unless it be allowable to say that it agrees with the Arabic mode of notation. This kind of agreement it has, in common with every other base. It is this that gives it character. On this account alone it is believed by many to be the perfection of harmony. They get the base of numeration and the mode of notation so mingled together, that they cannot separate them sufficiently to obtain a distinct idea of either; and some are not conscious that they are distinct, but see in the Arabic mode nothing save decimal notation, and attribute to it all those high qualities that belong to the mode only. The Arabic mode is an invention of the highest merit, not surpassed by any other; but the admiration that belongs to it is thus bestowed upon a quite commonplace idea, a misapplication, which, in this as in many other cases, arises from the fact, that it is much easier to admire than to investigate. This result of carelessness, if isolated, might be excused; but all errors are productive, and it should be remembered that this one has produced that extraordinary perversion of truth to be found in the reply to the question, How is all this confusion to be brought into harmony? It has produced it not only in words, but in deed. Was it not this reply that led the French commission to extend the use of the present base from numeration to gradation also, under the delusive hope of producing a perfectly homogeneous system, that would be practical also? Was it not under its influence, that, adhering to the base to which the world had been so long accustomed, instead of attempting to regulate ideal division by real, which might have led to the adoption of the true base and a practical system, they committed the one great error of endeavoring to reverse true order, by forcing real division into conformity with a preconceived ideal? This attempt was made at a time supposed by many to be peculiarly suited to the purpose, a time of changes. It was a time of changes, truly; but these were the result of high excitement, not of quiet thought, such as the subject requires,—a time for rushing forward, not for retracing misguided steps. Accordingly, a system was produced which from its magnitude and importance was truly imposing, and which, to the present day, is highly applauded by all those who, under the influence of the error alluded to, conceive decimal numeration to be a sacred truth: applauded, not because of its adaptation to commerce, but simply because of its beautiful proportions, its elegant symmetry, to say nothing of the array of learning and power engaged in its production and inauguration: imposing, truly, and alike on its authors and admirers; for the qualities they so much admire are not peculiar to the decimal base, but to the use of one and the same base for numeration, notation, and gradation. But if the base ten agrees with nothing, over, on, or under the earth, can it be the best for scientific use? can it be at all suited to commercial purposes? If true order is the object to be attained, and that for the sake of its utility, then agreement between real and ideal division is the one thing needful, the one essential change without which all other changes are vain, the only change that will yield the greatest good to the greatest number,—a change, which, as volition is with the ideal, and inertia with the real, can be attained only by adaptation of the ideal to the real.
A full investigation of the existing heterogeneous or fragmentary system will lead to the discovery that it contains two elements which are at variance with natural division and with each other, and that the unsuccessful issue of every attempt at regulation hitherto made has been the proper result of the mistake of supposing agreement between those elements to be a possible thing.
The first element of discord to be considered is the division of things by personal proportion, as by fathom, yard, cubit, foot, etc. It is obvious at a glance, that these do not agree with binary division, nor with decimal, nor yet with each other. It is this element that has suggested the duodecimal base, to which some adhere so tenaciously, apparently because they have not ascertained the essential quality of a base.
The second is the numeration of things by personal parts, as fingers, hands, etc.,—suggesting a base of numeration that has no agreement with the binary, nor with personal proportion, neither can it have with any proper general system. Are there any things in Nature that exist by tens, that associate by tens, that separate into tenths? Are there any things that are sold by tens, or by tenths? Even the fingers number eight, and, had there been any reflection used in the adoption of a base of numeration, the thumbs would not have been included. The ease with which the simplest arithmetical series may be continued led our fathers quietly to the adoption, first, of the quinary, and second, of the decimal group; and we have continued its use so quietly, that its propriety has rarely been questioned; indeed, most persons are both surprised and offended, when they hear it declared to be a purely artificial base, proper only to abstract numbers.
The binary base, on the contrary, is natural, real, simple, and accords with the tendency of the mind to simplify, to individualize. In business, who ever thinks of a half as two-fourths, or three-sixths, much less as two-and-a-half-fifths, or three-and-a-half-sevenths? For division by two produces a half at one operation; but with any other divisor, the reduction is too great, and must be followed by multiplication. Think of calling a half five-tenths, a quarter twenty-five-hundredths, an eighth one-hundred-and-twenty-five-thousandths! Arithmetic is seldom used as a plaything. It generally comes into use when the mind is too much occupied for sporting. Consequently, the smallest divisor that will serve the purpose is always preferred. A calculation is an appendage to a mercantile transaction, not a part of the transaction itself; it is, indeed, a hindrance, and in large business is performed by a distinct person. But even with him, simplicity, because necessary to speed, is second in merit only to correctness.
The binary base is not only simple, it is real. Accordingly, it has large agreement with the popular divisions of weights, etc. Grocers' weights, up to the four-pound piece, and all their measures, are binary; so are the divisions of the yard, the inch, etc.
It is not only simple and real, it is natural. On every hand, things may be found that are duplex in form, that associate in pairs, that separate into halves, that may be divided into two equal parts. Things are continually sold in pairs, in halves, and in quantities produced by halving.
The binary base, therefore, is here proposed, as the only proper base for gradation; and the octonal, as the true commercial base, for numeration and notation: two bases which in combination form a binoctonal system that is at once simple, comprehensive, and efficient.
MY LAST LOVE
I had counted many more in my girlhood, in the first flush of blossoming,—and a few, good men and true, whom I never meet even now without an added color; for, at one time or another, I thought I loved each of them.
"Why didn't I marry them, then?"
For the same reason that many another woman does not. We are afraid to trust our own likings. Too many of them are but sunrise vapors, very rosy to begin with, but by mid-day as dingy as any old dead cloud with the rain all shed out of it. I never see any of those old swains of mine, without feeling profoundly thankful that I don't belong to him. I shouldn't want to look over my husband's head in any sense. So they all got wives and children, and I lived an old maid,—although I was scarcely conscious of the state; for, if my own eyes or other people's testimony were to be trusted, I didn't look old, and I'm quite sure I didn't feel so. But I came to myself on my thirty-second birthday, an old maid most truly, without benefit of clergy. And thereby hangs this tale; for on that birthday I first made acquaintance with my last love.
Something like a month before, there had come to Huntsville two gentlemen in search of game and quiet quarters for the summer. They soon found that a hotel in a country village affords little seclusion; but the woods were full of game, the mountain-brooks swarmed with trout too fine to be given up, and they decided to take a house of their own. After some search, they fixed on an old house, (I've forgotten whose "folly" it was called,) full a mile and a half from town, standing upon a mossy hill that bounded my fields, square and stiff and weather-beaten, and without any protection except a ragged pine-tree that thrust its huge limbs beneath the empty windows, as though it were running away with a stolen house under its arm. The place was musty, rat-eaten, and tenanted by a couple of ghosts, who thought a fever, once quite fatal within the walls, no suitable discharge from the property, and made themselves perfectly free of the quarters in properly weird seasons. But money and labor cleared out all the
