Giants nickname (June 3, 1885?)

[bapopik at AOL.COM]

http://www.barrypopik.com/article/848/giants-national-league-baseball-team-now-in-san-francisco
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Can anyone help on "Giants" as well as "Dodgers"? I didn't find the "my big fellows" part of it before much later, about the 1950s.
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What historical documentation shows June 3, 1885?
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COMPLETELY OT: I'll try to go to the Metropolitan Republican Club Ball on Thursday (today) and meet the mayor. After parking tickets, of course.