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. This theodolite is similar to the Troughton and Simms theodolite manufactured in 1921
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.