In the Third Edition I have, the number "50" appears on the cover.
It does not appear in the title page, which is "Sailors' Songs or Chanties," and which bears the label "Revised Edition" at the top of the page.
The preface to the Third Edition (not the revised) says "The demand for a third edition, within a short time after the appearance of the second, has induced the Authors to add ten more Songs to the previous collection." This statement suggests that it appeared soon after the Second, possibly before the "1906" suggested above.

The ten additional songs in the Third Edition are credited to two sources-
Laura A. Smith, 1888 (date of 1st. Ed.), "The Music of the Waters, A Collection of Sailors' Chanties, or Working Songs of the Sea, of All Maritime Nations. Boatmen's, Fisherman's. and Rowing Songs, and Water Legends." Kegan Paul, Trench & Co.
and "Those officers of the Royal Navy and Mercantile Marine who have assisted them [the editors] in obtaining airs of "Chanties" which otherwise they could not have secured."

If a Second Edition with 40 songs is available, it could be checked against the 50 in the Third Edition to identify the 10 songs added from Laura Smith and other sources.