men

27 * 140


27 x 140
And therefore

is the number of hours in the days, which


27 x 140 are such that 45 contain


27 x 140 And

hours =

7 hours, the answer. 8. In Simple or Single Rule of Three, the method of performing

12 x 45 which was explained in the last lesson, it will be found that

EXAMPLE 4.-How long will 20 men take to build a wal 10 questions of the following kind often occur :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

length, but only 7. feet high? many acres can 12 men reap in 15 days ?

This we will work by the rule. Such questions can always be solved in a manner similar to

Here the amount of wall built increases if the number of men the following :

is increased, and if the time they work is increased.
Since 8 men can reap

acres in
6 days,

If æ be the time required, we have therefore

acres in 6 days,

7) 17 11
1 man
acres in

10 x 2 11 x 17 187
Therefore 2 =

1957 = 120 days. 15

15 Therefore, 12 men

12 x
acres in


And 12 men
12 x 15 x acres in 15 days.

1. If 12 horses can plough 11 acres in 5 days, how many horses es

plough 33 acres in 10 days?
And 12 x 15 x
120 days, the answer.

2. If 40 gallons of water last 20 persons 5 days, how many gallous

will 9 persons drink in a year? EXAMPLE 2.-If the carriage of 6 cwt. 3 qrs. for 124 miles 3. If 16 labourers earn £15 12s. in 18 days, how many labourers costs £3 4s. 8d., what weight would be carried 93 miles for will earn £35 2s. in 24 days? £1 4s. 3d. ?

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 ? Since 6 cwt. 3 qrs. is carried 124 miles for £3 4s. 8d., or £376, 5. If 6 men can make 120 pairs of boots in 20 days of 8 hours each, Therefore, 61 cwt.

1 mile for

how many days will it take 12 men to make 360 pairs, working 10

hours a day? 376

1 mile for £ Aud 1 cwt.

6. If 12 men can build a wall 30 feet long, 6 feet high, and 4 fost 124 x 61

thick in 18 days, how long will it take 36 men to build a wall 360 let


93 miles for £93 X Therefore, 1 cwt.

long, 8 feet high, and 6 feet thick ? 124 x 61

7. If £250 gain £30 in 2 years, how much will £750 gain in 5 years? i.e., for £y.

8. What will £500 gain in 4 years, if £600 gain £42 in 1 year? £1 4s. 3a.

9. If 8 persons spend £200 in 9 months, how much will 18 persoas Henco cwts. will be carried 93 miles for £1 4s. 3d.

spend in 12 months ?
£1 4s. 3d
= %= 3..

10. If 15 men working 12 hours a day can hoe 60 acres in 90 days,

how long will it take 30 boys working 10 hours a day to hoe 96 acres, The answer therefore is 3} cwt., or 3 cwt. 1 qr. 14 lbs.

3 men boing equivalent to 5 boys ? 9. Questions of this kind can always be solved by the method

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.? given above-i.e., by finding what quantity of one kind corre

12. If 35 barrels of water last 950 men 7 months, how many Do sponds to one unit of each of the other kinds. Thus we have would 1464 barrels last for 1 month ? found, in the first example, how many acres can be reaped by 13. If 13908 men consume 732 barrels of flour in 3 months, in how one man in one day. In the second example we have found long will 425 men consume 175 barrels ? what is the cost carrying one cwt. one mile. After this has 14. If 3 men with 4 boys earn £5 168. in 8 days, and 2 men with been done, the process is easy.

3 boys earn £4 in the same time, in what time will 6 men and 7 bort The result, can, however, be always arrived at more simply earn 20 guineas ? by means of the following rule, which depends, however, upon

15. If 5 men with 7 women earn £7 138. in 6 days, and 9 mies with an algebraical principle which we cannot explain here.

3 women earn £3 3s. in the same time, in what time will 6 men with

12 women earn £60 ? 10. Double Rule of Three. There are five quantities given to find a sixth. Call this 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. 2 bushel, sixth quantity o. These six quantities will consist of 3 kinds

17. If 20 men can perform a piece of work in 12 days, how the in pairs.

Observe which kind increases with the increase of men will perform a piece of work half us large again in a fifth part



1 man



1 day;


8 x 6

8 x 6

1 day,

8 x 6

8 x 6


1. £225 158.

the time, if they work the same number of hours a day, supposing that far beavier to bear. An obstacle is something in the traveller's 2 of the second set can do as much work in an hour as 3 of tho first?

path; a disappointment is something in himself—a wounded 18. If a man, his wife, and child drink a barrel of beer in 14 days, spirit or a chagrined heart. Well, let him still press on, for the how long would it take 3 couples, each with 3 children, to drink 2 barrels, noblest heroism is to endure, and, like all emotions, the smart of a man drinking twice as much as a woman, and a woman twice as

wounds caused by disappointment gets dulled in time, and the much as a child ?

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 KEY TO EXERCISE 51, LESSON XXXII. (Vol. II., page 295).

conquer ourselves as well as the great outside world, and the 8. 15s. 9a.

15. £32 14s. 31d. hour of victory will bring compensation for all the hard struggle 2. £56 16s. 8.113. 9. 211 days.

16. 66.

and toil. 3. 2156 lbs. 10. 4 men.

17. 3229 15s. 63335d. Perseverance becomes, however, in time a pleasant thing. 4. £811 158, 60, 11. 4s. 1130.d.

18. 4658 sovereigus,

Even digging up Greek roots is an enjoyable mental agriculture 5, 7066 dols.40 cents. 12. 15 oz.

19. £92 5s. 8;d.

to the learned professor, and pursuit of all kinds has in it the 6. £45.

13. 7000 grains. 20. 70. in the pound. 7. €16480.

power to stir our energies, quicken our pulses, and by filling all 14. 144. 21. 4 days.

the channels of our being with life, to produce that healthy state

of energetic existence which is happiness in and of itself. PerESSAYS ON LIFE AND DUTY.-X. severing people must be content to lose many passing advan

tages of a pleasing kind, and in seeking the higher end to lose PERSEVERANCE.

many nearer ambitions. After all, it is the ideal to which the CHARACTERS that lack the element of perseverance seldom pursuer aspires which regulates all his energies; and he who is roach any goal worth attaining. There is very little of what content to be complimented as the painter of a sign-post will feel is called luck in the world, and a careful analysis of many no pang of disappointment that his productions are excluded seemingly easy successes would discover, not a chance success, from the Academy walls. All earnest students should aim high, but a strenuous persistence in the path which has led to victory. and in doing so they must remember that if the path be toilsome The humblest plodder often outstrips the cleverest genius so far and wearisome, yet the end is worth more than all the energy as ultimate attainment is concerned. The old fable of the hare of their will, and all the investment of their time--for the and the tortoise has a lesson for us all, as it often happens that pursuit itself invigorates their own nature as well as secures mediocrity wins the day, whilst superiority tires and wearies in for them the triumph they sought. Perseverance will have its the long course of pursuit. Constitutional temperament has sphere also in the conquests of temper and in the regulation of doubtless something to do wiki perseverance, both in a physical common life. It is not easy to tame the propensities and and moral sense. Some are by nature endowed with powers of passions which are inherent in us; and in the use we make of endurance which their less-famed compeers do not enjoy ; they those instrumentalities which a kind Providence has placed seldom suffer from headache or ailment, whilst others have to within our reach, there will be ample scope for the arduous bind the wet towel round the hot brain, and to humour in many exercise of perseverance. No more difficult work can be ag. ways the weakness of the flesh. There is, too, in a moral sense, signed to us than the introspective care which is necessary in some inherent tendency to laziness that has to be fought against the sphere of our own inner life; but without this all other with unremitting energy; whilst to others early rising and peren. rewards of perseverance will be shorn of their sweetest joy; for nial activity are fraught with no difficulty at all. There is an unless we have persevered in self-conquest, the world-conquest air of vigour about them, so to speak, as to "the manner without us will only bring successes to hearts which have not born.” It cannot, however, be questioned that the differences learnt the first lesson of how to enjoy them. Perseverance is of natural temperament are not so influential as the influences the stern duty of all who would be victors; even in the humblest of habit; and that perseverance is one of those moral virtues ambition it is quite true that the persevering will not always which may be attained and cultured even by those who are by win the race; but for the most part they will, and they will have nature inclined to ease and averse to difficulties. There can be the felicity of feeling that they deserved to do so. Checks and no necessity to hide from any of the racers in the great arena of defeats, howover, sometimes serve higher ends than success life that there are hedges and obstacles in any path, whichever would do, and it is alike the duty and the privilege of dependent they may choose. The attainment of success results from a beings to believe and trust in the wisdom of a Superior Will. In succession of obstaclos overcome. If one of these difficulties the main, let it be remembered that in the records of history daunts us, we lose that prestige which is one of the great secrets and in the experience of common life we have abundant evi. of victory. An army accustomed to defeat is soon demoralised, dence that, amongst all races, and in all ages, the persevering, and a man who finds himself thwarted by early difficulties, loses even when mediocre in their talents, have been honoured with that moral tone which is of such supreme importance in the triumph over the most brilliant geniuses and over many much oncoming struggles of life. In highly civilised nations like our more highly favoured with opportunities for securing the coveted own, every path becomes more and more hedged about with end. Therefore, let it be well understood that the grand element preparations and conditions. The Civil Service, the Army, the of success is within the reach of most, and that the voice of all Navy, the Church in all its sections, the law, the department time keeps whispering in the ear of the earnest plodderof medicine, even to the pharmaceutical examination for which "Persevere." the chemist has earnestly to prepare-all these and other de. partments of duty have their standard of necessary qualification raised from year to year; and he must give up the race as hope.

LESSONS IN DRAWING.—XXI. less who is not prepared in the engagements of commerce, THERE are a few more observations to make upon the propor. as well as in the practice of the professions, to exercise that tions of the entire figure, before we introduce those relating to persevering energy which will sustain him in the conflicts of the face and head. We consider this to be necessary, because, the course. All this is well. Perseverance is not only a virtue when practically employed in drawing the figure, we must deterin itself-it educes, sustains, and strengthens all other virtues, mine upon its action and proportions before the details are for those are indebted to perseverance for the opportunities entered upon. Then the head and face claim our first attention. they have for healthful exercise. Memorable are the instances Some artists design their groups in the nude, and clothe them in which judges and bishops have risen from lowly ranks to wear afterwards, by which means they obtain a more life-like reprethe ermine or the lawn, and wonderful are the cases in which, sentation than when they proceed by drawing drapery only in amidst pain and weakness, the seeker after truth has plodded conjunction with the extremities—the head, hands, and feet. By on his way. When pained with incurable heart-disease, the this process not only are the proportions better maintained, but celebrated Robert Hall lay on his back to learn a continental the contour of the body and limbs is established also; and, espelanguage that he might be the better acquainted with its cially when the costumes fit closely, we know of no course of literature; and when deserted by the Johanna men, the adven. practice more favourable than this for giving expression and turous Livingstone pursued his onward way through the desert character to the whole design. wilds of Africa. These men teach us, in the study and in the The unit of proportion employed to regulate the height of field, what it is indeed to persevere! Obstacles, however, are the figure is the head, and various have been the opinions and not the greatest difficulties in our path-disappointments are practice of artists as to the number of lengths of the head to

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be used. Some have drawn their figures as low as seven heads, of the whole frame is subject to such a variety of change and others as high as eight and a half and nine, and occasionally, expression as the face. We look into it for a reflex of the mind; even more ; the heroic cannot be less than eight. But certainly, it is stronger than the arm in its power of repelling or attract whichever of these units of measurement we may choose, if ing those who seek to approach us; and the whole state of the the one employed represents the head large in proportion to the mind, whether as friend or foe, is revealed in the countenance. body, it is not a distinctive mark of beauty; this defect may In short, so keen are our detective powers when reading the be noticed amongst Laplanders, Tartars, and some other signs depicted in the human face, that dissimulation must be a nations. Consequently, if we desire to give dignity and beauty practised art before it can be thoroughly successful. The smile to the figure, we must endeavour to avoid littleness of style, of some men is repulsive because it is not genuine, and we seg which unavoidably belongs to lowness of stature, unless, of that it is not; there is a raising of the upper lip and exposure of course, the character of the subject demands it. The Apollo the teeth along with it, which betrays envy or malice. The kind. Belvedere, a celebrated ancient Greek statue, is eight heads and hearted man can frown only with his brows, and in spite of a half high. Rubens, a painter who flourished in the reign of himself the generous feelings of his heart will linger about Charles I., occasion.

the corners of the ally drew his figures

mouth, slightly eight heads high ;

raised by the swellbut there is gene

ing muscles of the rally an appearance


Thus, in of heaviness in most.

either case, the chaof his figures, which Fig. 128.

racter of the indivimay be partly attri

dual, which is one of buted to their being

the most difficult only seven heads

things to conceal, high. Michael An.

will show itself; the gelo, the Florentine

most trifling acci painter and sculptor,

dental circumstance who was born in

will serve to reveal 1474, did not restrict

it, and he will be es. himself to any fixed

teemed or disliked proportion, but

accordingly. When would employ that

we reflect that the which he deemed the

same features are best for his purpose.

capable of express Eight heads might

ing opposite pas have been his lowest

sions, such as N standard, but Projessor Camper says,

and sorrow, love and

hatred, compassica “C. Vander Mander

and revenge, we hata has proved that in

to make the estar some of the figures

blished rules of proof Michael Angelo,

portion subservient the size is equal to

to the end sought nine, ten, nay twelve

for. There are occaheads, in order to

sions when these te communicate more

ceived regulations grace to a stooping

must be set aside attitude.” It is ge

when some particunerally allowed that

lar passion or emoeight heads is the

tion is to be ei. better proportion

pressed. According for & figure than

to the scale of depar. one of a less num.

ture from true prober. Men above six

portion, in like man. feet high, for the

ner does the ratio of most part, reach

deformity increase that standard, some a little more.

18. Deformity in the The

countenance onght reason of lowness of stature in men

opti only to be employed is, in most cases,

le par to express deformity

of mind; and theroattributable to the

fore, in order to be shortness of their

able to represent the legs; and this leads us to another proportion proper to be bad passions, the rules of proportion must be learnt that we observed, namely, that the distance from the top of the head to may know when and how to break them. the pubis should be equal to that from the pubis to the feet; When animal expression is associated with the human face, the face to be one-tenth, and the foot one-sixth of the figure it degenerates into caricature, and although there are brutal Therefore, adopting the above standards of proportion, the passions found amongst men, and they are deeply imprinted on heights of the figures we draw are determined by the number their countenances, yet those countenances must be humanised; of the repeated measurements of the head; two figures may be for, notwithstanding the similarity of character which exists drawn, each on a separate piece of paper, and although the one between the most degraded of mankind and the brute creation, may not occupy a larger space than the other, yet it is accord- we cannot go so far as to transgress the laws which regulate the ing to the size of the head that we decide which is the tall man, human face as a whole, so entirely as to divest it of the higher and which the short.

nature belonging to man, and substitute that of the animal

. The next consideration connected with this part of our sub- We select an example from Lavater's “Essays on Physiognomy. ject relates to the head and face alone, and the proportions of to illustrate our observations, " The head of Judas, after Hol their parte relative to each other ; a knowledge of these is as bein” (Fig. 128). It is the personification of selfishness, doceit

, important as those of the body, but there is a difference in the and hypocrisy, combined with other latent and bad qualities use and application which must not be overlooked. No part that nurture them and contribute to their development. It

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