Congratulations "TDM" fror the correct guess... A firemans ladder brace.
It clamped onto the back of the ladder and stopped the ladder from slipping side ways. the device worked so well on wood and stone that everyone who used ladders started using it. you can still buy more modern versions today.
Todays device may be a little easy (every time i say this it seems not to be) but it was an gizzmo that helped create an industry. when it first came on the market it was sold to individuals at hardware and department stores. It has an over all length of 46 inches, and was introduced in the 1870's.
WHAT IS IT ???