The pattern calls for “cotton, Nos. 40 or 50.” In the early 1900s, the manufacturing process for making thread was changed, so that historic 40 wt cotton is equivalent to modern 50 wt, so I would suggest using modern 50 wt or something slightly finer.

The “finest knitting needles” are required for this project. Based on the thread weight, 1mm (5/0) or 0.75mm (6/0), should suffice. (This interpretation is based on this chart https://goo.gl/Z9dA34).

The pattern was published in the February issue and can be found on page 171 of the Peterson’s 1862 Annual.