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 cobwebs, (for ghosts are but spiritual cobwebs, you know,) and the old house soon wore a charming air of rustic comfort.
I used to look over sometimes, for it was full in view from my chamber-windows, and see the sportsmen going off by sunrise with their guns or fishing-rods, or lying, after their late dinner, stretched upon the grass in front of the house, smoking and reading. Sometimes a fragment of a song would be dropped down from the lazy wings of the south wind, sometimes a long laugh filled all the summer air and frightened the pinewood into echoes, and, altogether, the new neighbors seemed to live an enviable life. They were very civil people, too; for, though their nearest path out lay across my fields, and close by the doorway, and they often stopped to buy fruit or cream or butter, we were never annoyed by an impertinent question or look. Once only I overheard a remark not altogether civil, and that was on the evening before my birthday. One of them, the elder, said, as he went away from my house with a basket of cherries, that he should like to get speech with that polyglot old maid, who read, and wrote, and made her own butter-pats. The other answered, that the butter was excellent at any rate, and perhaps she had a classical cow; and they went down the lane laughingly disputing about the matter, not knowing that I was behind the currant-bushes.
"Polyglot old maid!" I thought, very indignantly, as I went into the house. "I've a mind not to sell them another cake of my butter. But I wonder if people call me an old maid. I wonder if I am one."
I thought of it all the evening, and dreamt of it all night, waking the next morning with a new realization of the subject. That first sense of a lost youth! How sharp and strong it comes! That suddenly opened north door of middle life, through which the winter winds rush in, sweeping out of the southern windows all the splendors of the earlier time; it is like a sea-turn in late summer. It has seemed to be June all along, and we thought it was June, until the wind went round to the east, and the first red leaf admonished us. By-and-by we close, as well as we may, that open door, and look out again from the windows upon blooms, beautiful in their way, to which some birds yet sing; but, alas! the wind is still from the east, and blows as though, far away, it had lain among icebergs.
So I mused all the morning, watering the sentiment with a bit of a shower out of my cloud; and when the shadows turned themselves, I went out to see how old age would look to me in the fields and woods. It was a delicious afternoon, more like a warm dream of hay-making, odorous, misty, sleepily musical, than a waking reality, on which the sun shone. Tremulous blue clouds lay down all around upon the mountains, and lazy white ones lost themselves in the waters; and through the dozing air, the faint chirp of robin or cricket, and ding of bells in the woods, and mellow cut of scythe, melted into one song, as though the heart-beat of the luscious midsummer-time had set itself to tune.
I walked on to loiter through the woods. No dust-brush for brain or heart like the boughs of trees! There dwells a truth, and pure, strong health within them, an ever-returning youth, promising us a glorious leafage in some strange spring-time, and a symmetry and sweetness that possess us until our thoughts grow skyward like them, and wave and sing in some sunnier strata of soul-air. In the woods I was a girl again, and forgot the flow of the hours in their pleasant companionship. I must have grown tired and sat down by a thicket of pines to rest, though I have forgotten, and perhaps I had fallen asleep; for suddenly I became conscious of a sharp report, and a sharper pain in my shoulder, and, tearing off my cape, I found the blood was flowing from a wound just below the joint. I remember little more, for a sudden faintness came over me; but I have an indistinct remembrance of people coming up, of voices, of being carried home, and of the consternation there, and long delay in obtaining the surgeon. The pain of an operation brought me fully to my senses; and when that was over, I was left alone to sleep, or to think over my situation at leisure. I'm afraid I had but little of a Christian spirit then. All my plans of labor and pleasure spoiled by this one piece of carelessness! to call it by the mildest term. All those nice little fancies that should have grown into real flesh-and-blood articles for my publisher, hung up to dry and shrivel without shape or comeliness! The garden, the dairy, the new bit of carriage-way through the beeches,my pet scheme,the new music, the sewing, all laid upon the shelf for an indefinite time, and I with no better employment than to watch the wall-paper, and to wonder if it wasn't almost dinner- or supper-time, or nearly daylight! To be sure, I knew and thought of all the improving reflections of a sick-room; but it was much like a mild-spoken person making peace among twenty quarrelsome ones. You can see him making mouths, but you don't hear a word he says.