The following information on carrying a revolver while running comes from Section 48 of Shooting by J. Henry FitzGerald. Shooting is also available to purchase in print.
It is very important that an officer be properly taught how to carry his revolver when running. Here is a safe and sane way: Carry the revolver with muzzle toward the object to be shot at, elbow held close to the side, and the forearm pointing straight ahead. Never raise the hammer of the revolver while running. Never place the finger in the trigger guard or on the trigger; in this way you will eliminate the possibility of stumbling and shooting yourself or some innocent bystander.
I have known several cases where officers have fired accidental shots in this manner and safety first is the best preventive. It is agreed that the best place to carry a revolver when it may be needed instantly is in the hand, but it must be carried safely. An incident related to me by a police lieutenant may be repeated to show the up-to-date firearms knowledge possessed by some police officers. It seems that in a burglary scare a couple of shots were fired. The lieutenant was standing in a doorway a short time afterward, when one of his men came along, revolver in his hand and cocked ready for business. “Here!” called the Lieutenant. “What’s the idea of that revolver carried that way; you know that the war is over.”
“Oh, yes, sir, I know, but I cocked this revolver and I am going up to the station to have some one let the hammer down for me.”
Think of a man carrying a loaded and cocked revolver around for a half hour on the street not knowing what to press to let the hammer down. Whew! some men have all the luck.