a little thrown back, so as to leave the point visible, which would otherwise be quite covered. But it becomes a formidable weapon when the claw is unsheathed, as in the act of

a

striking, as it is represented in the lower engraving, for by single blow the lion can rip up the side of a horse or a buffalo. The engravings show also the pads with which the toes are furnished; and as, to preserve the points of the claws constantly sharp, it is necessary they should not rub on the surface of the ground, they are always directed with their points upwards, and sunk in the hair on the upper surface of the toes. The bones of the fore-limbs are remarkable for their strength and firmness, and the muscles are singularly large and dense. Those of the jaws and neck are equally powerful. The upper surface of the tongue is covered with sharp and strong points, and there are teeth to cut as well as to crush.

The lion has no objection, as he roams abroad during the night, to feast on a banquet already provided, when various game quadrupeds have fallen by the bullets of the hunter's rifle. But, commonly, he provides his own meal, preying on reptiles, and on the larger varieties of antelopes; attacking the zebra, a favourite object of his pursuit; and frequently attending the vast herds of buffaloes, that he may prove at pleasure a match for one of these animals, which, in size and strength, greatly surpass the most powerful breed of English cattle.

The celebrated traveller, Mungo Park, passed a lion with impunity, but it was during the day; the animal was then reposing at his ease, and had probably satiated his appetite during his nocturnal rambles. Another traveller, Mr. Burchell, says, "While all of us were lying in the waggons, the dogs commenced a barking and howling; the whole of the oxen suddenly made efforts to get loose, and began to express that kind of uneasiness which, in a very intelligible manner, told us that a lion was not far off. He continued prowling round us till midnight; but his fears to encounter men were the only obstacle to prevent his carrying off his prey, and, finding it thus too strongly protected, he at last withdrew." Of the fatal success of the lion's attacks, there are, unhappily, many instances. In ancient times, he appears to have been employed as the public executioner. The case of Daniel in the lions den is well known; as well as the fate of those who acted as spies on his conduct. Rapid must have been their execution, when "the lions had the mastery of them, and brake all their bones in pieces or ever they came at the bottom

of the den."

FEMALE EDUCATION.-No. II.
BY ELIZA METEYARD.

IMPROVEMENT OF THE MIND.

FEW young girls now begin their work in the factory, the warehouse, or the shop without some knowledge, at least, of reading, if not of writing. I will, therefore, presume that they can read, for without this elementary key to knowledge, mental improvemer.t, at least from books, is impossible. If, however, such is unfortunately not the case, and the young girl is fifteen or sixteen years of age, let her at once set about acquiring this invaluable power by attending some respectable evening school, if she work in a factory or warehouse; or if in a shop, where the hours are late, by going to a Sunday-school regularly each Sabbath. Or some friend or young companion may be able to teach her; but at any rate let means be taken to give daily food to the mind as well as to the body.

Thus being able to read, and I will say to write, a world of power to good or evil rests in a young girl's hands. She may, if only ordinarily diligent, carry on her mental improvement to a great extent, or she may, if only a reader of the low, pernicious fictions of the cheap press, live to lament that any ignorance that was hers, was ever broken by such a simple thing as the knowledge of the alphabet. I speak of this matter in the first place, and this emphatically, because I am well aware to how great an extent this vile trash of fiction circulates in the manufacturing towns, and amongst the operative classes; because I have all an educated woman's abhorrence of what tends to corrupt the minds of the young; and because I well know from much which has been confided to me, and from much which I have read, the inevitable evils which take their rise in young minds from a continuous perusal of this debasing literature. There are no such scenes in nature as it paints; no such men and women as its heroes and heroines, except amongst the most debased and vile; no such queens and countesses, lords and ladies, as it draws; no human beings of ordinary intelligence speaking such language as its personages speak; and rarely in the round of human interest, startling and often strange as things are, do such murders, such seductions, such plots, and such crimes happen as fill its execrable pages. Mind, I do not object to fiction, for I know its worth when pure, and the charm it has for the young; but I do say to all young women who may read these pages, avoid this class of fiction as you would the gin-shop or a disreputable acquaintance, for its power to contaminate is as great, or even greater; and whilst there is so much that is interesting and pure in literature of this kind, pass by the common novel, as you would any other undoubted form of evil. And let not its ghastly woodcuts, its improbable narrations, its detestable advice in regard to marriage and courtship, have the least charm for your eye or ear. Of what is pure in literature I will presently speak.

Of time for mental improvement I must say a word. I am not amongst those who ask impossible things of the operative classes, or forget that rest and amusement are naturally sought for, after a hard day's labour. But indeed that, which is a happy law in nature, change of occupation is often equivalent to rest, and they who have worked all day with their hands usually find, if it be not too severe, or too protracted, an intense degree of pleasurable repose in mental occupation, just as the intellectual classes find a ride or walk restoring and refreshing after a long morning's study. But beyond some small amount of reading or preparation of brief lesson, the leisure that the dinner-hour gives ought scarcely to be used for the purposes of mental improvement. The labour of the morning has exhausted the body, and the process of digesting the noon-day meal calls still further upon its powers; it is, therefore, in the well-husbanded hours of the evening, when both mind and body have been refreshed by washing the person, by change or arrangement of dress, and by a cup of tea, that the young women of the operative classes should seek the self-improvement they can with ordinary diligence make theirs.

In the first place, I would say, let a young woman try to write a fair, open hand. I do not mean the angular, wire-drawn, disjointed writing some fond mothers of the middle classes call "fashionable," when they show off or praise their daughters' correspondence, but the natural handwriting of the individual, which, if left free in its cultivation, will always be full of character. Indeed, with the present facilities for self-improvement which exist, and with the leisure their hours of labour leave, I think that, with

few exceptions, every young woman of the operative class ought to write a fair hand, and spell well. Fifty years ago, most ladies spelt ill, and wrote badly, without exciting either surprise or comment; but now such things would be inadmissible in any one pretending to the character of a gentlewoman; and I hope the day is not far distant when general education will make it equally so in the young women of the operative classes. For when once persons have acquired the rudiments of penmanship, by the careful imitation of those large text copies which can be bought at any stationer's shop for a few pence, they may carry on their self-improvement to what degree they please; and the young woman who will be at the pains to write a single copy of one of these, well and carefully, each evening, will soon find a wonderful improvement, for it is the practice of large-hand that lays the foundation of freedom and grace in writing. The next step, when large-hand is thus written well, and a smaller one undertaken, should be to make short extracts into a copy-book from a book or newspaper. Such are usually written with grammatical precision, and the spelling is invariably good so that a young woman would not only thus learn to spell well, but to use the style of those who, from habit and education, have been able to express their thoughts on paper with facility, and without mannerism or vulgarity. Of all methods of self-help, I know none comparable to this, especially when habit and facility are so far advanced as to enable the copyist to condense the material into a few lines, and in her own anguage, so that it thus becomes, what is called by lawyers and students, 'note-taking.' In this way, 'grammar and correct spelling are not only acquired, but a precision given to remembered facts and habits of thought which become invaluable.

It is not in my province here to more than mention grammar and arithmetic as branches of knowledge it is desirable all should acquire,—there are departments of this work especially devoted to them as studies, but this much I will say that the study of grammar, if properly undertaken by those who teach and those who learn, is far from being the repulsive and difficult thing many consider it; for if we begin by exercising thought and investing our study with a reality that may be easily made to belong to it, we become interested in our mental search and observation as we proceed, and what at first seemed abstract and difficult disappears. Thus I say, the chair on which I sit, the table at which I write, the goodness that I admire in my friend, are nouns, because they are objects which I can see, or which exist; the strength of my chair, the height of my table, the greatness of the goodness of my friend, put thus, as strong chair, high table, great goodness, are adjectives, because they express some, or add some, quality to the nouns; and when I further say my strong chair stands, my high table shakes, the goodness of my friend is rewarded, I show verbs, because I speak of something belonging to these nouns which is, or does, or exists. Next to grammar arithmetic is invaluable; for besides its great use in relation to domestic matters, especially to those of the operative classes who have much dealing with small shops and in small purchases, its acquirement and use train certain faculties in a woman's mind, which by a curious physical law are often reflected in the capacity of her children, and in their power to easily acquire notions of quantity and form, to say nothing of a woman's value when she can assist her husband, her father, her brother, or her employers in calculations connected with work or wages.

together you have syllab, which with the termination ble makes syllable. A syllable then is so much of sound as may be taken or uttered at once. Number 1 means equal (pari found in the English par and pair); parisyllabic, then, signifies that which is equal in its syllables; and nouns are called parisyllabic which have the same number of syllables in all the cases of the singular number. I say of the singular number because the plural of all nouns is not parisyllabic, inasmuch as the genitive plural, as in the cases of arum and orum, has a syllable more than the other cases. Now nouns which have in the genitive singular a syllable more than they have in the nominative singular are called imparisyllabic. In this word, as here given, you find an additional syllable, namely im from in, the n becoming m, before the p, which signifies not. Imparisyllabic then is not-parisyllabic; and the words denote those nouns which in the genitive sing. have not the same number of syllables as they have in the nominative. Piscis, a fish, is parisyllabic; for in the genitive it is piss, having two syllables as in the nominative. But cantor, a singer, is imparisyllabic, for in the genitive it is cantoris, having three syllables, whereas the nominative has but two. Here then we have one distinction,—namely, nouns of the third declension are either parisyllabic or imparisyllabic.

Now, inquiry has shown that parisyllabic nouns have a vowel stem, and imparisyllabic nouns a consonant stem; that is, that the stem of the former ends in a vowel, and the stem of the latter ends in a consonant. Of the stem of a noun and a verb, I have already said something. It is better to repeat than not to be understood. Take nubes, a cloud, and form the genitive; the genitive is nubis. You get the stem by cutting off the sign of the genitive, which in this case is (as in the English cloud, cloud's). You thus obtain nubi. Nubi has two syllables, the same as the nominative nubes. It is therefore Take also dolor, grief; parisyllabic, and ends in a vowel. genitive, doloris. Cut off is, the sign of the genitive, and you Dolor ends, you see, in a consonant, and is a consonantal stem. The word is also imparisyllabic, because it increases in the genitive singular. Imparisyllabic nouns, In this case the stem and the then, have consonantal stems. nominative are the same, both being dolor. But in nomen, a name, genitive nominis, stem nomin, the nominative and the stem are unlike. Of consonantal stems, then, there are two classes; first, those of which the stem is identical with the nominative; second, those in which it is different. The consonants in which the stem terminates are

obtain dolor.

From these stems the nominative is formed with or without An instance of the formation of the nomithe addition of 8. native with the addition of s, is found in nom. rex, a king, gen. regis, stem reg, add and you have rege, which is proAn instance of the formation of the nominative nounced rex. without the addition of you find in nom. leo, a lion, gen. leonis, stem, leon, shortened into leo. THIRD DECLENSION.-Sign is.

CASE-ENDINGS.
Cases.

case.

LESSONS IN LATIN.-No. V.
By JOHN R. BEARD, D.D.

NOUNS, SUBSTANTIVE AND ADJECTIVE.-Continued.
WE pass on to the third declension. In the third declension
we find, in the nominative case, so great a variety of termina-
tions, that we must endeavour to arrange the nouns in certain
classes. The genitive singular, however, is the characteristic
And the genitive singular ends in is.
Before classifying these nouns, I must give you some expla-
nations. Parisyllabic is a word I have to use. It consists of
three words, which I will mark thus pari syl lab(ic), of these
the two latter are of Greek origin. The former is Latin. As
La word is thus made up of terms from two languages, it is
a sort of hybrid. Number 2 signifies with; number 3 signifies
taken; the io is merely the termination. If you put 2 and 3

1 2 3

Plural.

M. F. OF N.

The genders of the nouns of the third declension may be stated thus, though the rules are not without exceptions: FIRST, nouns ending in o, or, os, er and imparisyllabics in es, are masculine; SECOND, nouns ending in as, is, aus, us (gen. utis or udia) and s, and those which end in s blended with the preceding consonant, as well as parisyllabics in es, are feminine; THIRD, nouns ending in a, e, e, l, en, ar, ur, ut and us (gen. oris, ris, aris,) are neuter. By practice, you will in time be come familiar with these somewhat complex facts, I proceed to set down specimens in classes,

Abl.

dolores, O griefs
doloribus, by griefs

ansere, by a goose
Plural.
anseres, geese
anserum, of geese
anseribus, to geese
anseres, geese
anseres, O gecse
anseribus, by geese

patre, by a father

Acc.

corpus, a body

Voc.

corpus, O body

Abl.

corpore, by a body

patres, fathers

patrum, of fathers
patribus, to futhers

Cases.

Nom.

Gen.

patres, fathers

Dat.

patres, O fathers

patribus, by fathers

Acc.

corpora, bodies
corporum, of bodies
corporibus, to bodies
corpora, bodies

Voc.

Cases,

dolores, griefs
dolorum, of griefs
doloribus, to griefs

Nom. guttur, a throat
Gen. guttăris, of a throat
Dat. gutturi, to a throat
Acc. guttur, a throat
Voc. guttur, O throat
Abl. gutture, by a throat
Cases.

corpora, O bodies corporibus, by bodies In vomis, vomeris, romer; corpus, corporis, corpor, and genus, generis, gener; the stems,-namely, vomer, corpor, and gener seem to end in r. The r, however, is only the representative of s, for between two vowels, as in corporis, the s by the laws of pronunciation passes into r. Thus, instead of corpus, corpusis, we have corporis, the s being changed into r and the u into o. Similar changes take place in tellus (tellúsis) tellúris, the earth; pulvis, pulveris, dust; mas, maris, a male; aes, áeris, brass; flos, flóris, a flower.

VOCABULARY.

Carbo, carbónis, m. cnarcoal; pavo, pavónis, m. a peacock; regio, regiónis, f. a region or district; occasio, occasiónis, f. an opportu

Nom. guttura, throats Gen. gutturum, of throats Dat. gutturibus, to throats Acc. guttura, throats Voc. guttura, O throats Abl. gutturibus, by throats calcaribus, by spurs animalibus, by animals Here observe, that as in the neuter nouns of the second de-nity; cardo, cardinis, m. a hinge; ordo, ordinis, m. order, series; clension, the neuter nouns of the third declension have in both the singular and the plural, three cases alike,-namely, the nominative, the accusative, and the vocative. In animal, the nominative plural is ia, instead of a. This is owing to its being originally from a vowel stem, as nominative animal, genitive animalis, stem, animali.

VOCABULARY.

cinis, cineris, m. ashes; pulvis, pulveris, m. dust; decus, decóris, breast; pignus, pignoris, n. a pledge; carmen, carminis, n. a poem; n. becomingness; littus, littoris, a shore; pectus, pectoris, n. a lumen, luminis, n. light; vulnus, vulneris, n. a wound; opus, operis, n. work.

EXERCISES-LATIN-ENGLISH.

Carbonem timeo; pavones ferit puer; pulchrae sunt regiones; occasio est tibi; movemus cineres; cardo movetur; ordinis decus delectat matres; magnus est pulvis cineris; in littore sunt pavones; carmina non sunt nobis; vulnus est in pectore; regionis magnum est lumen; illi est nomen magnum; pignora non laudantur.

ENGLISH-LATIN.

Color, colóris, m. colour; odor, odóris, m. odour, smell; rumor, rumóris, m. report; error, erroris, m. error; agger, aggeris, m. a mound or dam; passer, passeris, m. a sparrow; frater, fratris, m. a brother; mater, matris, f. a mother; fulgur, fulgaris, n. lightning; pulvinar, pulvináris, n. a cushion; vectigal, vectigális, n. a tax; est mihi, I have, used with the noun as nom. to est; thus, guttur est mihi, I have a throat; so in the plural, guttura sunt nobis, throats are to us) we have throats; in the same way, guttur est tibi (a throat is to thee) thou hast a throat; guttur est illi (a throat is to him) he has a throat; guttura sunt vobis (throats are to you)tunity; the man's opportunity is great. you have throats; guttura sunt illis (throats are to them) they have throats; observe that mihi, means to me; tibi, to thee; illi, to him; nobis, to us; vobis, to you; illis, to them.

EXERCISES-LATIN-ENGLISH.

Magnus dolor est mihi; non ne tibi est magnus dolor? sunt magni dolores matribus; color pulvinaris pulcher est; est ne pulcher pulvinaris color; funestus error est illi; cur funesti errores sunt patri? frater est mihi; fratribus sunt magni dolores; fulgura terrent animalia; non ne matres terrent fulgura? fulgura terrent passeres. ENGLISH-LATIN.

I have a spur hast thou a goose? they have geese; have you a mound? the odour of the lightning is on the cushion; I do not like (diligo) taxes; rumours are troublesome; have they a pillar? they have not a goose; you have a father, a brother, and a mother; they have griefs; thou hast a great cushion.

ii. the stem and the nominative are different; stem in n and s.

vomis, a ploughshare
voměris, of a ploughshare
vomeri, to a ploughshare

Dat.

vomerem, a ploughshare

Acc.

regem, a king

vomer, O ploughshare

Voc.

rex, O king

vomere, by a ploughshare

Abl.

rege, by a king

princeps, a chief or prince principis, of a prince principi, to a prince principem, a prince princeps, O prince principe, by a prince

principes, chiefs or princes principum, of princes principibus, to princes principes, chiefs or princes principes, O princes principius, by princes

city

urbs (
urbis, of a city

urbi, to a city
urbem, a city

urbs, O city urbe, by a city

A few words of explanation may here be desirable. The Latin c represents the Greek g (gamma), and for the most part was pronounced like our k. Thus, the Romans pronounced Cicero, the name of their great orator, Kikero. Now the a in judex, is made up of these letters thus judecs; the c ands blending together to form ; hence, judec, judicis, judecs; in the genitive, the laws of pronunciation convert the e of the nominative into i in the genitive; as it does in comes, comitis. You thus see that the variations which words undergo are not arbitrary. Those variations depend on the nature of the letters that come together, and in their ultimate causes, on the structure of the organs of speech, as these organs are in each nation modified by natural endowments, by climate, by culture, &c.

The b in urbs, may be considered as equivalent to p, for b and p being labials, that is letters in pronouncing which the lips are chiefly used, are as letters of the same organ, interchangeable, or may be used the one for the other, under certain conditions.

Artifex, artificis, m. an artist or artificer; pollex, pollicis, m. the thumb; cervix, cervicis, f. the neck; lex, legis, f. a law; grex, gregis, m. a flock; miles, militis, m. a soldier; eques, equitis; m. a horseman or knight; seges, segětis, corn land; aetas, aetatis, f. age; merces, mercedis, f. a reward; caelebs, caelebis, m. a bachelor, plebs, plebis, f. the people; (plebs has no plural), stirps, stirpis, f. a race, stem.

After proper names ending in z or 8, the s is sometimes omitted; as, in Felix' room; Achilles' wrath; Hercules' strength. This is common in poetry, but in prose it is unnecessary; it is quite as easy to say, the strength of Hercules, as it is to say, Hercules' strength. In old forms of devotion, many prayers conclude with the sentence, "For Jesus Christ his sake," it is much better to say, for the sake of Jesus Christ.

In sentences where several names are coupled together in the possessive case, the apostrophe and the letters may be joined to the last of them, and omitted, though understood, from the others; as, Thomas, William, and Samuel's pony; but if any words come between, the sign is necessary; as, Samuel's and William's, as well as Thomas's pony. Remember that s with an apostrophe, thus 's always signifies of, and denotes possession or relation, as in the example before given, the princess's jewels; that is, the jewels of, or belonging to the princess.

the multiplicand, and if it consist of units only, place it under the line in the place of units; and proceed to find the product of the multiplier and the tens' figure of the multiplicand. But, if the product of the multiplier and the units' figure of the multiplicand should consist of units and tens, then put down under the line, the units only as before, and add the tens of this product to the product of the tens' figure of the multiplicand by the multiplier, which will consist of so many tens; this is called in the language of the schools, carrying the tens to the next figure, or rather product, If this next product should consist of tens and hundreds, then put down under the line the tens only in its proper place, and carry the hundreds to the product of the hundreds figure of the multiplicand by the multiplier; but if it consist of tens only, then put it down as before. Again, if the product of the hundreds.' figure of the multiplicand by the multiplier (increased or not, as the case may have required, by the hundreds carried from the last product), should consist of hundreds and thousan is, then place under the line the hundreds only in its proper place, and carry the thousands to the next product. Proceed in the same manner, to find the products of the successive figures of the multiplicand by the multiplier, inBe careful in writing not to fall into the absurd, though not un-creasing them as they occur in order by the number of tous carried common, error, of putting 's to the plural number of nouns; as, from the products immediately preceding them; inasmuch as ten law's, virtue's, vice's, &c.; nor to the third person of verbs; as, of the rank in any one place in the product makes one of the rank she carry's plenty of sails; instead of laws, virtues, vices, carries, in the next place of the product, according to the decimal scale of &c. And be sure you never say or write hisen, hern, or ourn, in- notation; this part of the process being exactly the same as that of stead of his, hers, and ours. carrying the tens in addition. EXAMPLE 1.-Multiply 32768 by 8.

The possessive cases of the pronouns, mentioned in the lessons on nominatives, are, mine, thine, his, hers, its, ours, yours, theirs, whose. Thus this orange is mine; that book is his; yonder is its place; the blame is theirs; &c.

Our explanations and illustrations of the Objective Case of nouns, together with a few general remarks upon nouns, and some useful examples for exercise must be reserved for our next meeting. In the mean time let us find out how far you understand us by answering the following

QUESTIONS ON THE FOREGOING LESSON.

What is meant by the cases of nouns ?

How many cases are there in English grammar?

What does the Nominative express?

Here, beginning with the units' figure of the multiplicand, you say 8 times 8 are 64, that is 64 units, or 6 tens and 4 units.

You

What name do you give to that case which expresses the subject therefore put down under the line, the 4 units in the proper place,

of a sentence?

Name the nominatives of pronouns.

How may the nominative case be known?
Which is the nominative in the sentence," Bees make honey?"
Which in the sentence, "They came to dinner?"
Which in the sentence, "To gild refined gold is wasteful and
ridiculous excess ?"

What is said in this lesson about the verb and the nominative ?
What does the Possessive case imply or signify?
Give some examples.

How is the possessive case denoted?

What is an apostrophe ? and what does it signify or denote ?
Which are the pronouns of the possessive case?
What vulgar errors in writing or speaking should you avoid in
using possessive nouns ?

LESSONS IN ARITHMETIC.-No. VI.

RULE OF SIMPLE MULTIPLICATION. No one should attempt to begin the study and the practice of this rule, until he has made himself complete master of the multiplication table, given in page 37, No. III. This being learned, he may proceed to multiply any large number by any one of the nine digits. In order to explain the mode of performing this process, it will be necessary to recall to mind the definition of multiplication,-viz., that it is the process by which we find the sum of one number repeated as many times, as there are units in another number. Suppose, for instance, that we wished to know how much 8 times 32768 would come to; we know that if we put down the number 32768 eight times, successively in vertical or upright columns as in addition, and found the sum of these columns by that rule, we should have the answer or product required. Thus :Adding, as you see in the margin, we have the sum 262144 for the product of 32768 by 8. These considerations plainly suggest to us the following rule for the multiplication of large numbers by any one of the nine digits,-vis., 1, 2, 3, 4, 5, 6, 7, 8, 9.

32768

32768 32768 32768 32768

32768

32768
32761

Rule 1. Write down the multiplicand, or number to be multiplied, and under its units' place or figure, place the multiplier or number of times you are to repeat the multiplicand; then draw a line. Find the 262144 sum product of the multiplier and the units' figure of

and carry the 6 tens to the product of the tens' figure of the multiplicand; you then say 8 times 6 are 48, and to this product, which is 48 tens, adding (or carrying) the 6 tens, you have 54 tens; now 54 tens make 5 hundred and 4 tens; you therefore put down under the line the 4 tens in the proper place, and carry the 5 hundreds to the next product; you again say, 8 times 7 are 56, and to this product, which is 56 hundreds, you add the 5 hundreds carried, and you have 61 hundreds; now 61 hundreds make 6 thousands 1 hundred; you therefore put down under the line the 1 hundred in the proper place, and carry the 6 thousands to the next product. Proceed in this manner through all the figures of the multiplicand, the highest figure of each product as it comes in order to the next obtaining their successive products by the multiplier, and carrying product, until you come to the last figure, when you put down the last product in full without carrying its highest figure, this figure being then the highest figure in the whole product. By highest figure here, we mean the figure of highest value, or highest rank. The product is now obtained,-namely, two hundred and sixty-two thousand one hundred and forty-four.

In performing the preceding operation, the labour may be shortened by attending to a piece of practical advice, similar to what we gave under the rule of addition, namely, to look at the multiplier and the successive figures in the multiplicand, without naming them, to name their product and the sum of this product and the figure carried (if there be any) from the preceding product; then to put down the units' figure of the sum and mentally carry the tens' figure. Thus, in the preceding example, the operation would be shortened as follows:-Looking at the multiplier 8 and the figures 8, 6, 7, 2, and 3, in succession, you say 64, and put down 4; 48, 54, and put down 4; 56, 61, and put down 1; 16, 22, and put down 2; 24, 26, and put down 26. EXAMPLE 2.-Find the product of 7060080 by 6. Multiplicand 7060080 Multiplier 6

Factors.

Product 42360480

MODE OF OPERATION.

Here, beginning at the units' place of the multiplicand, the product of 0 and 6 is 0, you therefore put 0 in the units' place under the line. You then say 6 times 8 are 48, put down 8, and