could be so high as that of Rome, since Christ had given the keys to Peter, and Peter had founded the Romish Church. After this decision, the Irish monks, with thirty of their English followers, quitted Lindisfarne, and sailed for Iona. Such was the commencement of that subjection of the English Church to the Church of Rome, which lasted until the days of Henry VIII. It was not, however, until the time of Egbert, king of Wessex, that anything like a real solidification of the Heptarchy took place; and even then it was very far from complete. Still, it is unquestionable that the six other states acknowledged in the king of Wessex a practical supremacy such as had not until then been exercised by any other Anglo-Saxon monarch. A general council of the clergy and laity was summoned at Winchester, where Egbert was crowned king of England in 827. After this voluntary submission to one directing will, the country might not unreasonably have looked for greater strength, and for enduring peace. But in truth a time of grievous trouble was at hand, and England was destined to be torn in pieces by a fresh irruption from the North. It was in 832 that the Danes first made their appearance on the coast of England. Their original visit was of a very trivial description, and after committing some depredations they retreated to their ships. But a few years later these daring marauders descended on the kingdom of Northumbria, where they pillaged a monastery, but were afterwards slain by the people. At first it appeared as if the English were fully able to cope with the small and scattered bodies of Northmen who from time to time landed from their galleys on the seashore. But the Danes of the ninth century were animated by precisely the same spirit as the Angles, Saxons, and Jutes of the fifth and sixth centuries. They were, in fact, a cognate people, coming from the same Northern peninsula, speaking a similar language, inspired by the same wild spirit of adventure and rapacity, and believing in the same gods as those which had been worshipped by the followers of Hengist and Horsa. Pillage alone seemed to be their object during the earlier years of their appearance; but they soon determined on forming settlements. Several of them took up their quarters in the Isle of Thanet, always one of the most vulnerable spots in England. Afterwards they subdued Northumbria and East Anglia, penetrated into Mercia, and thence swept down on Wessex. Nothing could exceed the ferocity with which they slew, burnt, and destroyed; yet they were not simply pirates, for they succeeded in engrafting themselves on the earlier English population, and a good deal of Danish blood still flows in the veins of Englishmen. It would be impossible in this sketch to follow in any detail the long contests that were waged between the native English and their Scandinavian oppressors; and we need only glance at the heroic achievements of Alfred, who, after being brought to the lowest ebb of fortune, recovered possession of his kingdom, reduced the Danes to submission, organised his country politically and socially, and left for all time the memory of a splendid life. His reign extended over thirty years-from 871 to 901.

The successors of Alfred were, for the most part, men little worthy to fill the seat which he had so magnificently adorned. The Danes were subdued, but the spirit of anarchy was still rampant. To this rule there was one exception. Athelstan, the grandson of Alfred, who succeeded to the throne in 925, exhibited some of the highest powers of governing, combined with brilliant success as a martial sovereign. Scots, Welsh, and Danes were alike vanquished by his armies, and the fame of Athelstan was such that it extended to the Continent, where the alliance of this English monarch was deemed of importance by sovereigns whose territories were greater than his own. He was a lawgiver as well as a soldier, and religion, letters, and civilisation had in him a powerful and efficient patron. Nevertheless, the social condition of England was full of elements of decay, which Athelstan arrested, but could not extirpate. The celebrated monk, Dunstan, promoted the power of the clergy, and weakened the power of the State in proportion. The martial virtues of the English race declined. The Danes again became formidable, and Ethelred, in the latter part of the tenth century, compounded with them for peace. This fatal imbecility was followed, in 1002, by an act still more blamable. On the 13th of November in that year, all the Danes in England are said to have been treacherously massacred. The slaughter was probably not so complete as has been stated; but it was general and pitiless. The Danes beyond the seas deter

mined on revenge, and Sweyn, king of Denmark, appeared off the western coast of England with a large fleet. Ethelred, whose cowardice was equal to his ferocity, fled into the dominions of the Norman Duke, and the whole of England was reduced by Sweyn, who died six weeks afterwards. Ethelred then returned to England, where, refraining from any attack upon the Danes, he reigned feebly, at London and its neighbourhood, until his death in 1016.

The decease of Ethelred was followed by a short but obstinate contest between the Danish monarch, Canute, and the heroic Edmund Ironside. The kingdom was for a time divided between the two; but the English ruler was assassinated in the course of a few months, and Canute, who had the qualities of a truly great sovereign, extended his sway over the whole land. In 1042, the English line was restored in the person of Edward the Confessor, who had been educated in the court of Normandy, and who was continental in all his tastes and predilections. He brought with him to England many natives of Normandy, and thus prepared the way for that Norman conquest which was soon to follow. Undoubtedly his sympathies were far more with the country where he had lived as an exile than with that to which he belonged. Yet Edward the Confessor was beloved by his subjects, and regarded in after ages with a veneration that amounted to worship. His piety and amiability endeared him to his people, and the prosperity which characterized his reign gave him a greater reputation as a statesman than he deserved. The actual work of government was performed by his father-in-law, Earl Godwin, and the laws of Edward the Confessor, which were often appealed to in subsequent ages as the standard of perfection, were due to the organizing skill of that nobleman.

On his death, at the beginning of 1066, Edward the Confessor was succeeded by Harold, the son of Godwin. Several years before the death of Edward-indeed, as early as 1051-there had been a violent quarrel between the king and Godwin, and the latter had been compelled to withdraw into Flanders; but he had returned in the following year, and, on regaining his former power, had driven the king's Norman favourites out of the land. He died almost immediately afterwards, and the direction of affairs passed into the hands of his son Harold. On the death of king Edward, Harold was elected by the nobles and bishops as his successor. The reign of this unfortunato monarch extended from the 6th of January, 1066, to the 14th of October in the same year, when he and his Englishmen were defeated at Hastings by William of Normandy, to whom the crown of England had (as he asserted) been bequeathed by Edward the Confessor.

LESSONS IN PENMANSHIP.-I. POSITION OF THE BODY, THE HAND, AND THE PEN. GooD handwriting is essential to almost all persons who have to make their way in the world. Great stress is laid upon it in the examinations for all Government appointments; it is required in every merchant's counting-house, in every office, in almost every shop. The boy who can write well obtains a situation--however humble the situation may be far more readily than the boy whose "pot-hooks and hangers" are almost as difficult to decipher as the cuneiform characters of ancient Nineveh. It is our purpose to devote a portion of our space to "Lessons in Penmanship." Our efforts, at the outset, will be directed towards the instruction of those who have never learned to write, and the improvement of those who write badly; and we shall follow these lessons by a series of papers exhibiting the different styles of handwriting required in Government offices, the merchant's counting-house, and the office of the solicitor, etc. etc., with instructions in German chirography and the ordinary kinds of ornamental writing, especially the black letter, or German text, so necessary to the solicitor's clerk in engrossing deeds and legal documents.

With these preliminary remarks, we hope our students will attend very carefully to our directions in endeavouring to acquire an elegant system of penmanship, as by this means, combined with constant practice, they will surely become good writers.

In the first place you should sit right in front of the desk or

table at which you intend to write; then, placing your left arm on the table and your left hand on the edge of the book or paper to hold it firm, if necessary, by pressure with the fingers, take the pen in the right hand, and grasp it firmly, but not too much so, between the thumb and the two fingers next to the thumb, that is, the forefinger and the midfinger, as shown in the accompanying representation of the hand with a pen in it. In this position, remember carefully that before you can draw a stroke, the point of the pen must be placed at the distance of about five-eighths or three-quarters of an inch from the tip of the midfinger, with its face or open part downwards, and not leaning to one side or other; the pen must also be placed alongside of the nail of the midfinger, not on the nail itself, but on the fleshy part of the finger close by it. The upper part of the pen must likewise be raised above the knuckle of the fore-finger, as seen in the figure of the hand, so that a thin paper-folder might pass a little way between this part of the pen and the knuckle. It is of essential importance to observe this part of the directions as well as the preceding,

kept upright, so that the top of the pen may point to the right ear when the hand is at the commencement of a line which you aro about to write, and that as you move it along it must be kept parallel to this position throughout. It will assist you very much in obtaining and keeping this position of the hand to observe that the knuckle of the little finger and the knuckle or second joint of the thumb should both be kept always as near as possible at the same distance from the paper, say about an inch and a half, while in the act of writing. It will also be of the greatest advantage if, at the commencement of a line in writing, you should have the elbow of the right hand pretty close to your right side, and as you move the hand along the line, in writing, to preserve the arm parallel to this position as well as the pen to its first posi tion; in fact, if you do the one correctly you will necessarily do the other, unless you choose to twist the wrist, which would be equally painful, absurd, and unnecessary.

because for want of attention to these apparently trifling minutiæ, or small matters, many bad writers have arisen, and some of them even teachers, who ought to know better what they are engaged in. For it stands to reason, and any one may prove it to himself by a few trials, that if the pen be allowed to fall below the knuckle, there is an instant loss of power, and of all real command over the pen.

Another direction of equal importance with any of those we have now given, is the position of the thumb; this you bend outwards from the pen so as to cause the tip or fleshy part of the point of the thumb to rest upon the pen directly opposite the first joint of the forefinger, as shown in the figure of the hand. This completes the directions for the position of the three fingers which hold the pen. Now let us attend to the other two fingers. One of these, the little finger, must be held so as to touch the paper on which you intend to write, just on the tip of it, close by the side of the nail, while the hand itself is made to rest upon its heel, that is, close by the wrist, not pressing heavily, but as lightly as possible. In fact, the pressure on the tip of the finger should be light also, so that in writing the heel of the hand should assist the tip of the little finger, and the tip of the little finger assist the heel of the hand, by mutually bearing the weight of the hand, and acting alternately

As to the position of the head and shoulders, stoop as little as possible; a gentle inclination of the head is all that is necessary in general, in order that you may observe earnestly and accurately the motion of the hand and the formation of the letters. In near-sighted persons a greater inclination of the head is required than in ordinary cases; but in all cases whatsoever this rule is absolutely essential, to keep the chest entirely free of pressure on the table or desk at which you write; if once you acquire a habit of leaning on the table, or lolling upon it with your chest or stomach, you need never expect to be a good writer. We believe that many pupils have been seriously injured in their health by the practice or habit of leaning upon the chest while learning to write, and that such injury has followed them through life. What can be more absurd than to see boys or girls sprawling on a table or desk with their arms akimbo, and their noses almost upon the paper, imitating the motion of the pen? What more foolish or disagreeable than to see every stroke of the pen imitated by the mouth or the tongue, as if the writer were approaching a state of idiocy ? Let every student of penmanship sit erect while writing, and let him only stoop his head with a gentle inclination, as we said before, sufficient to enable him to see clearly what he is doing, and to produce such a specimen of writing as will do credit to his care, attention, and ingenuity. With all these directionsand we have not spared them-you will require both time and

as momentary fulcrums or resting-points, while the hand moves forward, making one stroke or letter after another. The other finger, next the little finger, usually called the ring finger, because ladies wear their rings upon it, is the most difficult to dispose of, but it must be done. Endeavour, then, to give it an elegant curvilinear form, something in the shape of part of a ring itself, so that it may lie passively between the midfinger and the little finger without interfering with their movements; it should be considerably within the little finger, and its first joint should rest very nearly upon the first joint of the little finger, in a crossing position. This completes the directions for the position of the little finger and the ring finger. Lastly, as to the position of the whole hand, you must carefully observe that while resting upon the heel of the hand and on the little finger, it must be

perseverance, and constant practice, either to learn the art of writing from the commencement, or to correct and improve the system you have already acquired. But perseverance, practice, and determination will do all that you require; and you will soon reap a rich reward for all your care, attention, and earnest application.

We have given above a copy slip in which is shown the first stroke that demands the attention of the writer. It is a down stroke, commonly called a pothook, square at the top, and brought down with an equal or uniform pressure of the pen, near the foot becoming a hair line, which is turned at the bottom and carried upwards to the right. Students desirous of additional practice in these exercises may procure Cassell's Graduated Copy-books, which cost twopence each.

LESSONS IN ARITHMETIC.—I.

THE term Arithmetic, which is derived from the Greek verb apioμew (pronounced a-rith'-me-o), to count, is properly applied to the science of Numbers, and the art of performing calculations by them, and investigating their relations. To a certain extent, this science must have been coeval with the history of man. As an art, arithmetic is indispensable in daily business; and the man who is best acquainted with its practical details has usually the preference in every mercantile establishment. Our object in these lessons shall be twofold-to develop its principles as a science, and to show the application of its rules as an art. For this purpose, it will be necessary to begin with the first principles of Numeration and Notation, and to give such rules as will enable any one to read and write a given number correctly.

NOTATION AND NUMERATION.

1. Any single thing-as for instance, a pen, a sheep, a house -is called a unit: we say there is one such thing. If another single thing of the same kind be put with it, there are said to be two such things; if another, three; if another, four; if another, five; and so on.

Each of these collections of things of which we have spoken is a number of things; and the terms one, two, three, four, five, etc., by which we express how many single things or units are under consideration, are the names of numbers. A number therefore is a collection of units. This is also sometimes called an integer, or whole number.

It will be seen that the idea of number is quite independent of the particular kind of units, a collection of which is counted. Thus, if there are four pigs, the number of pigs is the same as if there were four pens. We can thus abstract a number from any particular unit or thing, and talk of the number four, the number five, etc. Numbers thus abstracted from their reference to any particular unit or thing are called abstract numbers. When a collection of things or objects is indicated, it is called a concrete number.

We shall treat first of abstract numbers.

2. The art of expressing numbers by symbols, or figures, is called Notation.

In the system of notation which we are about to explain, all numbers can be expressed by means of ten symbols (figures, or digits, as they are called), representing respectively the first nine numbers, and nothing, i.e., the absence of number. These

Thus 79|4|3| would denote seven thousands, nine hundreds, four tens, and three ones; or, as it would be expressed, seven thousand, nine hundred, and forty-three.

Similarly, 8|3|0|5|4|7|would denote eight times a hundred thousand, three times ten thousand, no thousands, five hundreds, four tens, and seven ones; or, as it would be more briefly expressed, eight hundred and thirty thousand, five hundred and forty-seven.

We need not, however, draw the columns: it will be the same thing if we imagine them, and, instead of columns, talk of figures being in the first, second, third, fourth places, etc. The symbol 0 put in any place, as already indicated in the previous example, denotes that the number corresponding to the particular column or place in which it stands is not to be taken at all: the 0 only fills up the place-thus, however, answering the important purpose of increasing tenfold the figure after which it stands.

Thus, 10 means that once ten and no units are taken-i.e., it denotes the number ten; 100 means that once a hundred but hundred; 5001 means that five thousands, no hundreds, no tens, no tens and no units are taken-i.e., it denotes the number a and one unit, are taken, or, as it would be more briefly expressed, five thousand and one.

4. Before proceeding further, we will give the names of the successive numbers:

The numbers between twenty and thirty are expressed thus: twenty-one, twenty-two, twenty-three, etc., up to twenty-nine, to which succeeds thirty; and similarly between any other two of the names above given, from twenty up to a hundred: thus, 95 is called ninety-five.

After one hundred, numbers are denoted in words, by mentioning the separate numbers of units, tens, hundreds, thousands, etc., of which they are made up. For example, 134 is one hundred and thirty-four; 5,342 is five thousand three hundred and forty-two; 92,547 is ninety-two thousand five hundred and forty-seven; 84,319,652 is eighty-four millions, three hundred and nineteen thousand, six hundred and fifty-two.

5. It is useful, in reading off into words a number expressed in figures, to divide the figures into periods of three, commencing on the right, as the following example will indicate :

Billions. Thousands of Millions. 561

234

Thus the figures 561,234,826,479,365 would denote five hundred and sixty-one billions, two hundred and thirty-four thousand eight hundred and twenty-six millions, four hundred and seventynine thousand, three hundred and sixty-five.

We have then the following

Rule for reading numbers which are expressed in figures :— Divide them into periods of three figures each, beginning at the right hand; then, commencing at the left hand, read the figures of each period in the same manner as those of the right hand period are read, and at the end of each period pronounce its name.

The art of indicating by words numbers expressed by figures is called Numeration.

EXERCISE 1.

Write down in figures the numbers named in the following exercises :

* In the foreign system of numeration a thousand millions is called a billion, a thousand billions a trillion, and so on.

1. Thirty-four.

2. Four hundred and seven. 3. Two thousand one hundred and nine.

4. Twenty thousand and fifty

seven.

5. Fifty-five thousand and three. 6. One hundred and five thousand and ten.

7. Seven hundred and ten thousand three hundred and one.

8. Two millions, sixty-three thousand and eight.

9. Eleven thousand eleven hun

dren and eleven.

10. Fourteen millions and fifty

six.

11. Four hundred and forty millions and seventy-two. 12. Six billions, six millions, six

thousand and six.

13. Ninety-six trillions, seven hundred billions and one.

EXERCISE 2.

exercises :

15. 400031256 16. 967058713

17. 20830720000 18. 8503467039

19. 450670412468

20. 58967324104325

LESSONS IN LATIN.-I.

INTRODUCTION.

IN giving to the readers of the POPULAR EDUCATOR lessons which may enable them to learn the Latin language, with no other resources than such as may be supplied by their own care and diligence, we take it for granted that they are desirous of acquiring the necessary skill, and willing to bestow the necessary labour. If the study were not recommended as a good mental discipline; if it were not recommended as giving a key to some of the finest treasures of literature; if it were not recommended as a means of leading us into communion with such minds as those of Cicero, Virgil, Horace, Livy, and Tacitus, it would have a sufficient claim on our attention, as greatly conducing to a full and accurate acquaintance with our mother-tongue--the English. The English language is, for the most part, made up of two elements-the Saxon element and the Latin element. Without a knowledge of both these elements, we cannot be said to know English. If we are familiar with both these elements, we possess means of knowing and writing English, superior to the means which are possessed by many who have received what is called a classical education, and have spent years in learned universities. In order to be in possession of both these elements, we should, for the Saxon element, study German; for the Latin element, the lessons which ensue will suffice.

In the instructions which we are to give, we shall suppose ourselves addressing a reader who, besides some general acquaintance with his mother tongue, has acquired from the English lessons in the POPULAR EDUCATOR, or from some other source, a knowledge of the ordinary terms of English grammar, such as singular, plural, noun, adjective, verb, adverb, etc. The meaning of such words we shall not explain. But everything peculiar as between the English and the Latin shall be explained, as well as any grammatical term which, though used sometimes in English grammar, the reader possibly may not understand. In these explanations we think it safer to err on the side of superfluity rather than on the side of deficiency. We have said that we shall suppose the reader to possess a general acquaintance with the English language. But it is well to suspect oneself as being probably acquainted with it but in an imperfect manner. And this advice is given in the hope that it may lead to the constant use of a good English dictionary. In every case in which there is the least doubt whether or not the exact meaning of any word used is known, the word should be looked out in a dictionary, and put down in a note-book to be kept for the purpose, with the meaning added. When there are, say, a score of words thus entered in the note-book, they must be looked at again and again until their signification is impressed on the memory. If the reader listens to this sugges tion, and continues to make progress, he will soon find numerous exemplifications of the assertion above made-namely, that a large proportion of the words of the English language are of Latin origin. Take, for instance, the last sentence. In that sentence alone the following words are derived from the

PRONUNCIATION OF LATIN.

We might regard the Latin alphabet as the same as the English; and in the pronunciation, too, we might in the main follow the hitherto accepted English usage, remembering always that every vowel is pronounced in Latin, and that some words which in English would be words of one syllable are words of two syllables in Latin, owing to the distinct pronunciation of every vowel. Thus the word mare, in English the feminino of horse, in Latin the sea, would be pronounced ma-re in Latin, just as we pronounce the English name Mary.

We have said that the Latin alphabet might be regarded as the same as the English; but the tendency in this country is now towards a pronunciation of the vowels more in accordance with the fashion prevailing in those of the Continental languages which preserve in themselves the stock of the old Roman speech These languages, the Romance languages as they are calledItalian, French, Spanish, &c.-generally sound a as we have it in our father, e like our a in fate, i like our e, o as in English, u as near as may be with the sound of that letter in our word full. An example of the difference between these two modes of pronunciation is afforded in the Latin word for sea already quoted. The Continental method sounds the vowel not as in Mary but as in Margery. Purists are also inclined to pronounce the consonants c and g invariably hard-c as in cart, g as in gaze. In Latin the vowels are what is called long or short. In other words, on some the accent or stress of the voice is thrown, on others it is not thrown. The vowel a, for instance, is mostly long; the vowel i is mostly short. A long vowel is said to be equal to two short vowels. It is also a fact that in Latin the same vowel sometimes has and sometimes has not the accent on it: thus the i in dominus, a lord, is without the accent, while the i in doctrina, learning, has the accent: the former, therefore, is pronounced thus, dóm-i-nus; the latter thus, doc-tri-na. Now observe that these words are trisyllables, or words of three syllables. Of these three syllables the last-namely, us-is called the ultimate; the second, in, is called the penult; the first, or dom, is called the antepenult. And the general rule for pronouncing Latin words is, that the accent is thrown on the penult, or if not on the penult, then on the antepenult. In doctrína the accent is on the penult or last syllable but one. In dóminus the accent is on the antepenult, or last syllable but two. In order to indicate where to lay the stress of the voice, we shall mark, as in dóminus and doctrína, on which syllable the accent lies. It will then be understood that when we put a mark thus over a vowel, we mean thereby that the voice should rest, as it were, on that vowel. For example, in the word incur, the accent falls on the last syllable, for the stress of the voice is thrown on the syllable cur. This is indicated thus, incúr. So in the Latin amicus, a friend, the accent is on the i, and the word is to be pronounced