Tremlett tells him that she seems strangely upset; he goes to her room and finds that she has discovered that she has been robbed.

She naturally suspects Edith Crawford, recollects the incidents of the other night, and probably expresses her feelings to David Graham, and threatens immediate prosecution, scandal, what you will.
"I repeat it again, I dare say he had no wish to kill her.

Probably he merely threatened to.

A medical gentleman who spoke of sudden heart failure was no doubt right.

Then imagine David Graham's remorse, his horror and his fears.