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 empiro 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.

The answer therefore is 33 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.

140 hours; 27 x 140 hours; 27 × 140 hours;

And therefore

27 men 1 man 24 boys or 12 men 27 × 140 12 x 45 are such that 45 contain 27 × 140 12 × 45

"

33

12

is the number of hours in the days, which 27 x 140 12 hours 7 hours, the answer.

hours,

And

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

feet high, if 11 men require 17 days to build one of the same 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

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 gallons will 9 persons drink in a year?

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

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

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

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

15. If 5 men with

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 bushel? 16. If the penny loaf weigh 6 oz. when wheat is 58. a bushel, what 17. If 20 men can perform a piece of work in 12 days, how many men will perform a piece of work half as large again in a fifth part of

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 will 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