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With all his ability and force, Byng had been always much of a boy, so little at one with the hidden things the springs of human conduct, the contradictions of human nature, the worst in the best of us, the forces that emerge without warning in all human beings, to send them on untoward courses and at sharp tangents to all the habits of their existence and their character.
The problem of the Sirex is now solved. The trajectory is composed of equal elements, with an invariable angle between them; it is the curve whose tangents, divided by infinitely small distances, retain the same inclination between each one and the next; the curve, in a word, with a constant angle of contingence. This characteristic betrays the circumference of the circle.
That good lady refused flatly to absorb it, grew ludicrously plaintive and aggrieved and flew off at tearful tangents into complicated segments of family history from which it was possible to extricate only the most ridiculous of facts, chief among them the reiterated assurance that her own father had been, in the bosom of his family, of a delightfully sportive nature, but nothing like the Westfalls dear no! that he had a genteel figure, my dear, for all he had developed a somewhat corpulent tendency in later years; that the corn-beef which mother procured was highly superior to those portions of salted quadruped which Johnny obtained in the village and facts of similar irrelevancy.
I remember, however, laughing as I thought, if my right leg were to be shot away, how Uncle Kelson and I should go stumping about Southsea Common together, he had lost his left leg, now our heads almost knocking against each other, now going off at tangents. I pictured to myself the curious figure we should cut. Hagger thought, as he looked at me, that I had gone daft.
If, without others to counteract and restrain them, the parts converge, the eye, being forced to the centre, becomes stationary; in like manner, if all diverge, it is forced to fly off in tangents: as if the great laws of Attraction and Repulsion were here also essential, and illustrated in miniature.
To this hour, knowing all her life as I do, I can only regard her as a splendid achievement of nature, convincing even when at the most awkward tangents with the general sense and the straitest interpretation of life; convincing even in those other and later incidents, which showed her to be acting not so much by impulse as by the law of her nature.
It would seem that the Horizontals and the Perpendiculars had made so many spurious and mystified ballots, in order to propitiate the Tangents, and to cheat each other, that this young blackguard actually stood at the head of the poll! a political phenomenon, as I subsequently discovered, however, by no means of rare occurrence in the Leaplow history of the periodical selection of the wisest and best.
Besides the scholarship, there were ways provided so he could earn money by private tutoring and giving lectures in the absence of the professors. He had written his essay on fluxions, described their application to fluents and tangents, and devised a plan for finding the radius of curvity in crooked lines.
If now from these points B, O, A, there are drawn the straight lines BK, ON, AR, through the centres of the same ellipses, and if through these centres there are drawn also the diameters LD, PP, QQ, parallel to the tangents BM, OH, AS; these will be conjugate to the aforesaid BK, ON, AR. And because the three ellipses are similar and similarly disposed, and have their diameters LD, PP, QQ parallel, it is certain that their conjugate diameters BK, ON, AR, will also be parallel.
And though gravity might give the planets a motion of descent towards the sun, either directly, or with some little obliquity, yet the transverse motions, by which they revolve in their several orbs, required the divine arm to impress them, according to the tangents of their orbs.
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