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LONDON:

ALFRED SWEETING, FRINTER, BARTLETT'S BUILDINGS,

FOR

1850.

PART I. GENERAL INFORMATION ON SUBJECTS OF MATHEMATICS, NATURAL PHILOSOPHY AND HISTORY, CHRONOLOGY, GEOGRAPHY, STATISTICS, &c.

I.-ON ANCIENT AND MODERN USAGE IN

RECKONING,

THE year 1850, to which the present number of our work belongs, is a year one designation of which depends upon the settlement of a controversy. About the end of last century, there was a fierce contest upon its proper termination: some said that the nineteenth century began with January 1, 1800, others with January 1, 1801. The former would say that 1850 is the first year of the second half of the century, the latter that it is the last year of the first half. In taking up this subject, we do not look at the century question (which is of no consequence whatever, and is easily settled in favour of the second-named interpretation) so much as at the mode in which it arose, and at the genus of which it is a species. We make it a peg on which to hang a short dissertation on the distinction of ancient and modern reckoning, which the lawyer generally ignores, the scholar often disregards, and the mathematician almost always denies the existence of upon demonstration.

Those who are accustomed to settle the meaning of ancient phrases by self-examination, will find some strange conclusions arrived at by us; but nothing, we believe, which may not be justified by even a moderate examination of old writers.

Language and counting both came before the logical discussion of either. It is not allowable to argue that something is or was, because it ought to be or ought to have been. That two negatives make an affirmative, ought to be: if no man have done nothing, the man who has done nothing does not exist, and every man has done something. But in Greek, and in uneducated English, it is unquestionable that “no man has done nothing" is only an emphatic way of saying that no man has done anything ; and it would be absurd to reason that it could not have been so, because it should not.

B

The manner in which any common reckoning of time is made would, we might suppose, be a matter admitting of neither dispute nor ambiguity, and of little, if any, change. It is the object of this paper to point out that such is not the case-that language is to this day but ill adapted to express precise meaning—that serious and not sufficiently marked changes have taken place in the modes of reckoning-and that the confusion which these changes have made continues.

At the same time, there is nothing on which we are so positive, each for himself, as upon what is and what is not, right in the matter of reckoning time. Every one has, or thinks he has, a permanent meaning attached to the phrases in common use; which meaning no small number think these phrases must of necessity bear: others, aware of the very different senses which the phrases have borne, are content to admit that their meanings are conventional, but are prepared to contend for the existence of a well-settled and universal convention.

Suppose that at ten o'clock on Monday morning, a person engages to do something in four days. There are four distinct meanings, each of which will bear argument or citation of authority, and each of which may have been in the understanding of the speaker or of the hearer.

First, not counting Monday, on which the engagement is made, Tuesday, Wednesday, Thursday, Friday, may be claimed as appertaining to the four days; in such manner that the pledge cannot be considered as broken, until some moment of Saturday has arrived without its performance. This is one extreme case, and is the debtor's version.

Secondly, counting Monday, the day of the engagement, the four days may be reckoned as Monday, Tuesday, Wednesday, Thursday, and the claimant may consider that at any moment of Thursday proof of performance is due. This is the other extreme case, and is the creditor's version.

Thirdly, different tendencies towards a mixed mode of interpretation may lead to the result that Friday is the day on which the performance may be claimed : and for this many will pronounce, when they consider the question, from mere indecision between the preceding two cases.

Fourthly, those who consider a day as capable of beginning at any moment will say that from ten o'clock on Monday morning to ten o'clock on Friday morning it is four complete days; and that therefore proof of performance may be claimed on Friday, but not before ten o'clock in the morning.

If we had to make a meaning for the phrase, we might well fix on the third, which perhaps would be most generally agreed on in our day as the proper interpretation. But we are to con

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