Hi,
From your photos, I cannot tell if the second pipe is a replacement or not. It would be nice to see what condition the other pipes are in. Bailey wrote that production of the pattern 1777 began without using the Pratt pipe. However, Goldstein and Mowbray contend no example of that survives and all surviving guns they've examined have the flared second pipe, even those made in Liege. Perhaps you have an example of one without the pipe, which Bailey suggests were early production of the 1777. Of course, it could also be a poor restoration but I cannot tell from the photos.
dave