The Circular Staircase by Mary Roberts Rinehart

As I drove rapidly up to the house from Casanova Station in the hack, I saw the detective Burns loitering across the street from the Walker place. So Jamieson was putting the screws on -- lightly now, but ready to give them a twist or two, I felt certain, very soon.

The house was quiet. Two steps of the circular staircase had been pried off, without result, and beyond a second message from Gertrude, that Halsey insisted on coming home and they would arrive that night, there was nothing new. Mr. Jamieson, having failed to locate the secret room, had gone to the village. I learned afterwards that he called at Doctor Walker's, under pretense of an attack of acute indigestion, and before he left, had inquired about the evening trains to the city. He said he had wasted a lot of time on the case, and a good bit of the mystery was in my imagination! The doctor was under the impression that the house was guarded day and night. Well, give a place a reputation like that, and you don't need a guard at all -- thus Jamieson. And sure enough, late in the afternoon, the two private detectives, accompanied by Mr. Jamieson, walked down the main street of Casanova and took a city-bound train.