My guess was for "wire drawing". Apparently jewelers did this for some of their parts. The pulley is what makes me think that this was for drawing long lengths of wire. A rope could have been threaded thru the hole and the other end made fast. If a crank handle were placed on the 3/8 square, the wire could have been drawn fairly quickly thru the die.
Les, wire stretching would also make sense.
John, I took a look at the listing in the Directory to see where the Company was located, but that information is missing. Also, based on what I found and what Rusty found, I think this entry is in error. The Wm. Wilkinson & Sons that I found, and that Rusty found, were definitely an English manufacturer.
An ad I found says the following: Manufacturers of every description of SHEEP AND GARDEN SHEARS, Farriers', Butchers', & Shoe Knives, &c., &c." But no mention of any type of vise.
They appear to have won a prize at the Centennial Exhibition of 1876 that was held in Philadelphia, PA for Sheep and Garden Shears. Maybe this is what led the EAIA astray during their research.
Thanks for the info.
Mike