This leads to his murder by someone who is, we will suppose, an avenger, someone from outside.
This avenger, for some reason which I confess I am still at a loss to explain, took the dead man's wedding ring.

The vendetta might conceivably date back to the man's first marriage, and the ring be taken for some such reason.
"Before this avenger got away, Barker and the wife had reached the room.
The assassin convinced them that any attempt to arrest him would lead to the publication of some hideous scandal.

They were converted to this idea, and preferred to let him go.

For this purpose they probably lowered the bridge, which can be done quite noiselessly, and then raised it again.

He made his escape, and for some reason thought that he could do so more safely on foot than on the bicycle.