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?