Is the regulator arm on a 940 interchangeable with any other Hamilton grade, the year of watch is 1905
serial number 409002 (all advice welcome)

Roland, the 1920 Hamilton materials book lists the regulator for 18s open face single and double roller movements as part number 62. It also lists part number 60 regulator as old style for double roller movements. I'm not sure what the difference between the 60 and 62 is but your 940 should be single roller based on the serial number, so if you are looking for a replacement the regulator from a 924 or 926 would work. Regulators are not easy to find as I recently discovered. I needed a replacement regulator for a 936 and finally had to resort to buying a 'parts' 926 movement to get one.

missing arm on watch