111,111,111. Those figures are read as one hundred and eleven millions one hundred and eleven thousands one hundred and eleven. Observe, that I thrice repeated one hundred and eleven; and as we continue to annex triple ones so we must continue to repeat one hundred and eleven, one hundred and eleven, and merely unite a new name to each successive one hundred and eleven. Thus all progress in all modes of notation, howsoever extensive, is in strict accordance with the first principles which govern our most simple comparisons. The very figures of notation are distributed into threes by arithmeticians, and thus afford a striking contradiction to their first principle assumed, that ten fingers suggested the combination of numbers. Whereas my first principles carry me onward without any end, and without a contradiction. In the arithmetic of Lacroix we find the following pernicious instruction. The translator says: "In the number thirty-three, which is written 33, we see the figure 3 repeated-but each time with a different value. The value of the 3 on the left is ten times greater than the value of that on the right." The author alludes to the degrees of relation denoted by thirty and three in a consecutive progression from a first one assumed, and he thus confounds a compounded equality of relative things with a consecutive increase of the same. He first assumes that a 3 is great, then he says that thirty is ten times greater than 3, which is manifestly absurd. Thirty is only 9 times greater than three, though it is ten times as great. Assume any figure we please, and repeat it as often as we please, then each figure on the left will always be nine times greater than the next figure on the right, because the figure on the right is the measure (i. e. a relative part) of the figure on the left. It is surely clear that a gallon is not four times more than a quart, but only four times as much. The error thus exposed, perhaps may be found in all arithmetics, and vitiates the instruction of arithmeticians. To speak of a compounded equality, as the aforesaid author evidently does, we confuse a pupil's mind with multiplication while we are falsely explaining numeration. Whereas, we should commence with things seen correlatively, then combined accordingly-being always explained in correlative progression. Effects must have a cause, and the properties of 3 and 9 are more conspicuous than those of any of the numbers. If we multiply any number by 9, the product will be nine or nines by simply adding, thus: 9 times 3 are 27, then 2 and 7 are 9; 9 times 17 are 153, then I and 5 and 3 are 9. If we make a weight of 1 pound, another of 3, another of 9, another of 27, and another of 81, we shall have five weights with which we can weigh more various quantities than with any other five weights conceivable. These are truths, and they are such because products from 3 and 9 are the compounded combinations of correlative things, when each combination is correlatively unbroken, in conformity with a law of mind which universally governs our comparisons. To farther corroborate my analysis of numeration, I would refer to the well-known rule of proving a product of multiplication, by extracting all the nines and multiplying remainders. Dr. Johnson says: "The course of time is so visibly marked, that it is even observed by the birds of passage, and by nations who have raised their minds very little above animal instinct. There are human beings whose language does not supply them with words by which they can number four; but I have read of none that have not names for day and night-for summer and winter." Surely such beings had fingers as we have; therefore he who builds his science of numbers on ten fingers, must confess that such tribes had each only one-third sufficient sense to comprehend all one's fingers.Dean Swift's analysis of zeal, in his "Tale of a Tub," is strictly analogous to the solution of ten, as performed by arithmeticians. He declares that a notion became a word, and the word during a hot summer ripened into a substance. A geographical view of the world declares: "It is diverting to observe Kamtschadales when they reckon above ten; for, having counted the fingers of both hands, they clap them together, which signifies ten. Then they begin with their toes and count twenty; after which they are quite confounded, and ery metcha ?'-that is, where shall I take more?" Such historical extracts confound the meaning of a number with a sum. A man must learn to number before he can reckon, because reckoning includes addition, and often subtraction. Addition includes numeration, but numeration does not include addition; subtraction includes numeration and addition, but numeration and addition do not include subtraction. They are the three fundamental consecutive rules of all arithmetic, and closed in obedience to a universal law of mind. In my analysis of numeration, I first used the relative, then the correla tive, and thirdly and lastly, the element of combination; and he who acquires numbers without being conscious of those three elements, must be allowed to use them according to that rule by which a parrot learns to talk. We speak of common things (for example, coal) as being each literally one, and not as several particles agglutinated; but the chemist analyzes them and finds each a compound. Accordingly we use common words, like numeration, as though each can denote only one perception; but a metaphysician analyzes them, and finds that the meaning of each is complex, yet acquired under such simple laws, and so consecutively, that the most careless mind will associate extensive combinations without being conscious of their complexity. As an experimentum crusis, I would refer to the natural scale of music, for I contend that a musician's scale and an arithmetician's mode of numeration are results alike under one law. A writer says: "We change the mode at every time when we moderate three notes in succession. It ought not, then, any longer to surprise us that we feel some difficulty while we ascend the scale in singing three tones in succession, because this is impracticable without changing the mode; and if we pause in the same mode, the fourth sound above the first note will never be higher than a semitone above that which immediately precedes it." Dr. Rush, in his "Philosophy of the Human Voice," says: "Whether this triform nature of the cadence, and its exclusion from the current melody, proceed from the habit of the musical scale on the ear, similar to that which prevents a greater rise than of three tones, or whether these circumstances are resolvable into some hidden instinct of the voice, I will not determine." He also says: "We may perhaps prudently despair, that even the keenest inquiry will teach us the reason why the melody of speech is prone to the diatonic progression, and why the voice so accurately falls in with the definite intervals of the musical scale." These authors allude to diatonic melody, which is a term of music to de note degrees of relation consecutively, and I trust I have proved that all such degrees cannot be apprehended, except conformable to the same law that governs our mode of numeration. Dr. Lardner says: "Sounds, in order to be musical, must be caused by a continued succession of equal and regular vibrations of the air produced by the sounding body." If I understand the Doctor, he is certainly wrong. In singing a musical note, we begin gently to emit pulsations of air, then we increase, and gradually finish; hence a note is a kind of fluid swell, which contains within itself degrees of intensity. And all correlative combinations of notes must accord with the vanishing nature of a single note. We may commence from any note we please as the sound first assumed, then, in ascending the scale, we can only produce two notes correlative to the first; but those three notes must have a vanishing effect agreeably with a single note, otherwise they would not be melodious in their ascension.Therefore, the fourth note in the natural scale is necessarily a semitone, which gives the requisite vanishing effect to the three prior ones. A grammarian's three degrees differ from a musician's three only so far as their first assumptions are of a different nature. When I listen to some tunes, I conceive that I hear a rattling crowd of notes, forming one combination, with a gradual rise and a vanishing fall, in accordance with music's loneliest note. Such tunes pass by me as a windy refinement, which makes me feel that simplicity is the garb of all truly useful, beautiful or sublime. Play a purely plaintive air to entrance me in bliss, till joy finds relief in tears, then you may pause till I call you again, and so tune my life for heaven. SONNET. THE STRUGGLE OF ENDOWMENT WITH FORTUNE. 66 WHEN thou shalt put my name upon the tomb, To patient courage and ambition still, His tasks decreed, his industry decried, A hill forever growing,-still his draught Was water in a sieve that could not fill, And bitter was his cup, or drunk, or left unquaff'd." THE RED ROSE. A TALE OF THE WAR IN LA VENDee. FROM THE FRENCH OF A. DUMAS. WHOEVER, On the evening of the 15th December, 1793, had walked from the town of Olisson, toward the village of Saint Crepin, and, on the way thither, from the ridge of the hill whose base is laved by the Maine, had looked down into the valley below, would have witnessed a singular spectacle. There, along the dusky horizon, had he looked for the village, which lay half-concealed amid the trees, he would have seen three or four columns of smoke, which, isolated at the base, spreading and uniting as they ascended, formed a dark canopy, and, moved by the damp west wind, rolled slowly onward to mingle with the clouds, which hung low and threatening over the earth. He would have seen how the pillars of this fearful vault by degrees became tinged with red-how the smoke was scattered, while tongues of fire leaped from the roof, now winding spiral-formed, now stooping, and now towering aloft like burning columns. From time to time, as a roof fell in, he would have heard a deadened crash; he would have seen a brighter glow, with a thousand crackling sparks; and by the blood-red light of the spreading fire, have beheld soldiers have seen the flashing of their weapons-have heard their cries and laughter; then would he have shuddered and exclaimed, "God help us! an army has fired a village, to warm themselves by the flames." It was, in fact, a Republican brigade of from twelve to fifteen thousand men, who, having found the village of Saint Crepin deserted, had set fire to it to satiate their vengeance. A single isolated hut had been spared from the flames; it seemed as if they even endeavored to protect it from the raging element. Two sentinels stood before the door, while orderly-officers and adjutants passed in and out, bringing and receiving orders. He who gave these orders was a young man, apparently from twenty to twenty-two years of age; his hair, parted upon his forehead, fell in long, fair curls down his cheeks; his features and mien wore that impress of melancholy which is so often stamped upon those who are destined to an early death. His blue cloak but partially concealed his person, so that the symbols of his rank the epaulettes of a general, were visible. Leaning over a table, upon which lay a map of the country, he was busied, by the light of a lamp, in tracing out the road to be pursued by his soldiers. It was General Marceau, who, three years later, met his death at Altenkirchen. "Alexander!" he exclaimed, partly raising himself “ Alexander, everlasting sleeper! are you dreaming of St. Domingo, that you cannot wake?” "What is the matter?" cried the individual thus accosted, as he sprang up in haste, almost striking his head against the roof of the chamber."What is the matter?-is the enemy approaching?" "No-but an order from General Westerman has just reached us." While his comrade read the order which he handed to him, Marceau gazed with child-like curiosity upon the powerful proportions of the gigantic mulatto who stood before him. He was a man of about twenty-eight years of age, with short, curly hair, brown complexion, open brow, white teeth, and whose almost supernatural strength was the admiration of the whole army. They had seen him cleave in battle the head of a hostile cuirassier, through helmet and skull, down to his very cuirass; when his horse ran with him on parade, they had seen him press the headstrong animal to suffocation by the strength of his knees. It was General Alexander Dumas.* "Who brought this order?" asked the latter. "The representative of the people-Delmar." "Well-and where are the poor devils assembling?" "In a wood, a league and a half from here. Look at the map ;-here is the place." "Yes-but neither ravines, nor mountains, nor felled trees are marked out upon the map-nor a thousand other obstacles which bar the road; so that we can scarce find our way by day-light. Accursed country, where, besides this, it is always cold!" "Look here," said Marceau, as he pushed open the door with his foot, and pointed to the blazing village-" go out and warm yourself. Halloo! what is the matter, citizens?" These words were addressed to a group of soldiers, who, in searching for plunder, had ransacked a kind of stall which joined the hut, occupied by the generals, and had there discovered a Vendean peasant who appeared to be so drunk that, in all probability, he had not been able to accompany the inhabitants of the village in their retreat. Imagine a boor, whose face, covered by his long hair, bore the stamp of stupidity, dressed in his ordinary apparel, with a gray jacket and slouched hat, and apparently so intoxicated as to have lost all command of his senses. Marceau put a few questions to him, but the wine which he had swallowed, and his patois, rendered his replies almost unintelligible. He was about to hand him over to the soldiers for their amusement, when General Dumas suddenly directed every one to leave the chamber; then following them with his friend, he gave orders that the prisoner should be confined in the hut. The boor was standing at the threshold; they pushed him in; he stumbled against the wall, tottered for a moment on his bending knees, and then falling at his length, lay motionless. A sentinel was stationed without, but they did not think of securing the window. "In an hour we shall be able to commence our march," said General Dumas to Marceau.-" We have a guide." "Whom?" "That fellow!" "Yes; if we wait until to-morrow he might answer; for what he has drank contains at least four and twenty hours' sleep." Dumas smiled. "Come with me,' he said, and led his friend to the stall in which the peasant had been discovered. A thin partition separated the stall from the hut, through the chinks and crevices of which they could see and hear everything that passed in the chamber in which the boor was confined. Here!" added Dumas, softly, "observe what passes.". Marceau obeyed. It was with difficulty that he could distinguish the prisoner, as the latter had accidentally fallen in the darkest corner of the chamber. Upon looking around for his colleague, he found that he had disappeared. As he turned his glance again to the interior of the hut, it seemed as if the prisoner made a slight movement. In a few moments the boor opened his eyes, gaping like a man who has *Father of the Author. t |