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 plausibility be reckoned a composite subject of the verb. Once, twice, and thrice, are adverbs; and each of them may, in general, be 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,