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These gloomy reflections have been forced on me by the re-discovery of all those educational books which I absorbed, or was supposed to have absorbed, at school and college. They made an imposing collection when I had got them all together; fifty mathematical works by eminent Den, from a well-thumbed, dog's-eared Euclid to a clean uncut copy of Functions of a Quaternion.

The mail-coach, as the national organ for publishing these mighty events, became itself a spiritualized and glorified object to an impassioned heart; and naturally, in the Oxford of that day, all hearts were awakened. There were, perhaps, of us gownsmen, two thousand resident in Oxford, and dispersed through five-and-twenty colleges. In some of these the custom permitted the student to keep what are called "short terms;" that is, the four terms of Michaelmas, Lent, Easter, and Act, were kept severally by a residence, in the aggregate, of ninety-one days, or thirteen weeks. Under this interrupted residence, accordingly, it was possible that a student might have a reason for going down to his home four times in the year. This made eight journeys to and fro. And as these homes lay dispersed through all the shires of the island, and most of us disdained all coaches except his majesty's mail, no city out of London could pretend to so extensive a connection with Mr. Palmer's establishment as Oxford. Naturally, therefore, it became a point of some interest with us, whose journeys revolved every six weeks on an average, to look a little into the executive details of the system. With some of these Mr. Palmer had no concern; they rested upon bye-laws not unreasonable, enacted by posting-houses for their own benefit, and upon others equally stern, enacted by the inside passengers for the illustration of their own exclusiveness. These last were of a nature to rouse our scorn, from which the transition was not very long to mutiny. Up to this time, it had been the fixed assumption of the four inside people, (as an old tradition of all public carriages from the reign of Charles II.,) that they, the illustrious quaternion, constituted a porcelain variety of the human race, whose dignity would have been compromised by exchanging one word of civility with the three miserable delf ware outsides. Even to have kicked an outsider might have been held to attaint the foot concerned in that operation; so that, perhaps, it would have required an act of parliament to restore its purity of blood. What words, then, could express the horror, and the sense of treason, in that case, which had happened, where all three outsides, the trinity of Pariahs, made a vain attempt to sit down at the same breakfast table or dinner table with the consecrated four? I myself witnessed such an attempt; and on that occasion a benevolent old gentleman endeavored to soothe his three holy associates, by suggesting that, if the outsides were indicted for this criminal attempt at the next assizes, the court would regard it as a case of lunacy (or delirium tremens) rather than of treason. England owes much of her grandeur to the depth of the aristocratic element in her social composition. I am not the man to laugh at it. But sometimes it expressed itself in extravagant shapes. The course taken with the infatuated outsiders, in the particular attempt which I have noticed, was, that the waiter, beckoning them away from the privileged salle-

The play of chances which brings up a ternion or a quaternion is nothing compared to what has been required to prevent the combination of which I am reaping the fruits from being disturbed. If my origin had been less lowly in the eyes of the world, I should not have entered or persevered upon that royal road of the intellectual life to which my early training for the priesthood attached me.

To describe the character of the quaternion calculus would be unsuited to the pages of this work, but we may quote an interesting letter, written by Hamilton from his deathbed, twenty-two years later, to his son Archibald, in which he has recorded the circumstances of the discovery:

Farther he avers the virtue of ten consists in the quaternion; the reason whereof is this, if any person start from one, and add numbers so as to take in the quaternary, he shall complete the number ten; if he passes the four, he shall go beyond the ten; for one, two, three, and four being added up together make ten.

He is bidden to arise quickly, but there is no hurry in the stages of his liberation. 'Gird thyself and bind on thy sandals. He is to take time to lace them. There is no fear of the quaternion of soldiers waking, or of there not being time to do all.

Those charms and amulets, those dark gnomic aphorisms which constitute the stock-in-trade of all religious cheap-jacks, the bribe of future life, the sacerdotal tinge with its complement of mendacity, the secrecy of doctrine, the pretentiously-mysterious self-retirement, the "sacred quaternion," the bean-humbug . . . He had the true maraboutic note.

Pilgrims in future ages will doubtless visit the spot commemorated by the invention of Quaternions. Perhaps as they look at that by no means graceful structure Quaternion Bridge, they will regret that the hand of some Old Mortality had not been occasionally employed in cutting the memorable inscription afresh. It is now irrecoverably lost.

It is doubtful if you even know what a quaternion is, still less how it functions; probably you think of it as a small four-legged animal with a hard shell. You may be right it is so long since I bought the book. How much better if I had learnt this, that, and the other instead! History for instance. How useful a knowledge of history would be to me now.

The Christian Godhead is usually spoken and written of as a Trinity, whereas it is in fact a Quaternion, consisting of God the Father, God the Son, God the Holy Ghost, and God the Devil. The Roman Catholics add yet another, Goddess the Virgin Mary.