This page features an image of a catalog page from "Watts Surveying and Engineering Instruments" Version R134. No date is available. I estimate it to be around 1927.
The Pilot Balloon Theodolite here is most likely what we would refer to as a Mark A or Mark B. Since it is not listed as a Mark B, it would be reasonable to assume that it the former. The Diaphragm "D" is a simple crosshair design. So it does not support the tail method. However ruled diaphragms were available.
Special Thanks to Herb Gold for Supplying the Watts Catalog Information.