And the first thing he must do, of course, was to define the problem. He
defined it in terms of mathematics. Granted that he had not the place to
himself; granted that the old house had inexpressibly caught and engaged
his spirit; granted that, by virtue of the common denominator of the
place, this unknown co-tenant stood in some relation to himself: what
next? Clearly, the nature of the other numerator must be ascertained.

And how? Ordinarily this would not have seemed simple, but to Oleron it
was now pellucidly clear. The key, _of course_, lay in his half-written
novel--or rather, in both _Romillys_, the old and the proposed new one.

A little while before Oleron would have thought himself mad to have
embraced such an opinion; now he accepted the dizzying hypothesis without
a quiver.

He began to examine the first and second _Romillys_.

From the moment of his doing so the thing advanced by leaps and bounds.
Swiftly he reviewed the history of the _Romilly_ of the fifteen chapters.
He remembered clearly now that he had found her insufficient on the very
first morning on which he had sat down to work in his new place. Other
instances of his aversion leaped up to confirm his obscure investigation.
There had come the night when he had hardly forborne to throw the whole
thing into the fire; and the next morning he had begun the planning of
the new _Romilly_. It had been on that morning that Mrs. Barrett,
overhearing him humming a brief phrase that the dripping of a tap the
night before had suggested, had informed him that he was singing some air
he had never in his life heard before, called "The Beckoning Fair
One."...