Even though we associate the Screw in style frame as the Black Powder frame and the Transverse Latch style as Smokeless, that is not accurate. The Transverse Latch was introduced in 1892, but the Screw in Frame was not completely phased out until 1896. Smokeless frames were advertised in 1897, but not proofed for smokeless with the "VP" mark until 1904. Generally 1900 is used as the cutoff between BP & Smokeless, but it is not recommended to bet your life on that.
The round "bull's eye" ejector head was changed to the oval, or "crescent moon" head at around serial number 52,000, in 1879, during the Intermediate Black Powder period, which was between serial numbers 22,000 - 130,000, or between 1876 - 1890.
So, both styles of heads are period correct for the Screw in style frame, or Black Powder frame as we call it, but the Transverse Latch style frame would be period correct only with a crescent style ejector head.