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July 9, 1862. "James River, Virginia. Sailors relaxing on deck of the U.S.S. Monitor." From photographs of the Federal Navy and seaborne expeditions against the Atlantic Coast of the Confederacy, 1861-1865. View full size. Wet plate negative, left half of stereograph pair. Photograph by James F. Gibson.
I also played this game with my grandmother, called Mill in the version she had. The game grid was basically rows of three by three, in concentric grids, each smaller than the outside one. By enlarging this photo the grid has four markers in place in a couple of rows, with what appears to be a vacant spot for a fifth marker. It looks like each half of the board is five across and four deep, for a total of five across and eight deep. I suspect it's a different game, but have not found what it might be in searching "5 x 8 grid" historic games on Google.
Now this is what real sailors look like.
The pair on the right of the picture seem to be playing Nine Men's Morris. I remember playing the game with my grandmother when I was a kid.
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