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So the sorely puzzled Colonel had procured her the necessary text- books, and she had plunged into her original method of self-education. She usually fought out her mathematical battles down by the river, using a stick on the sand for her calculations; history she studied in the fork of an old elm, declaiming the most dramatic episodes aloud, to the edification of the sparrows.

Petitions soon followed from coach-makers, soap-boilers, snuff-grinders, makers of mathematical instruments, manufacturers of sheepskin trousers in fact, nearly every form of industry wished to take advantage of this opportunity to secure national where they had formerly been able to get only local protection.

"If I saw the slightest loophole at which free-will might creep in, I would rush to it, but I do not; if man was created with a free will, he was also created with predispositions which made the acting of that will a matter of mathematical certainty.

It frightens me. The dryness of pure science is terrifying enough, but after all that has a kind of strange beauty, because it deals either with transcendental ideas of mathematical relation, or with the deducing of principle from accumulated facts. But here the object appears to be to eliminate the human element from humanity.

The reader will observe, too, that the method by which this explanation is made is strictly in accordance with the principle I am illustrating, which is by simply dividing the process into short steps. There is no ingenious reasoning on the part of the teacher, no happy illustrations, no apparatus, no diagrams. It is a pure process of mathematical reasoning, made clear and easy by simple analysis.

'And what is the appointment you have got? he asked at length, dismissing his own affairs with impatience. It was that of mathematical lecturer at a London college. 'I shall have a hundred and fifty a year, and be able to take private pupils. On two hundred, at least, I can count, and there are possibilities I won't venture to speak of, because it doesn't do to be too hopeful.

"Hopes realized!" exclaimed I. "Why, I didn't consider there was one chance in a thousand of success, did you?" "Why, yes," replied my exact mathematical friend; "I didn't think the chances so much against the success of the enterprise as that.

After a few more sleepings and a few more wakings we shall all lie dead, every living soul on this broad earth, all who, at this mathematical point in time called the present, breathe the breath of life will pass away; but even now the new generation is springing into life; within the next hour five thousand bodies will be born into the world to perpetuate mankind; the whole lives by the constant renewal of its parts; but the individual, what becomes of the individual?

It is true that theories cannot teach men with mathematical precision what they should do in every possible case; but it is also certain that they will always point out the errors which should be avoided; and this is a highly-important consideration, for these rules thus become, in the hands of skillful generals commanding brave troops, means of almost certain success.

Had these ideas been unreasonable, influences enough were at hand to correct them; but the point of the whole story, when Henry Adams came to look back on it, seemed to be that the ideas were more than reasonable; they were the logical, necessary, mathematical result of conditions old as history and fixed as fate invariable sequence in man's experience.