Reader, we are about to see Angela again, and to see a good deal of her; but you must be prepared for a change in her personal appearance, for the curtain has been down for ten years since last you met the child whose odd propensities excited Pigott’s wonder and indignation and Mr. Fraser’s interest; and ten years, as we all know, can work many changes in the history of the world and individuals. In ten years some have been swept clean off the board, and their places taken by others; a few have grown richer, many poorer, some of us sadder, some wiser, and all of us ten years older. Now, this was exactly what had happened to little Angela—that is, the Angela we knew as little, and ten years make curious differences between the slim child of nine and a half and the woman of nearly twenty.
When we last saw her, Angela was about to commence her education. Let us re-introduce ourselves on the memorable evening when, after ten years of study, Mr. Fraser, a master by no means easily pleased, expressed himself unable to teach her any more.
It is Christmas Eve. Drip, drop, drip, falls the rain from the leafless boughs on to the sodden earth. The apology for daylight that has been doing its dull duty for the last few hours is slowly effacing itself, and the gale is celebrating the fact, and showing its joy at the closing-in of the melancholy night by howling its loudest through the trees, and flogging the flying scud it has brought with it from the sea, till it whirls across the sky like a succession of ghostly racehorses.
This is outside the vicarage; let us look within. In a well-worn arm- chair in the comfortable study, near to a table covered with books and holding some loose sheets of foolscap in his hand, sits Mr. Fraser. His hair is a little greyer than when he began Angela’s education, about as grey as rather accommodating hair will get at the age of fifty-three; otherwise his general appearance is much the same, and his face as refined and gentlemanlike as ever. Presently he lays down the sheets of paper which he has been studying attentively, and says:
“Your solution is perfectly sound, Angela; but you have arrived at it in a characteristic fashion, and by your own road. Not but what your method has some merits—for one thing, it is more concise than my own; but, on the other hand, it shows a feminine weakness. It is not possible to follow every step from your premises to your conclusion, correct as it is.”
“Ah!” says a low voice, with a happy ripple in it, the owner of which is busy with some tea-things out of range of the ring of light thrown by the double reading-lamp, “you often blame me for jumping to conclusions; but what does it matter, provided they are right? The whole secret is that I used the equivalent algebraic formula, but suppressed the working in order to puzzle you,” and the voice laughed sweetly.
“That is not worthy of a mathematician,” said Mr. Fraser, with some irritation; “it is nothing but a trick, a tour de force.”
“The solution is correct, you say?”
“Quite.”
“Then I maintain that it is perfectly mathematical; the object of mathematics is to arrive at the truth.”