Paul,
Your machine is a Sears version. You can tell by the shape of the legs. We don't know what the model number is, only the catalog number, which is not tied to the model number as it became after WW-II. The serial number should be stamped into the top of the front way at the right end. If yours has the nameplate (none have so far), that would supply the Model Number.
And when I wrote "both or your serial numbers", I meant your 9" serial number and Ernst's. I didn't know that you had a Van Norman, and I don't know of anyone doing a serial number database on the VN.
Ernst.
The first catalog I have that your exact machine appears in is No. 26 from, we think, late 1936 or early 1937. The first one that the 9" compound drive lathe appears in that I have is No. 5 possibly dated 1933. It is mostly the same lathe but has smaller feet (but not the same ones used on the Sears machines), a knob instead of a crank on the compound feed screw, and the ON-OFF switch is in a cast switch box (commercial) mounted to the front of the headstock. I Cat. No. 5, there is no model number shown, just the four bed lengths. In Catalog No. 8, possibly 1934, the model numbers 936, 942, 948 and 954 appear but no apparent changes to the lathe. In Catalog No. 15 (1935?), the feet change to the same as yours but the swwich box and knob are still present, and the four model numbers. In Catalog No. 26, the photo looks exactly like your machine. The 918 Utility Bench Lathe appears, with a 3-speed countershaft and without the compound drive. And only the 936 model number is shown (no 942, 948 or 954).