It is 35mm. I appreciate any help you can give me. And I was wrong the Lord Elgin is bigger than I thought, it is 34mm.
McK
Although I have a few Hamiltons, including a Rodney, I am far from a Hamilton expert. Now that I am home I can reference my own Rodney in the flesh and do a little research. Do you have pictures of the back of your Hamilton? Are there any markings or inscriptions?
Here is a link to a short article about the Hamilton Rodney
http://www.hamiltonchronicles.com/2012/08/1953-rodney.html . The article notes that the Rodney was produced from 1953 to 1964, came in four different dial variations, and was produced with several different movements. The article does not mention the Rodney having more than one case design. Both my Rodney and your Hamilton appear to have the same dial -- i.e., two-tone quadrant dial.
Some observations: I believe my Rodney is original, it has a 34.24mm diameter case (as measured by a digital caliper); the only marking on my case back is,although the dial of your Hamilton appears identical to the dial of my Rodney, your watch has different lugs/case, hands and a taller crown; I did a a quick Google Images search of "Hamilton Rodney" -- all results with two-tone quadrant dials appear to be identical to mine except one, which appears to have the same lugs/case, hands and crown as yours. Here is a link to that watch
https://itsawindup.com/watches/hamilton-rodney-10k-gold-gents-vintage-watch-1950s-2
Note that the dial of the above linked watch differs from mine and yours. It appears to be a "presentation" watch. "Hamilton" has been moved from just below the 12:00 marker, where it normally appears on a Rodney, to just above the 6:00 marker. In its place, "Safe Driver" appears below the the 12:00 marker.
It is my understanding that Hamilton used the product designation, "Masterpiece", twice during its history. "Masterpiece" was first used as a designation for its higher end watches. Later on, "Masterpiece" referred to corporate gifts/presentation watches.
Given the above example of the "Safe Driver" presentation "Rodney" -- which appears to have the same lugs/case, hands and crown as your Hamilton -- perhaps your watch is a "Masterpiece" corporate gift/presentation watch. Is there any inscription on the case back of your watch?
Although Hamilton did use two-tone quadrant dials on other regular production models -- e.g., Stormkinkg III, Hartman -- I am unaware of any regular production models using the same lugs/case as yours. That doesn't mean they don't exist.
That's about all I can offer. I hope some of it is helpful to you. I have attached some photos of my Rodney "before" and "after" for reference. I did not replace my crystal but, rather, had it polished. It looks like yours might just need a good polishing/buffing.
Cheers!