"coincidence" could be established.

It was all done with Machiavellian cunning; but Ballmeyer had
reckoned without Joseph Rouletabille.

Now that the Mystery of The Yellow Room has been cleared up, this
is not the time to tell of Rouletabille's adventures in America.
Knowing the young reporter as we do, we can understand with what
acumen he had traced, step by step, the story of Mathilde Stangerson
and Jean Roussel. At Philadelphia he had quickly informed himself
as to Arthur William Rance. There he learned of Rance's act of
devotion and the reward he thought himself entitled to for it. A
rumour of his marriage with Mademoiselle Stangerson had once found
its way into the drawing-rooms of Philadelphia. He also learned of
Rance's continued attentions to her and his importunities for her
hand. He had taken to drink, he had said, to drown his grief at
his unrequited love. It can now be understood why Rouletabille
had shown so marked a coolness of demeanour towards Rance when they
met in the witnesses' room, on the day of the trial.

The strange Roussel-Stangerson mystery had now been laid bare. Who
was this Jean Roussel? Rouletabille had traced him from Philadelphia
to Cincinnati. In Cincinnati he became acquainted with the old aunt,
and had found means to open her mouth. The story of Ballmeyer's
arrest threw the right light on the whole story. He visited the
"presbytery"--a small and pretty dwelling in the old colonial style
--which had, indeed, "lost nothing of its charm." Then, abandoning
his pursuit of traces of Mademoiselle Stangerson, he took up those
of Ballmeyer. He followed them from prison to prison, from crime
to crime. Finally, as he was about leaving for Europe, he learned