Something resembling this is the old interpretation of the intercalary day in leap-year. It was not a new and additional day, nor counted as such: it would not have been held correct to say that leap-year has 366 days. It is one day repeated and the two days of bis-sextile have but one name. It counted as one day in the calendar: and was allowed for, not by letting it take a letter, and altering the letters of the following days but by letting the second sextile day keep the letter of the first, and shifting the dominical letter of the year on its arrival. Moreover, the double length of the bissextile was not allowed to add a day to the moon's age at the time. So that the idea mentioned in the note, of the double day representing the long day of Joshua, is a misapprehension of easier occurrence than might have been supposed.

A person who is born on the 10th of June, in our day, counts a year as completed so often as a 10th of June arrives. He says, I shall not be of age until the 10th of June; ask him how old he is on the 9th, and he will say, I shall not be of age till to-morrow. If he were born at noon, it is true that he does not complete twenty-one years of days divisible into fractions until noon of the 10th. Nevertheless, in the law, which here preserves the old reckoning, he is of full age on the ninth : though he were born a minute before midnight on the 10th, he is of age to execute a settlement at a minute after midnight on the morning of the 9th, forty-eight hours all but two minutes before he has drawn breath for the space of twentyone years. The law reasons thus ;-there are no parts of days; he who is born on the 10th takes the whole of the 10th as part of his life; he is a year old when he has completed 365 days; the 9th of next year is his 365th day; as soon as he has commenced* the 9th, he has lived through the whole of it, for a day has no parts; therefore he has lived a complete year, or is one year old, as soon as the 9th arrives. And the conclusion is unavoidable so soon as it is granted that a day has no parts. The anniversary of birth used to be celebrated as the first day of a new year; it is now considered as the completion of the old one.

the intercalary day was called bissextile, because each year contributed twice six points towards it by a point he means, as he says, a quarter of an hour. Each year then, according to him, contributes three hours: so that not only does he himself reckon by days and pass over nights, but he asserts his belief that such had been the custom of his predecessors.

"Five years auld exactly this blessed day,' answered the lady, 'so we may look into the English gentleman's paper.'....... 'No, my dear, not till to-morrow. The last time I was at Quarter Sessions, the Sheriff told us that...... a term day is not begun till it's ended.'-'That sounds like nonsense, my dear.'-' May be so, my dear, but it may be very good law for all that."-Guy Mannering. Whether the Scotch law differs from the English, or Scott intended the Laird to blunder the point, or blundered it himself, are matters which I must leave to the learned,

We can never without explanation get at the meaning of a person who tells us he was ill for two days. Some will apply the phrase to the last half of one day and the first half of the next; some to two whole days with a fraction before and after; some to an interval of forty-eight hours, made out of one day, and parts of the preceding and following.

But there is another difference between old and new times yet more remarkable, for we have nothing of it now: whereas, in things indivisible, we count with our fathers, and should say, in buying an acre of land, that the result has no parts, and that the purchaser, till he owns all the ground, owns none, the change of possession being instantaneous. This second difference lies in the habit of considering nothing, nought, zero, cipher, or whatever it may be called, to be at the beginning of the scale of numbers. Count four days from Monday: we should now say Tuesday, Wednesday, Thursday, Friday; formerly it would have been Monday, Tuesday, Wednesday, Thursday. Had we asked, what at that rate is the first day from Monday, all would have stared at a phrase they had never heard. Those who were capable of extending language would have said, Why it must be Monday itself: the rest would have said, There can be no first day from Monday, for the day after is Tuesday, which must be the second day; Monday, one; Tuesday, two.

We should say, Monday does not count, being the day itself we reckon from: in Roman numeration, described by us, it would be, every day counts: though a Roman would probably also have said that Monday did not count. His scale of numeration beginning at one, the mere repetition of one would not have been considered as counting, which would begin with the entrance of plurality into the reckoning. We know that it was long usual to deny* that one is a number: an assertion derived partly from the idea of plurality being attached to the word. number, which would have justified the assertion that enumeration begins at two, not at one, and partly from unity being a kind of starting point.

When, at the time of the reformation of the Calendar, the moon of the heavens was full, as we should say, four days before

* This denial lurks in the following old rhyme, which some will remember to have heard, and which Mr. Halliwell has inserted in his collection of nursery rhymes:

One's none,
Two's some,
Three's a many,
Four's a penny,

Five's a little hundred.

The last line refers to five score, the so-called hundred being more usually six score, The first line, looked at etymologically, is One is not one, and the change of thought by which none, the denial of one, comes to be associated with the denial of plurality, is

curious.

the ecclesiastical moon, the phrase was five days: and when a mode of reckoning this by syllables was invented (see the Companion for 1845, p. 22), Nova luna hic, the reckoning started with its first syllable on the day of the ecclesiastical

moon.

European counting, antecedent to the introduction of the Indian numerals, was entirely fashioned upon the Roman system, in which no symbol for nothing exists. The Indian zero, or cipher, in the first instance, was not an express symbol for nothing, any more than the blank between two words is an express symbol for no amount of letter-press: it merely served the purpose of the blank type, namely, to keep the rest in their places. The notion of absence of value, or value not yet attained, as a starting point from which to reckon the introduction of successive amounts of value, was an idea of very slow growth, an ultimate consequence of the suggestion of the symbol 0, but not a part of its first intention. The complete mastery of this notion is among the masonic signs by which one mathematician can detect another in his writings on any subject. But many have it now, to an extent which makes 0, 1, 2, 3, 4, &c., a common series enough; though those who have cast their eyes over books of arithmetic will remember that 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, is a much more usual exposition of the numeral symbols than 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Our language now groans under the difficulty of expressing the various ways in which the two terms may be connected with the interval. From Monday to Thursday may mean both inclusive, or both exclusive, or either inclusive and the other exclusive. But this is not the fault of our language, so much as of our imperfect habits: a complete distinction might be made without forcing a single word. For instance

From Monday to Thursday

Between Monday and Thursday
After Monday to Thursday
From Monday before Thursday

Monday, Tuesday, Wednesday,
Thursday

Tuesday, Wednesday

Tuesday, Wednesday, Thursday
Monday, Tuesday, Wednesday.

It is not by any means certain, in our language, whether the word until includes what follows or not: "until Thursday," when it refers to an action which does not occupy the whole day, would certainly imply that the day is broken by the action, as in "I remain until Thursday." But take this sentence"In England, preserve old style until September 14, 1752;" is September 14 the last day of old style or the first day of new? In Roman reckoning it would be both, and this sentence would make us sure that September 15 (that would have been)

was the first of the nominal days omitted in the change of style. But, though it be frequently said that old style lasted till September 14, it means that September 2 was the last day of old style, and that, to use the words of the act, "the Natural Day next immediately following the said Second Day of September, shall be called, reckoned, and accounted, to be the Fourteenth Day of September."

There was no confusion as to this matter, of old; for the reckoning always included both its terms or endings, unless otherwise distinctly specified. Whenever it did not do so, the exception required statement. In matters of law, an extension was sometimes admitted by way of privilege, where the usual interpretation would involve penalty or forfeiture: but the distinctness with which this is stated causes the exceptions to confirm the rule. Taking up an old digest of the canon law, we find it stated that in the days of a citation the day of service is not counted in the term; so that a man cited on Monday to appear within three days need not appear before Thursday. When a benefice lapsed to the bishop by non-presentation on the part of the patron, it is stated that the day on which the vacancy occurred was not counted; and the interference of a bishop on the 6th of October, the vacancy having occurred on the 6th of July, was held void. But the case was recent (1703), and the compiler of the digest seems to doubt that the decision was according to the old law.

The French to this day speak of this day week as huit jours from to-day (which is therefore included), and of this day fortnight as quinze jours. We use seven and fourteen; but it is not to be inferred that the mode of counting is different. For our old reckoning is by nights, as was that of the ancient Germans; this day week was "this day se'nnight," and this day two weeks is still this day fortnight (fourteen nights). Now from Wednesday to Wednesday there are but seven nights intervening, though the inclusion of both Wednesdays may make eight days.

In music, the note immediately above another is not merely called the second but the second above: though, in modern idiom, the ascent being A, B, C, &c., the second above A must be C. And there being seven notes in the scale, the A which comes next above any A is called its eighth, or octave ; and the next A the fifteenth, after the manner in which the French reckon days, or that in which the day week of a saint's day is called the octave of the Saint. But one of the most decided effects of the old custom of counting both terms as part of the period is the practice of calling the time from the 1st of January to the 1st of January, not a year, but a year and a day. The

...

origin of this phrase we take to be obvious enough, though it may be questioned whether those who have given it have always seen how it arose. Coke expressly lays it down that in the phrase year and day, the day from which reckoning is made must be included; but without any allusion to the mode of entrance of the phrase. Cowell, in his Interpreter, says "Year and day. is a time thought in construction of our common law, fit in many cases to determine a right in one, and to work an usucapion or prescription in another:" he might have added that it is frequently mentioned in old statutes. And in almost all the cases then cited, it is obviously either an allowance to avoid hardship, or a stretch of the term by the king's prerogative, for the benefit of the crown. In old poetry it is a very common term, and its imitators frequently do not understand it. In Walter Scott's ballad of The Noble Moringer,' said by him to be translation from old German, the translation has what we should not believe to be in the original, unless we saw it. The lady has engaged to await her husband's return seven years and a day, according to which, by the old method of counting, she would be at liberty to marry again on any hour of what we should call that day seven years. But the ballad (the translation at least) makes the lady, who is true to the letter of her word, sit waiting till twelve o'clock at night on that day seven years, before she will have the ceremony performed with her new bridegroom. The husband arrives just in time, and the lady says

We will answer for it, that in the fourteenth century, the lady would not have waited till the odd day was finished. In the ballad called the Eve of St. John' there is a similar failure of attention to the old custom. The baron of that ballad goes away for "three days' space," and on his return the page, who is a spy on the lady, tells him where she has walked for three successive nights; according to which, in the language of the time, the baron was away for four days' space.

The necessity of taking in the terminus of reckoning on each side, follows immediately from one being the commencement of all counting; those who begin from nought, make 0 to represent the initial term, from which they reckon. The former reckon three from Wednesday to Friday; the latter two. The Romans carried the former process to its extreme; or ra