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and three quarters of the money was, or were, sent back?"-"As 2 is to 4, so is 6 to 12;" or, "As two are to four, so are six to twelve?"

OBS. 15.-Most of the foregoing expressions, though all are perhaps intelligible enough in common practice, are, in some respect, difficult of analysis, or grammatical resolution. I think it pos sible, however, to frame an argument of some plausibility in favour of every one of them. Yet it is hardly to be supposed, that any teacher will judge them all to be alike justifiable, or feel no interest in the questions which have been raised about them. That the language of arithmetic is often defective or questionable in respect to grammar, may be seen not only in many an ill choice between the foregoing variant and contrasted modes of expression, but in sundry other examples, of a somewhat similar character, for which it may be less easy to find advocates and published arguments. What critic will not judge the following phraseology to be faulty? "4 times two units is 8 units, and 4 times 5 tens is twenty tens."-Chase's Common School Arithmetic, 1848, p. 42. Or this? "1 time 1 is 1. 2 times 1 are 2; 1 time 4 is 4, 2 times 4 are 8."-Ray's Arithmetic, 1853. Or this? "8 and 7 is 15, 9's out leaves 6; 3 and 8 is 11, 9's out leaves 2."-Babcock's Practical Arithmetic, 1829, p. 22. Or this again? "3 times 3 is 9, and 2 we had to carry is 11."-Ib., p. 20.

OBS. 16.-There are several different opinions as to what constitutes the grammatical subject of the verb in any ordinary English expression of multiplication. Besides this, we have some variety in the phraseology which precedes the verb; so that it is by no means certain, either that the multiplying terms are always of the same part of speech, or that the true nominative to the verb is not essentially different in different examples. Some absurdly teach, that an abstract number is necessarily expressed by "a singular noun," with only a singular meaning; that such a number, when multiplied, is always, of itself, the subject of the assertion; and, consequently, that the verb must be singular, as agreeing only with this "singular noun." Others, not knowing how to parse separately the multiplying word or words and the number multiplied, take them both or all together as "the grammatical subject" with which the verb must agree. But, among these latter expounders, there are two opposite opinions on the very essential point, whether this "entire expression" requires a singular verb or a plural one:-as, whether we ought to say, "Twice one is two," or, "Twice one are two:"-" Twice two is four," or, "Twice two are four;" -“Three times one is three," or, "Three times one are three;"-"Three times three is nine," or, "Three times three are nine." Others, again, according to Dr. Bullions, and possibly according to their own notion, find the grammatical subject, sometimes, if not generally, in the multiplying term only; as, perhaps, is the case with those who write or speak as follows: "If we say, Three times on are three,' we make 'times' the subject of the verb."-Bullions, Analyt, and Pract. Gram., 1849, p. 39. "Thus, 2 times 1 are 2; 2 times 2 are four; 2 times 3 are 6."-Chase's C. S. Arith., p. 43. Say, 2 times 0 are 0; 2 times 1 are 2."-Robinson's American Arith., 1825, p. 24. OBS. 17.-Dr. Bullions, with a strange blunder of some sort in almost every sentence, propounds and defends his opinion on this subject thus: "Numeral adjectives, being also names of numbers, are often used as nouns, and so have the inflection and construction of nouns: thus, by twos, by tens, by fifties. Two is an even number. Twice two Is four. Four is equal to twice two. In some arithmetics the language employed in the operation of multiplying-such as 'Twice two are four, twice three are six-is incorrect. It should be, Twice two is four,' &c.; for the word two is used as a singular noun-the name of a number. The adverb 'twice' is not in construction with it, and consequently does not make it plural. The meaning is, 'The number two taken twice is equal to four.' For the same reason wo should say, "Three times two Is six,' because the meaning is, 'Two taken three times is six.' If we say, 'Three times one are three,' we make 'times' the subject of the verb, whereas the subject of the verb really is 'one,' and 'times' is in the objective of number (§ 828). 2: 4:: 6: 12, should be read, 'As 2 is to 4, so is 6 to 12;' not 'As two are to four, so are six to twelve.' But when numerals denoting more than one, are used as adjectives, with a substantive expressed or understood, they must have a plural construction.". Bullions, Analyt, and Pract. Gram., 1849, p. 39.

OBS. 18.—Since nouns and adjectives aro different parts of speech, the suggestion, that, “Numeral adjectises are also names, or nouns,” is, upon the very face of it, a flat absurdity; and the notion that "the name of a number" above unity, conveys only and always the idea of unity, like an ordinary" singular noun," is an other. A number in arithmetic is most commonly an adjective in grammar; and it is always, in form, an expression that tells how many, or-"denotes how many things are spoken of."— Chase, p. 11. But the name of a number is also a number, whenever it is not made plural in form. Thus four is a number, but fours is not; so ten is a number, but tens is not. Arithmetical numbers, which run on to infinity, severally consist of a definite idea of how many; each is a precise count by the unit; one being the beginning of the series, and the measure of every successive step. Grammatical numbers are only the verbal forms which distinguish one thing from more of the same sort. Thus the word fours or tens, unless some arithmetical number be prefixed to it, signifies nothing but a mere plurality which repeats indefinitely the collective idea of four or ten.

OBS. 19.-All actual names of numbers calculative, except one, (for naught, though it fills a place among numbers, is, in itself, a mere negation of number; and such terms as oneness, unity, duality, are not used in calculation,) are collective nouns-a circumstance which seems to make the discussion of the present topic appropriate to the location which is here given it under Rule 15th. Each of them denotes a particular aggregate of units. And if each, as signifying one whole, may convey the idea of unity, and take a singular verb; each, again, as denoting so many units, may

quite as naturally take a plural verb, and be made to convey the idea of plurality. For the mere abstractness of numbers, or their separation from all "particular objects," by no means obliges us to limit them always to the construction with verbs singular. If it is right to say, "Two is an even number;" it is certainly no error to say, "Two are an even number." If it is allowable to say, "As 2 is to 4, so is 6 to 12;" it is as well, if not better, to say, "As two are to four, so are six to twelve." If it is correct to say, "Four is equal to twice two;" it is quite as grammatical to say, "Four are equal to twice two." Bullions bids say, "Twice two is four," and, "Three times two is six;" but I very much prefer to say, "Twice two are four," and, "Three times two are six." The Doctor's reasoning, whereby he condemns the latter phraseology, is founded only upon false assumptions. This I expect to show; and more-that the word which he prefers, is wrong.

OBS. 20. As to what constitutes the subject of the verb in multiplication, I have already noticed three different opinions. There are yet three or four more, which must not be overlooked in a general examination of this grammatical dispute. Dr. Bullions's notion on this point, is stated with so little consistency, that one can hardly say what it is. At first, he seems to find his nominative in the multiplicand, "used as a singular noun;" but, when he ponders a little on the text, "Twice two is four," he finds the leading term not to be the word "two," but the word "number," understood. He resolves, indeed, that no one of the four words used, "is in construction with" any of the rest; for he thinks, "The meaning is, The number two taken twice is equal to four.'" Here, then, is a fourth opinion in relation to the subject of the verb: it must be "number" understood. Again, it is conceded by the same hand, that, "When numerals denoting more than one, are used as adjectives, with a substantive expressed or understood, they must have a plural construction." Now who can show that this is not the case in general with the numerals of multiplication? To explain the syntax of "Twice two are four," what can be more rational than to say, "The sense is, Twice two units, or things, are four ?'" Is it not plain, that twice two things, of any sort, are four things of that same sort, and only so? Twice two duads are how many? Answer: Four duads, or eight units. Here, then, is a fifth opinion,—and a very fair one too, according to which we have for the subject of the verb, not "two," nor "twice," nor "twice two," nor "number," understood before “two," but the plural noun “units,” or “things,” implied in or after the multiplicand.

OBS. 21.-It is a doctrine taught by sundry grammarians, and to some extent true, that a neuter verb between two nominatives "may agree with either of them." (See Note 5th to Rule 14th, and the footnote.) When, therefore, a person who knows this, meets with such examples as, "Twice one are two;"-"Twice one unit are two units;"-"Thrice one are three ;"—he will of course be apt to refer the verb to the nominative which follows it, rather than to that which precedes it; taking the meaning to be, "Two are twice one;"-" Two units are twice one unit;" "Three are thrice one." Now, if such is the sense, the construction in each of these instances is right, because it accords with such sense; the interpretation is right also, because it is the only one adapted to such a construction; and we have, concerning the subject of the verb, a sixth opinion, a very proper one too,-that it is found, not where it is most natural to look for it, in the expression of the factors, but in a noun which is either uttered or implied in the product. But, no doubt, it is better to avoid this construction, by using such a verb as may be said to agree with the number multiplied. Again, and lastly, there may be, touching all such cases as, "Twice one are two," a seventh opinion, that the subject of the verb is the product taken substantively, and not as a numeral adjective. This idea, or the more comprehensive one, that all abstract numbers are nouns substantive, settles nothing concerning the main question, What form of the verb is required by an abstract number above unity? If the number be supposed an adjective, referring to the implied term units, or things, the verb must of course be plural; but if it be called a collective noun, the verb only follows and fixes "the idea of plurality," or "the idea of unity," as the writer or speaker chooses to adopt the one or the other.

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OBS. 22.—It is marvellous, that four or five monosyllables, uttered together in a common simple sentence, could give rise to all this diversity of opinion concerning the subject of the verb; but, after all, the chief difficulty presented by the phraseology of multiplication, is that of ascertaining, not "the grammatical subject of the verb," but the grammatical relation between the multiplier and the multiplicand-the true way of parsing the terms once, twice, three times, &c., but especially the word times. That there must be some such relation, is obvious; but what is it? and how is it to be known? To most persons, undoubtedly, "Twice two," and, "Three times two," seem to be regular phrases, in which the words cannot lack syntactical connexion; yet Dr. Bullions, who is great authority with some thinkers, denies all immediate or direct relation between the word two," and the term before it, preferring to parse both "twice" and "three times" as adjuncts to the participle "taken," understood. He says, "The adverb 'twice' is not in construction with 'tuo,' and consequently does not make it plural." His first assertion here is, in my opinion, untrue; and the second implies the very erroneous doctrine, that the word twice, if it relate to a singular term, will "make it plural." From a misconception like this, it probably is, that some who ought to be very accurate in speech, are afraid to say, "Twice one is two," or, "Thrice one is three," judging the singular verb to be wrong; and some there are who think, that ". usage will not permit" a careful scholar so to speak. Now, analysis favours the singular form here; and it is contrary to a plain principle of General Grammar, to suppose that a plural verb can be demanded by any phrase which is made collectively the subject of the assertion. (See Note 3d, and Obs. 13th, 14th, 15th, and 16th, under Rule 14th.) Are is, therefore, not required here; and, if allowable, it is so only on the supposition that the leading nominative is put after it.

OBS. 23.-In Blanchard's small Arithmetic, published in 1854, the following inculcations occur: "When we say, 3 times 4 trees are 12 trees, we have reference to the objects counted; but in saying 3 times 4 is twelve, we mean, that 3 times the number 4, is the number 12. Here we use 4 and 12, not as numeral adjectives, but as nouns, the names of particular numbers, and as such, each conveys the idea of unity, and the entire expression is the subject of is, and conveys the idea of unity."P. iv. Here we have, with an additional error concerning "the entire expression," a repetition of Dr. Bullions's erroneous assumption, that the name of a particular number, as being "a singular noun," must "convey the idea of unity," though the number itself be a distinct plurality. These men talk as if there were an absurdity in affirming that "the number 4" is plural! But, if four be taken as only one thing, how can three multiply this one thing into twelve? It is by no means proper to affirm, that, "Every four, taken three times, is, or are, twelve;" for three instances, or times," of the figure 4, or of the word four, are only three 4's, or three verbal fours. And is it not because "the number 4" is plural—is in itself four units—and because the word four, or the figure 4, conveys explicitly the idea of this plurality, that the multiplication table is true, where it says, "3 times 4 are 12?" It is not right to say, "Three times one quaternion is twelve;" nor is it quite unobjectionable to say, with Blanchard, “3 times the number 4, is the number 12." Besides, this pretended interpretation explains nothing. The syntax of the shorter text, "3 times 4 is 12," is in no way justified or illustrated by it. Who does not perceive that the four here spoken of must be four units, or four things of some sort; and that no such "four," multiplied by 3, or till "3 times," can "convey the idea of unity," or match a singular verb? Dr. Webster did not so conceive of this "abstract number," or of "the entire expression" in which it is multiplied; for he says, "Four times four amount to sixteen."-American Dict., w. Time.

OBS. 24.-In fact no phrase of multiplication is of such a nature that it can, with any plausi bility be reckoned a composite subject of the verb. Once, twice, and thrice, are adverbs; and each of them may, in general, bo parsed as relating directly to the multiplicand. Their construction, as well as that of the plural verb, is agreeable to the Latin norm; as, when Cicero says of somebody, "Si, bis bina quot essent, didicisset," If he had learned how many twice two are."— See Ainsworth's Dict., w. Binus. The phrases, "one time," for once, and "two times," for twice, seem puerile expressions: they are not often used by competent teachers. Thrice is a good word, but more elegant than popular. Above twice, we use the phrases, three times, four times, and the like, which are severally composed of a numeral adjective and the noun times. If these words were united, as some think they ought to be, the compounds would be adverbs of time repeated; as, threetimes, fourtimes, &c., analogous to sometimes. Each word would answer, as each phrase now does, to the question, How often? These expressions are taken by some as having a direct adverbial relation to the terms which they qualify; but they are perhaps most commonly explained as being dependent on some preposition understood. See Obs. 1st on Rule 5th, and Obs. 6th on Rule 7th.

OBS. 25.-In multiplying one only, it is evidently best to use a singular verb: as, "Twice naught is naught;"-"Three times one is three." And, in multiplying any number above one, judge a plural verb to be necessary: as, "Twice two are four;"-"Three times two are six:" because this number must be just so many in order to give the product. Dr. Bullions says, "We should say, 'Three times two is six,' because the meaning is, ‘Two taken three times is six." This is neither reasoning, nor explanation, nor good grammar. The relation between "two" and "three," or the syntax of the word "times," or the propriety of the singular verb, is no more apparent in the latter expression than in the former. It would be better logic to affirm, “We should say, 'Three times two are six;' because the meaning is, 'Two (units), taken for, to, or till three times, are six.'" The preposition till, or until, is sometimes found in use before an expression of times numbered; as, "How oft shall I forgive? till seven times? I say not unto thee, Until seven times; but, Until seventy times seven."- -Matt., xviii, 21. But here is still a difficulty with repect to the multiplying term, or the word "times." For, unless, by an unallowable ellipsis, "seventy times seven," is presumed to mean, "seventy times of seven," the preposition Until must govern, not this noun "times," expressed, but an other, understood after "seven;" and the meaning must be, "Thou shalt forgive him until seventy-times seven times:" or "until seven times taken for, to, or till, seventy times."

OBS. 26. With too little regard to consistency, Dr. Bullions suggests that when "we make times' the subject of the verb," it is not "really" such, but "is in the objective of number." He is, doubtless, right in preferring to parse this word as an objective case, rather than as a nominative, in the construction to which he alludes; but to call it an objective of number," is an uncouth error, a very strange mistake for so great a grammarian to utter: there being in grammar no such thing as "the objective of number;" nothing of the sort, even under his own "Special Rule," to which he refers us for it! And, if such a thing there were, so that a number could be "put in the objective case without a governing word," (see his § 828,) the plural word times, since it denotes no particular aggregate of units, could never be an example of it. It is true that times, like days, weeks, and other nouns of time, may be, and often is, in the objective case without a governing word expressed; and, in such instances, it may be called the objective of repetition, or of time repeated. But the construction of the word appears to be such as is common to many nouns of time, of value, or of measure; which, in their relation to other words, seem to resemble adverbs, but which are usually said to be governed by prepositions understood: as, "Three days later;" i. e., "Later by three days."- -"Three shillings cheaper;" i. e., "Cheaper by three shillings."-"Seven times hotter;" i. e., "Hotter by seven times."-" Four feet high;" i. e.,

"High to four feet."-" Ten years old;" i. e., "Old to ten years."-" Five times ten;" i. e., "Ten by five times;" or, perhaps, "Ten taken till five times."

NOTE TO RULE XV.

A collective noun conveying the idea of unity, requires a verb in the third person, singular; and generally admits also the regular plural construction: as, "His army was defeated.”- "His armies were defeated."

IMPROPRIETIES FOR CORRECTION.

FALSE SYNTAX UNDER RULE XV.

UNDER THE RULE ITSELF.-THE IDEA OF PLURALITY.

"The gentry is punctilious in their etiquette."

[FORMULE-Not proper, because the verb is is of the singular number, and does not correctly agree with its nominative gentry, which is a collective noun conveying rather the idea of plurality. But, according to Rule 15th, "When the nominative is a collective noun conveying the idea of plurality, the verb must agree with it in the plural number." Therefore, is should be are; thus, "The gentry are punctilious in their etiquette."]

"In France the peasantry goes barefoot, and the middle sort makes use of wooden shoes."HARVEY: Priestley's Gram., p. 188. "The people rejoices in that which should cause sorrow." -See Murray's Exercises, p. 49. "My people is foolish, they have not known me."-Jer., iv, 22; Lowth's Gram., p. 75. "For the people speaks, but does not write."-Philological Museum, i,

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"So that all the people that was in the camp, trembled."-Exodus, xix, 16. "No company likes to confess that they are ignorant."-Student's Manual, p. 217. "Far the greater part of their captives was anciently sacrificed."-Robertson's America, i, 339. "Above one half of them was cut off before the return of spring."—Ib., ii, 419. "The other class, termed Figures of Thought, supposes the words to be used in their proper and literal meaning."-Blair's Rhet., p. 133; Murray's Gram., 337. "A multitude of words in their dialect approaches to the Teutonic form, and therefore afford excellent assistance."-Dr. Murray's Hist. of Lang., i, 148. "A great majority of our authors is defective in manner."-James Brown's Crit. "The greater part of these new-coined words has been rejected."-Tooke's Diversions, ii, 445. "The greater part of the words it contains is subject to certain modifications and inflections."-The Friend, ii, 123. "While all our youth prefers her to the rest."-Waller's Poems, p. 17. "Mankind is appointed to live in a future state."-Butler's Analogy, p. 57. "The greater part of human kind speaks and acts wholly by imitation."- Wright's Gram., p. 169. "The greatest part of human gratifications approaches so nearly to vice."-Ibid.

"While still the busy world is treading o'er

The paths they trod five thousand years before."-Young.

UNDER THE NOTE.-THE IDEA OF UNITY.

"In old English this species of words were numerous."-Dr. Murray's Hist. of Lang., ii, 6. "And a series of exercises in false grammar are introduced towards the end."-Frost's El. of E. Gram., p. iv. "And a jury, in conformity with the same idea, were anciently called homagium, the homage, or manhood."- Webster's Essays, p. 296. "With respect to the former, there are indeed plenty of means."-Kames, El. of Crit., ii, 319. "The number of school districts have increased since the last year."-Governor Throop, 1832. "The Yearly Meeting have purchased with its funds these publications."-Foster's Reports, i, 76. "Have the legislature power to prohibit assemblies?"-Wm. Sullivan. "So that the whole number of the streets were fifty."-Rollin's Ancient Hist., ii, 8. "The number of inhabitants were not more than four millions."-SMOLLETT: see Priestley's Gram., p. 193. "The House of Commons were of small weight."-HUME: 1b., p. "The assembly of the wicked have enclosed me."-Psal. xxii, 16; Lowth's Gram., p. 75. 'Every kind of convenience and comfort are provided."-Com. School Journal, i, 24. "Amidst the great decrease of the inhabitants of Spain, the body of the clergy have suffered no diminution; but has rather been gradually increasing."-Payne's Geog., ii, 418. "Small as the number of inhabitants are, yet their poverty is extreme."-Ib., ii, 417. "The number of the names were about one hundred and twenty."-Ware's Gram., p. 12; see Acts, i, 15.

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RULE XVI.-FINITE VERBS.

When a Verb has two or more nominatives connected by and, it must agree with them jointly in the plural, because they are taken together: as, "True rhetoric and sound logic are very nearly allied."-Blair's Rhet., Aggression and injury in no case justify retaliation."— Wayland's Moral Science, p. 406.

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'Judges and senates have been bought for gold,
Esteem and love were never to be sold."-Pope.

EXCEPTION FIRST.

When two nominatives connected by and serve merely to describe one person or thing, they are either in apposition or equivalent to one name, and do not require a plural verb; as, “Immediately comes a hue and cry after a gang of thieves."-L'Estrange. "The hue and cry of the country pursues him."-Junius, Letter xxiii. "Flesh and blood [i. c. man, or man's nature,] hath not revealed it unto thee."-Matt., xvi, 17. "Descent and fall to us is adverse."-Milton, P, L., ii, 76. "This philosopher and poet was banished from his country."-"Such a Saviour and Redeemer is actually provided for us."- ·Gurney's Essays, p. 386. "Let us then declare what great things our God and Saviour has done for us."-Dr. Scott, on Luke viii. "Toll, tribute, and custom, was paid unto them.”—Ezra, iv, 20.

"Whose icy current and compulsive course

Ne'er feels retiring ebb, but keeps due on."-Shakspeare.

EXCEPTION SECOND.

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When two nominatives connected by and, are emphatically distinguished, they belong to different propositions, and, if singular, do not require a plural verb; as, "Ambition, and not the safety of the state, was concerned."-Goldsmith. Consanguinity, and not affinity, is the ground of the prohibition."-Webster's Essays, p. 324. "But a modification, and oftentimes a total change, takes place."--Maunder. Somewhat, and, in many circumstances, a great deal too, is put upon us." Butler's Analogy, p. 108. "Disgrace, and perhaps ruin, was the certain consequence of attempting the latter."-Robertson's America, i, 434.

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"Ay, and no too, was no good divinity."-Shakspeare.
"Love, and love only, is the loan for love."— Young.

EXCEPTION THIRD.

When two or more nominatives connected by and are preceded by the adjective each, every, or no, they are taken separately, and do not require a plural verb; as, "When no part of their substance, and no one of their properties, is the same."-Bp. Butler. "Every limb and feature appears with its respective grace.”—Steele. "Every person, and every occurrence, is beheld in the most favourable light."--Murray's Key, p. 190. Each worm, and each insect, is a marvel of creative power."

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"Whose every look and gesture was a joke

To clapping theatres and shouting crowds."-Young.

EXCEPTION FOURTH.

When the verb separates its nominatives, it agrees with that which precedes it, and is understood to the rest; as, "The earth is the Lord's, and the fullness thereof."-Murray's Exercises, p. 36.

"Disdain forbids me, and my dread of shame."-Milton.

-Forth in the pleasing spring,

Thy beauty walks, thy tenderness, and love."-Thomson.

OBSERVATIONS ON RULE XVI.

OBS. 1.-According to Lindley Murray, (who, in all his compilation, from whatever learned authorities, refers us to no places in any book but his own,) "Dr. Blair observes, that 'two or more substantives, joined by a copulative, must always require the verb or pronoun to which they refer, to be placed in the plural number:' and this," continues the great Compiler, "is the general sentiment of English grammarians."-Murray's Gram., Vol. i, p. 150. The same thing is stated in many other grammars: thus, Ingersoll has the very same words, on the 238th page of his book; and R. C. Smith says, "Dr. Blair very justly observes," &c.-Productive Gram., p. 126. I therefore doubt not, the learned rhetorician has somewhere made some such remark; though I can neither supply the reference which these gentlemen omit, nor vouch for the accuracy of their quotation. But I trust to make it very clear, that so many grammarians as hold this sentiment, are no great readers, to say the least of them. Murray himself acknowledges one exception to this principle, and unconsciously furnishes examples of one or two more; but, in stead of placing the former in his Grammar, and under the rule, where the learner would be likely to notice it, he makes it an obscure and almost unintelligible note, in the margin of his Key, referring by an asterisk to the following correction: "Every man and every woman was numbered."-Murray's Gram., 8vo, Vol. ii, p. 190. To justify this phraseology, he talks thus: "Whatever number of nouns may be connected by a conjunction with the pronoun EVERY, this pronoun is as applicable to the whole mass of them, as to any one of the nouns; and therefore the verb is correctly put in the singular number, and refers to the whole separately and individually considered."—. So much, then, for "the pronoun EVERY!" But, without other exceptions, what shall be done with the following texts from Murray himself? "The flock, and not the fleece, is, or ought to be the object of the shepherd's care.”—Ib, ii, 184. "This prodigy of learning, this scholar, critic, and antiquary, was entirely destitute of breeding and civility."—Ib., ii, 217. And, in the following line,

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