Many Newcomb transcription players found on Ebay are missing the 45 rpm adaptor. This isn't just a record adaptor. It's an entire assembly, consisting of the adaptor itself, a spring and a screw. In time, the screw has loosened and fallen out, releasing the adaptor and spring, ending up in the lost world. The plastic adaptor makes up the circumference for the record center hole. Once this adaptor is gone, the spindle circumference is too small for the record hole. Finding a replacement adaptor will be difficult, if not impossible.You must now become creative. The screw is standard, so that's the easy part. Building up the center spindle with heat shrink would accomodate for small hole records and a common 45 adaptor can be used for large hole records.
UPDATE: If your Newcomb 45 adaptor is missing, you're almost out of luck, but there's one last possible chance to make it as close to original as possible. I have located a company that has the raw stock replacement adaptor. By raw stock, there will have to be some work on your part to make it function properly. The center hole will have to be made larger, the shaft will have to be shortened slightly and a spring will have to be made, as well as locating the proper size screw. The original part does not exist, so this is your only option. The picture below shows the original assembly and is hyper-linked to the company supplying the replacement part. The part number for this item is VM-6572.