I found a book online at the web site for Pikes Peak Library District, Special Collections in the 1905 Carnegie Library http://rmoa.unm.edu/docviewer.php?docId=cocppmss0166.xml

Collection Summary
Title Albert E. Carlton - William K. Gillett, Correspondence
Dates (Inclusive) 1896-1916
Abstract Correspondence consisting primarily of letters, memos, and telegrams between Albert E. Carlton of the Colorado Trading and Transfer Company and William K. Gillett of the Midland Terminal Railway Company largely concerning railway and trading company business in what is now Teller and El Paso Counties, Colorado. Items date from December, 1896 to May 1916, with the bulk of the correspondence occurring between 1896 and 1902.
Collection Number MSS 0166
Size 2 boxes (.8 cubic feet)

There is a notation as follows:

"W. K. Gillett was auditor of the Midland Terminal Railway when it received its name in 1893. He became the major stockholder and in 1898 became president and general manager, a position he held until 1905. The town of Gillett, Colorado, through which the railroad ran, was named for him, as was the first Midland Terminal Railway engine, #1."

I think this will answer your question.
Eellitta