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Abl.

anseres, geese
anseres, O geese
anseribus, by geese

patres, fathers

Gen.

Dat.

patres, O fathers

patribus, by fathers

Acc.

corporum, of bodies
corporibus, to bodies
corpora, bodies

Voo.

Abl.

Cases.

dolores, O griefs
doloribus, by griefs

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

NEUTERS.
Singular.
calcar, a spur
calcaris of a spur
calcari, to a spur
calcar, a spur
calcar, O spur
calcari, by a spur
Plural.
calcaria, spurs
calcarium, of spurs
calcaribus, to spurs
calcaria, spurs
calcaria, O spurs

animal, an animal
animalis of an animal
animali, to an animal
animal, an animal
animal, O animal
animali, by an animal

animalia, animals
animalium, of animals
animalibus, to animals
animalia, animals
animalic, O animals

NEUTERS.

vomeres, ploughshares vomerum, of ploughshares vomeribus, to ploughshares vomeres, ploughshares vomeres, O ploughshares vomeribus, by ploughshares

Singular.
nomen, a name
nominis, of a name
nomini, to a name
nomen, a name

nomen, O name
nomine, by a name
Plural.
nomina, names
nominum, of names
nominibus, to names
nomina, names
nomina, O names
nominibus, by names

genus, a race generis, of a race generi, to a race genus, a race genus, O race genere, by a race

genera, races generum, of races generibus, to races genera, races genera, O races generibus, by races

corpora, O bodies corporibus, by bodies In vomis, vomeris, vomer; 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; filos, flóris, a flower.

VOCABULARY.

Nom. guttura, throats Gen. gutturum, of throats Dat. gutturibus, to throats Acc. guttura, throats Voc. guttura, O throats Carbo, carbónis, m. cnarcoal; pavo, pavónis, m. a peacock; regio, Abl. gutturibus, by throats calcaribus, by spurs animalibus, by animals regiónis, f. a region or district; occasio, occasiónis, f. an opportu 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.

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, passĕris, 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) 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.

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N. Judex, a judge
G. judicis, of a judge
D. judici, to a judge
A. judicem, a judge
V. judex, O judge
A. judici, by a judge

Cases.

N. judices, judges
D. judicibus, to judges
G. judicum, of judges

A. judices, judges
V. judices, O judges
A. judicibus, by judges

Singular.

comes, a companion

comitis, of a companion
comiti, to a companion
comitem, a companion
comes, O companion
comite, by a companion
Plural.

comites, companions
comitibus, to companions
comitum, of companions

comites, companions
comites, O companions
comitibus, by companions

Cases.

vomis, a ploughshare
voměris, of a ploughshare

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vomeri, to a ploughshare

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vomerem, a ploughshare

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vomer, O ploughshare

Voo.

rex, O king

vomere, by a ploughshare

Abl.

rege, by a king

Singular.
lapis, a stone
lapidis, of a stone
lapidi, to a stone
lapidem, a stone
lapis, O stone
lapide, by a stone

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 principibus, to princes principum, of princes

principes, chiefs or princes principes, O princes principius, by princes

urbs ( city urbis, of a city urbi, to a city urbem, a city urbs, O city urbe, by a city

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urbes, cities urbium, of cities urbibus, to cities urbes, cities urbes, O cities urbibus, by cities

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 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.

VOCABULARY.

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, segètis, 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.

EXERCISES.-LATIN-ENGLISH.

tence, it will be well to examine a number of sentences, beginning, of course, with those that are short and easy. The nominative may be known by asking the question, who, which, or what? For example in the sentence, bees make honey; ask, who make honey? answer, bees; therefore bees is the nominative. Try another sentence; the book is mine; ask, what is yours? answer, the book; the book, therefore is the nominative, that being the thing about which you speak.

Sometimes an infinitive mood (which will be explained in future lessons), answers as the nominative case to the verb; as, to be industrious is praiseworthy. Now apply the rule, just given, to this sentence, ask, what is praiseworthy? answer, to be industrious; then to be industrious is the nominative. Sometimes a sentence supplies the place of the nominative; as the habit of rising early conduces to health, ask, what conduces to health? answer, the habit of rising early; this, therefore, is the nominative.

In the following sentences the word forming the nominative is printed in italic letters ;-Charles gets on nicely; Mary fell down; he was wet through; she wore her new gown; we will go together; it was placed on the shelf; you are wise; they came In such sentences as these the nominative may be to dinner. easily found; but in the course of your reading you will meet with words which so nearly resemble verbs, that you may be a little puzzled. Take the following sentence from Shakspeare as an example:-" To gild refined gold-is wasteful and ridiculous excess: now, to gild, is evidently the subject in this sentence, and it will strike you that to gild is a verb. But if you call to mind what we said in a former lesson about nouns, namely, that some of them are derived from verbs, and that a noun may be the name of an action, or state of being,—your difficulty will be removed, and you will see that "to gild refined gold" is the subject of the sentence, and

therefore the nominative.

Remember further, first, that there is always some verb which follows, or is joined with, the nominative: hence grammarians say, "The verb must agree with its nominative case.' In the sen

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Artifices debent pueros docere: pollicem movet rex ; reges cus-tences,-man is an animal; the wolf broke into the fold; the todiunt leges; leges custodiuntur à regibus; filius pollicem mordet; equites vexantur; artifices ornant urbes; merces artificum nutriunt filios et filias; caelebs dormit; plebs defenditur; stirps artificis laudatur; est ne tibi seges? cervix militis laeditur; caelebis aetas magna est.

ENGLISH-LATIN.

I defend artists; artists are defended by me; has he a reward? he has not a flock; I am pricked in the neck; artists paint flocks; the laws of the kings are deadly; the corn-land of the horseman is yielded; why is the bachelor blamed? the people blame bachelors; soldiers have rewards; age teaches many things (multa).

LESSONS IN ENGLISH GRAMMAR.-No. VI.
NOUNS (continued).-CASE.

THE term CASE, as used in reference to grammar, in a general
sense, means a change in the form of a noun, pronoun, &c.

By the cases of nouns is meant, the change which nouns undergo when they agree properly with other words which happen to be connected with them in the same sentence.

According to most grammarians, there are three cases of nouns in the English language; namely, the nominative, the possessive, and the objective.

I. The NOMINATIVE CASE simply expresses the name of a person or thing; that person or thing which is the subject of a sentence, or of part of a sentence. In the sentences, Charles learns quickly; or, Mary rises early; or, Thompson bound my books; Charles, Mary, and Thompson are the nominatives, they being the names of persons about whom we speak.

The nominative case of a noun is its ordinary form, whether singular or plural; as, the prince was there; or, the princes were there. The nominatives of pronouns (that is, of words used instead of nouns), are I, thou, he, she, it, we, ye, you, they, who. These words, and all nouns, can be used as subjects of sentences. The nominative case may be regarded as the radical, or original form of the noun or pronoun.

In examining the form of a sentence, the chief point is to find out the nominative case. And in order that a learner may be able to tell quickly what is the subject in any sentence, or part of a sen

year rolls round; she sits as a queen among the nations; it works well for the people; you may observe that the verbs, is, broke, rolls, sits, works, all agree with the subject of the sentences, or the nominative. Secondly, bear in mind, that the nominative is almost always placed before the verb, and, generally, immediately before it. In some compositions, however, and especially in poetry, or in prose, the style of which is poetic, the verb is placed first; as, "Comes he to mock at our solemnities ?"-" Pleads he in earnest?" "Riding upon a white palfrey, Sir Hugo was seen approaching":the verb and the nominative in these sentences are the words printed in italics.

II. THE POSSESSIVE CASE of nouns-as indeed you may judge from its name-implies property, ownership, or possession; it denotes the condition of any person or thing that has possession of something else; as, that saw is Richard's; this is Mary's shawl; where are the child's shoes? a cat's paw; a ship's rudder. It will be easily seen from these sentences, that the same meaning as that for which we use the possessive case, may be expressed by the words of, or belonging to`; as, the rudder of a ship; the paw of a cat; the shoes belonging to the child; the shawl owned by Mary; the saw the property of Richard. When we speak of the head of Victoria stamped on a shilling, we may either say, this is the likeness of the queen, or, this is the queen's likeness.

To denote the possessive case it is usual to add an apostrophe, that is a comma placed thus ', after the last letter of the noun, and then the letter at the end, as in the sentences above, and in the word queen's. There are, however, exceptions to this practice; to plural nouns ending with the sound of s, and some singular nouns ending with that sound, the apostrophe (') without the s is added to form the possessive case; as, angels' visits, meaning the visits of angels; or, the horses' bridles were mislaid, meaning the bridles of more than one horse. In singular nouns ending in s, ss, or nce it is usual to add the apostrophe only; as, England's gracious queen; for righteousness' sake; for conscience' sake; for goodness' sake; the swallows' flight, &c. In ordinary writing, however, the same idea may better expressed by using the preposition of; as, the flight of the swallow; the gracious queen of England, &c.

When the singular ends in s, most writers follow the general rule, except in poetry and in reference to some abstract_nouns; thus we say, the witness's evidence; the princess's jewels; Charles's Ishoes; mistress's dresses, &c.

After proper names ending in x 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 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.

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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 hundreda' figure of the multiplicand by the multiplier (increased or not, as the case may have consist of hundreds and thousands, then place under the line the required, by the hundreds carried from the last product), should 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, infrom the products immediately preceding them; inasmuch as ten of the rank in any one place in the product makes one of the rank in the next place of the product, according to the decimal scale of notation; this part of the process being exactly the same as that of carrying the tens in addition. EXAMPLE 1.-Multiply 32768 by 8. Factors. (Multiplicand 32768 Multiplier

Be careful in writing not to fall into the absurd, though not un-creasing them as they occur in order by the number of tens carried common, error, of putting 's to the plural number of nouns; as, law's, virtue's, vice's, &c.; nor to the third person of verbs; as, she carry's plenty of sails; instead of laws, virtues, vices, carries, &c. And be sure you never say or write hisen, horn, er ourn, instead of his, hers, and ours.

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?

Product 262144

MODE OF OPERATION,

Here, beginning with the units' figure of the multiplicand, you say 8 times 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,-viz., 1, 2, 3, 4, 5, 6, 7, 8, 9.

32768

32768

32768

32768 32768

32768

32768 32768

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 I 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, obtaining their successive products by the multiplier, and carrying the highest figure of each product as it comes in order to the next product, until you come to the last figure, when you put down the ast 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, thousand one hundred and forty-four. The product is now obtained,-namely, two hundred and sixty-two

shortened by attending to a piece of practical advice, similar to
In performing the preceding operation, the labour may be
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.

Factors. Multiplicand 7060080
Multiplier

6

Product 42360480

MODE OF OPERATION.

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

carry 4; then, 6 times 0 being 0, put down the carried 4; again, the product of 6 and 0 being 0, put down 0, as nothing was carried, aud proceed. Next say C times 6 are 36, put down 6 and carry 3; and the next product being 6 times 0, or 0, put down 3 in the next place of figures; lastly, say 6 times 6 are 36, and put down the complete product being the last in the operation. On the abridged process, above recommended, this operation would be very short; thus you say 0, and put down 0; 48, and put down 8; 0, 4, and put down 4; 0, and put down 0; 36, and put down 6; 0, and put down 3; 42, and put down 42.

EXERCISES.—1. Find the products of the number 142857 by the nine digits.

2. Find the products of the number 98998, the smallest number contained in the table in Exercise 4, page 58, No. 4, by the nine digits, and you will find these products in the same table.

3. 857142X9; 76876898x2; 101040060 0x7; 79806090×8; and 999999999999 × 5.

DEFINITION. As the cipher or 0, denotes nothing by itself, and is only employed to keep the combinations of the other nine figures in any number, in their proper places according to their rank or value, it is called an insignificant (not-meaning) figure; but the nine digits are called significant (meaning) figures; yet when the cipher, or 0, occurs between any of the other figures, as in the numbers 206 and 3007, it is called, and reckoned by arithmeticians, as significant; but when it occurs at the end of any of the other figures, that is, on their right, it is called insignificant, as in the numbers, 90, 100, and 25000. Ciphers are never put at the beginning of other figures, except in decimal fractions, as shall be explained in future numbers of this work.

If the multiplier to any proposed multiplicand, happens to consist of any one of the nine digits, followed by one cipher or any number of ciphers, then multiply according to the following rule :Rule 2.-Place the multiplier under the multiplicand, so that the significant figure of the multiplier shall stand under the units figure of the multiplicand; and multiply the successive figures of the multiplicand by the significant figure of the multiplier according to Rule 1, explained above. Then place the same number of ciphers in a line at the end of the product thus obtained, (that is, on the right,) as are contained in the multiplier. The reason of placing these ciphers at the end of the product, is in order that the significant figures of the product may be preserved in their proper places, according to the decimal scale of notation.

EXAMPLES: Multiply 123456789 by 90, and by 90000.

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Product 71021111040000

(2)
Factors Multiplicand 45608008000
70000
Multiplier

Product 3192560560000000 In the first of these examples, you multiply by 9, according to Rule 1; you then annex to the product four ciphers, because the multiplier contains two ciphers, and the multiplicand two ciphers, in order to preserve the product in its proper place, as tens of thousands; for the multiplicand having two ciphers, expresses so many hundreds as the significant figures denote, and the multiplier produce tens of thousands; and this is manifest from the consideraexpresses 9 hundreds; now, hundreds multiplied by hundreds tion, that ten times a hundred are ten hundreds or a thousand; and ten times a thousand, are ten thousands.

That,

This operation might be further illustrated, by saying that 78912345600 789123456×100; and 900=9x100; therefore 78912345600 x 900 = 789123456 X 100X9X100=789123456X9 X100 x 100 = 7102111104 × 1000071021111040000. This illustration proceeds on two important principles : 1. the product of any two or more numbers is equal to the continued continued product of the factors of any number will be the same in (that is the successive) product of their factors; and 2. That the readers, we shall give some simpler examples of the application of whatever order they may be taken. For the sake of younger these principles. Thus, we know that the simplest factors of 12 tion in any of the following ways: 2×2×3-12; or 2×3×2=12; are 2, 2, and 3; now 12 is produced from these factors by multiplicaor 3X2X2=12; here, 12 is the continued product of the three factors, taken either way. In like manner, if we had to multiply 18 by 10, we might separate 18 into its factors 3, 3, and 2; and 10 order, thus 3X3X2X2X5=180; or, 3×2×3×2×5=180; or, into its factors 2 and 5; and then multiply these factors in any 2×2×3×3×5=180; or, 5×2×2×3×3=180; and so on, as often as the numbers can be varied as to their position: in all these cases, the product of the factors will be equal to the product of the two numbers,-viz., 18 × 10-180. ELUCIDATION OF THE PRECEDING REMARKS.

90

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In the first of these examples, you multiply first by 9, according to Rule 1; you then annex (i.e., join to) to the product one cipher, because the multiplier contains one cipher, in order to preserve the product in its proper place, as the product of 9 tens. In the second example, you follow the same rule, but you annex to the product four ciphers, because the multiplier contains four ciphers, in order to preserve the product in its proper place, as the product of 9 tens of thousands.

EXERCISES: 1. Multiply 76854 by 80; 90763 by 700; and 142857 by 70000.

2. Find the following products: 98998X7000; 692986×80000; and 395992X7000000.

When the multiplicand consists of figures, both significant and insignificant, and the multiplier of one digit followed by ciphers, then multiply according to the following rule :

Rule 3.-Place the multiplier under the multiplicand so that the significant figure of the multiplier shall stand under the first significant of the multiplicand, that is, the one nearest to the right hand, and multiply the successive figures of the multiplicand by the significant figure of the multiplier, according to Rule 1. Then place the same number of ciphers in a line at the end of the product thus obtained (that is, on the right), as are contained both in the multiplier and the multiplicand. The reason of this is, in

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EXERCISES.

1. Multiply 768432900 by 7000; and 142857000 by 80000. 2. Find the following products: 96985000 500000; 807060 × 7000; and 9999000 × 90000.

3. Show that the product of the factors of 20 and 15 may be varied in a variety of ways, and still produce the same result-viz., the product of 20 and 15.

CORRESPONDENCE.

To the Editor.

In No. 4 of the POPULAR EDUCATOR, page 64, Mr. Webster has given a few examples in simple subtraction, proved by the method of casting out the 9's, which are quite correct. This method of proof is far from being a new thing. The rules, both simple and compound, are handled in Mair's Arithmetic, Edinburgh Edition,

1799. Thus:

(1)

5847 major
2569 minor

3278 remainder

(2)

£73 15 10
48 12 6 7

£25 3 4

7

X

The major being equal to the sum of the minor and remainder, therefore the excess of the nines in the one must be equal to that in the other. 1. Place the excess of the nines in the major at the top of a cross, and the excess of the minor and remainder (as if they were items in addition) at the bottom; consequently, the figure at the top and bottom will be the same, if the work is right. 2. Begin with the highest denomination, reducing always the excess to the next inferior denomination.

Thus 7+ 3 10; the excess 1 reduced to shillings is 20; the excess is 2; then say 2 + 1 + 5 and the excess 6 + 1 = 7, which is the excess of the major. 8, which reduced to pence is 96; Again, 4+ 8 = 12, excess 3; then 3 + 2 + 5 20s.; then 2+1+2+3 10, excess 1 = 8, and 8 × 12 = 96, the excess is 6; and 6 + 6 = 12, excess 3; and 3 + 4 = 7, which is the excess of the minor and remainder. CHARLES CURRIE.

Glasgow, April, 1852.

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LITERARY NOTICES.

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SUPERIOR EDITION OF CASSELL'S ILLUSTRATED FAMILY BIBLE. Published in Monthly Parts, price One Shilling.-With the begining of 1861 was commenced a Superior Edition of the ILLUSTRATED FAMILY BIBLE. This Edition, which is supplied with the Marginal References complete, the larger notes being omitted, is printed on fine super-royal quarto paper, and will be completed in about Thirty Monthly Parts, of Forty-eight Pages, price One Shilling each. It will be embellished by all the costly designs which have rendered the ILLUSTRATED FAMILY BIBLE one of the most remarkable productions of the Press of the present day; from Twenty to Thirty Illustrations, which have been designed and engraved by Artists of the highest eminence, being given in each part. The following list of Illustrations contained in Part I. will serve to convey an idea of the character and profuseness of its Pictorial Embellishments :-Introduction to Genesis; Adam and Eve in Eden; Death of Abel; The first Musical Instrument; Noah and his Family entering the Ark; The Deluge; Noah's Sacrifice; The Builders of Babel Dispersed; Separation of Abram and Lot; Melchisedek blesses Abram; Abraham and the Three Angels; Destruction of Sodom and Gomorrah; Hagar and Ishmael cast forth; Hagar and Ishmael in the Wilderness; Abraham and Isaac; Abraham and the Sons of Heth; Abraham's Servant and Rebekah at the Well; Isaac meeting Rebekah; Esau going for Venison; Isaac blessing Jacob; Jacob's Vision; Jacob pouring Oil on the Stone; Jacob keeping the Flocks of Laban; Jacob and Laban-The Heap of Witness; Meeting of Jacob and Esau. Besides the above principal subjects, a large number of smaller Engravings are introduced to illustrate the natural objects mentioned in the Bible-the interesting remains of Antiquity, Articles of Costume and Ornament, &o.

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ANSWERS TO CORRESPONDENTS.

good many times, and try to remember as much of it as she M. L.-She should read the first lesson very carefully over a questions at the end of the lesson, in order to see if she can can; she should then get an intelligent friend to ask her the answer them; if so, she may then safely proceed to the second lesson, and do the same thing in reference to it; then to a third, a fourth, &c.

A. Z. B. Y.-The students of the POPULAR EDUCATOR are expected to answer the Problems and Queries in it if they can. If new and ingenious problems, either in Geometry or Algebra, or new and ingenious solutions of old problems be sent, they will be admitted. much in hand, that we must decline it at present. J. S. E.-We thank him for his offer, but really we have so

of the

French lessons, which he calls a vocabulary, is to give the student J. E. SMYTH.-The meaning of the exercise in section some good practice in learning to pronounce French words aright, or as they ought to be pronounced according to the rules laid down in the first section. There no necessity for committing such a mass of words to memory; but they should be read over and over several times, in order, if possible, to acquire a correct method of pronouncing vowels, diphthongs, and consonants, as well as the peculiar nasal sounds. While this is practised, the student will insensibly acquire a knowledge of a great many words, and that almost without effort; but if it be read as a task, it is to be feared Our reason for placing the sons of Noah in the ethnographic table in the order in which they stand, is simply this, that in Scripture that very little knowledge either of words or sounds will be gained. the same order is preserved; and we consider the reason of the order to be such as an attentive reader of the Bible might fairly discover. Shem was the head of the sacred line of descent in which the Saviour was born, and therefore ought to stand first. patriarch, and second head of the human race, and therefore ought Ham was guilty of a grievous offence towards his father, the aged to stand last; of course Japheth, under such circumstances, must naturally stand second.

of SI (pronounced SEE) that we may have a different initial letter J. G. A. S., Professor of Music.-The syllable TE is used instead from SOL (or SOH) for the simple "Interpreting Notation" which we afterwards use. The great variety of syllables used by different teachers (see prefaces to Hickson's "Part Music" and to Turle and Taylor's "Singing Book") will surely be sufficient excuse for this very slight innovation which Miss Glover has introduced. You have only to stop the sibilant s with the tongue at the root of your time signatures, are removed from the staff in the earlier exercises, teeth, and you make it a T. The clefs and flats, and sharps and to prevent the pupil attempting to learn too many things at once. At present he has to do only with the key-note, the chord, and the scale. The key-note is marked for him by a peculiar form. The pitch of the key-note is given him either in the title, thus, "Key D," "Key G," or by the general directions of the note below. The places of the semi-tones are already known to him in all keys. They are between ME FAH and TE DOH. If our correspondent will be patient, for a few weeks, he shall be gratified by seeing clefs and time signatures, and flats and sharps gathering in all their ominous dignity at the beginning of the staff. preferred to that of o, for the earlier scale exercises, because The key of D is its compass is more in the middle of the various voices. See Crivelli.

was not a subjugation. Upon the death of Queen Elizabeth LADY OF THE LAKE.-The union between Scotland and England without issue, she was succeeded by the rightful heir to the English throne, who was James VI., king of Scotland. Under him the kingdoms were necessarily and equally united. He derived his right to the throne of England from his mother, Mary Queen of Scots, who was descended from a sister of Henry VIII. Queen Elizabeth, upon her death-bed, recognised his claim, and expressed a desire that it should not be opposed.

our "Hand-book of Investments." The latter contains a complete H. C. should purchase our "Hand-book on Book-keeping," also account of the public securities, railway shares, foreign stocks, and other means of investment, explanatory and statistical, with information to the latest date.

HENRY.-The word constable means something like stablekeeper, or, more exactly, knight of the stable. The ancient French kings had an officer of very high rank, called a constable, similar kingly affairs. In the course of ages, the word acquired whose business it was to superintend tilts, tournaments, and all its present signification.

and will be sent post free on receipt of thirteen postage stamps. F. S.-Our "Hand-book of Letter-Writing" is published for 1s., It contains hints on composition and style, with fac-similes of handwriting.

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