I started with the purely tentative hypothesis that the person who signed the will was not Jeffrey Blackmore.

I assumed this; and I may say that I did not believe it at the time, but merely adopted it as a proposition that was worth testing.

I accordingly tested it, 'Yes ?' or 'No ?' with each new fact; but as each new fact said 'Yes,' and no fact said definitely 'No,' its probability increased rapidly by a sort of geometrical progression.
The probabilities multiplied into one another.

It is a perfectly sound method, for one knows that if a hypothesis be true, it will lead one, sooner or later, to a crucial fact by which its truth can be demonstrated.
"To resume our argument.

We have now set up the proposition that John Blackmore was the tenant of New Inn and that he was personating Jeffrey.
Let us reason from this and see what it leads to.
"If the tenant of New Inn was John, then Jeffrey must be elsewhere, since his concealment at the inn was clearly impossible.