Those who have seen Steven Martin's documentary film, ELECTRONIC ODYSSEY will recall the interview with the late L.A. thereminist and violinist, Paul "close enough for jazz" Schure. He explains that two theremins were used in THE DAY THE EARTH STOOD STILL - one was played by Paul and the other by Dr. Hoffman - and they were played at the same time so we know there were two theremins in the studio for the session (see below: a recording of the "out-takes"). The instrument you see in the photo is the second RCA used on the soundtrack.
There are two photos side-by-side on CRL's website (the Samuel Hoffman page) of the session for THE DAY THE EARTH STOOD STILL:
http://www.1377731.com/hoffman/
(scroll down to 1951)
The photo on the right is a picture of Hoffman playing the "other" RCA, but the one on the left, from the same recording session (notice that Dr. H. is dressed identically for both pix) definitely shows him playing his single-unit instrument (notice the hardware on the side of the cabinet and the brass scuff guard at the bottom).
The big question is: Where is the second RCA now? Who did it belong to? Paul Shure died in 2010, so he is unable to help solve this mystery. Shure says in ELECTRONIC ODYSSEY that when he was asked to play the second theremin for the soundtrack recording in 1951, he told Bernard Herrmann that if they could find a theremin for him to play, HE'D PLAY IT.
Here is the recording of the out-takes from the TDTESS session with Bernard Herrmann, Samuel Hoffman and Paul Shure.
http://www.youtube.com/watch?v=JzRb1OVpat0