Patee of Peoria or Indianapolis?? I would direct drive hub...track hub type fixed gear skip tooth cog,with lock ring. The Wheelman librarian Bill Smith may have cataloge of Patee, I know later they made pacing motorcycles.
My Patee is not the racer and it seems to have the '87 seat post and bars. There were a number of these assembled in Kansas in 1899 and badged under a different name (Swell During). This was the year that Patee was in jail in Illinois for accomplice to murder charges and the factory was closed. Parts were shipped from Peoria to Kansas and assembled and sold from During Cycle and Sales. Mr. During was in partnership with my wife's great grandfather and they were in business from 1898 through 1900. My bike was badged in 1899. I'm trying to authenticate the parts. There are some markings on the rear hub but I cannot make it out.