The Occult Publishing Company's second edition (Boston, 1890) contains a new Appendix, "A Rosicrucian Institution in Switzerland", pp. 183-88.
The 1910 Theosophical Society ed. also contains that Appendix, pp. 175-80.
HathiTrust Digital Library provides full views of those three US editions with original covers. See the publication records.
The stated "Second Edition, Revised" (1910, with foretitle With the Adepts) is translated from the German Unter den Adepten und Rosenkreuzern.
Library records report both 174 and 180 pages for William Rider & Son (UK) publications as year 1910, which suggests that some contain the 1890 Appendix as pp. 175-80 and some do not.
2nd edition
Expanded by the Appendix, "A Rosicrucian Institution in Switzerland" (replacing the publisher catalogue).
HathiTrust Digital Library provides full view of one copy with original cover:
-- front cover: burgundy? cloth with gold-stamped publisher logo (stylized "OPCo")
-- title page credits "Franz Hartmann, M.D.", dated 1890
-- narrative spans p3-181
-- Appendix, p183-88, "A Rosicrucian Institution in Switzerland"
-- 4-page "Prospectus" and updated advertisement for The Secret Symbols of the Rosicrucians, copied and translated by Hartmann (formerly as forthcoming 1887-11-01)
That is:
Identical to the 1st ed. except cover hue, title page credit and year, pp. 183-88; and advertisement update p[192].
Not found 2019-04-02 in automated search ("adventure among the rosicrucians"), also ("franz hartmann" rosicrucians), of 1887-1890 US newspapers.