This is the point we must keep in mind." He sat for a few moments staring at the dashboard with a puzzled frown.
"Broadly speaking," he said slowly, "I have found that you can place the motive of every wilful murder under one of three heads--avarice, fear or revenge.

Suppose we consider the first.

Could avarice have been the motive for Colonel Gaylord's murder?
The body had not been robbed, you tell me ?" "No, we found a gold watch and considerable money in the pockets." "Then, you see, if the motive were avarice, it could not have been immediate gain.

That throws out the possibility that the murderer was some unknown thief who merely took advantage of a chance opportunity.

If we are to conceive of avarice as the motive, the crime must have been committed by some person who would benefit more remotely by the Colonel's death.