London: Macmillan & Co. 1872. First Edition. xv, 592 pages. 8vo. Original green cloth, skillfully recased with renewed endpapers and minor sympathetic coloring. INSCRIBED by Thomson: "G. LeC. Egerton H.M.S. 'Northampton' with kind regards W. T. Dec 13, 1879" at the top of the title page. An unopened copy (with many pages not separated on the top page edges), otherwise minor wear to the extremities. Very Good. Cloth. 
While the title notes "Reprint" it is incorrect. While the book does collect and reprint papers published over 30 years in various scientific journals, about a quarter of the book is printed here "for the first time from manuscript" in order to fill gaps in the collection. As noted in the Preface "the dates of the fresh articles have all been carefully indicated."
During the time this book was signed, Thomson, an accomplished engineer and mathematical physicist, was in the midst of a campaign to get the Royal Navy to use his new mariner's compass which corrected for variations due to magnetic interference and other technical obstacles. The H.M.S. Northampton was one of the vessels on which Thomson did his testing. Thomson was successful in his campaign, getting the Admiralty to adopt his new compass - his supporters exclaiming it confirmed his brilliance as an engineer, his detractors noting his constant courting of various Navy luminaries on his yacht during frequent outings. Thomson is known to sign his books and letters in various ways, including "Kelvin" (he was also known as Lord Kelvin), "William Thomson" (the most common) and as here with his initials.
While we have no way to confirm if George Le Clerc Egerton (a Royal Navy officer who rose to become Second Sea Lord) was present during testing, it stands to reason that Thomson may have handed out a few copies to bolster his reputation in the course of a campaign to have his new compass adopted by the Admiralty.