It's a folding wantage rule, and a nice score. There's one at the Davistown Museum, and some information as well.
http://www.mainememory.net/artifact/9901/Firkin, hogshead, etc are barrel sizes. This tool measures the volume of liquid in a barrel, like a dip stick. With the barrel on its side, the rule is thrust through the bung hole with the thin side of the end parallel to the length of the barrel so the tip sits flat on the curve. The measurements on the rule determine the actual volume of liquid in the barrel.
The listing of sizes suggests to me that the sizes had been more or less standardized by the time of manufacture, eliminating the need for calculating from the dimensions of the individual barrel (one cooper's firkin, while a similar size to a firkin made elsewhere probably only held a *similar* volume) as had to be done in the 1700s. Sizes were approximations, and one of the earliest wantage rods looks more like a slide rule.
I couldn't find the manufacturer, but I did find that Stanley made wantage rules, and I know brewers who still use them.
