Since our original posting the following additional information has been received:

The Smithsonian library's extensive pamphlet file includes an unpublished essay on E.C. Rost (1866-1940). The following are excerpts from the essay:

• "Ernest C. Rost was born January 20, 1866, at Mt. Vernon, N.Y., and was probably the son of Christian Rost (a locally known engraver..) and Minna M. Rost. Nothing is known of his childhood.
  
  
• By the mid 1880's, E.C. Rost was exhibiting landscapes in oil at the National Academy of Design, N.Y. City...After 1887 his oil painting stopped and by 1891 etching became his primary occupation.
  
  
• Today, the Library of Congress (Prints and Photographs Division), maintains 63 etchings signed 'Ernest C. Rost' or 'E.C. Rost', with dates running from 1891 to 1896. These often portray country lanes, cottages, rural scenes, sea, river and bayside settings, mostly in N.Y. State, but several depict homes of famous statesmen and writers...
  
  
• With the outbreak of the Spanish-American War, Rost was sent by the U.S. War Department to Cuba, Puerto Rico, the Philippines, and Guam as a civilian photographer of military operations and installations. Today, 21 photographs taken by E.C. Rost of these islands are held by the National Archives (Audio-Visual Division), while still another 26 photographs, all of Cuba, are held by the Library of Congress...
  
  
• By 1898 Rost had apparently given up etching and entered photography full-time...Still, photography was not his only occupation during this period, for he began writing, too. Between 1899 and 1900, at least seven articles by Rost appeared in the popular 'Leslie's Illustrated Weekly Newspaper'..."
  

There were 3 generations of Rost artists and there is a small booklet on the family.

The "book" is only 16 pages in length and the complete bibliographic citation follows:

Author:† Walsh, John A., of Hampton, N.J.
Title: The fabulous Rosts : three generations of fine line artists, 1823-1961 / by John A. Walsh.
Imprint: [Hampton, N.J.? : J.A. Walsh, c1982]
Description:† 16 p. : ill. ; 22 cm. 

As far as locating the book , if your library does not own it, ask your librarian about getting it on interlibrary loan.