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.”

“Vox et preterea nihil. Come out of that corner, my dear.  I hate arguing with a person I cannot see.  But there, there, what is the use of arguing at all?  The fact is, Angela, you are a first-class mathematician, and I am only second-class.  I am obliged to stick to the old tracks; you cut a Roman road of your own.  Great masters are entitled to do that.  The algebraic formula never occurred to me when I worked the problem out, and it took me two days to do.”

“You are trying to make me vain.  You forget that whatever I know, which is just enough to show me how much I have to learn, I have learnt from you.  As for being your superior in mathematics, I don’t think that, as a clergyman, you should make such a statement.  Here is your tea.”  And the owner of the voice came forward into the ring of light.