He had plenty of time after the shooting to dispose of the weapon and the cartridges.

He neglected to do it.

It would have required but a minute or two for him to destroy the letter which he intercepted.

That letter, the last which Whitmore ever wrote, and the fact that Collins was aware of its contents, could be used by us to establish Collins's motive for the crime.

Collins must have known, in fact it was impossible for him to avoid the knowledge, that the police would eventually search his home.
Yet he permitted the letter and the pistol and the box of cartridges to remain in his room, where they could not possibly be overlooked.