Hamilton 936 PL info please

I have a Hamilton 936 that needs a new dial. I have a dial. I need someone with a ledger to let me know if this dial goes with this movement since the movement is marked Hamilton. It has a private label dial on it that is in pretty bad shape. The serial number is 568212 and the dial says "C. E. Masters Special". Hopefully someone just put the dial on this watch but I have a feeling it goes with it. If it does I will just hang on to it and when and if I sell it the dial will go with it. Thanks.

Watch was finished 4/20/1908 and sold to Burr N. Freir, San Fransisco on 3/7/1910.

regards,
bb

Thank you Buster!