Guessing by the serial number of 17478 and the SCSW on page 95 indicates that the serial numbers of the .38 Double-Action 2nd Model run from 4001 to 119000, and it definitely a .38, my guess is as noted, a .38 Double-Action 2nd Model.
What confuses me are the patent dates on the top rib. After the company name, etc. there are 4 hard to read patent dates, the first appears to be Jan x 05 and the last appears to be May 11 05 followed by 1880. I don't quite get that if the gun was made between 1880-1884.
The gun is pretty beat up, as you can see, the right side hard rubber stock is badly broken but I think I have a replacement. It makes a nice decorative piece.