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davidcyclebackIf under strong magnification the printing is made up of a fine pattern of multi color dots, it's a reprint. I assume 99 to 100 percent of the reprints will have these color dots. I'm not aware of the this issue being formally/officially reprinted by a printing house, so I assume most to all reprints were made on home computers or such.
For Pre-War black/sepia-and-white cards-- from Old Judges to Play Balls--, if the magnified printing shows multi color dots, you can assume it's a reprint. Some of the original PreWar b & w cards do have a dot pattern (Play Ball, 1915 Sporting Life, for examples), but it is monotone (black dots only). Other original Pre-War b & w cards are actual photographs (Old Judges, Pinkerton Cabinets, for examples) and have no dot pattern.
So, the multi-color dot pattern is a modern technique to reproduce antique b & w photos, cards, etc, but was not a technique originally used. Most computer printers, including the ones you and I have at home, will produce the multi color dot pattern, even when reproducing a black and white photograph. You don't notice the multi colors from naked eye level, just when examining the image under strong magnification.
If you look at most black and white cards or photos, they aren't strictly black and white. Old Judges and Heading Home cards are sepia, Sporting Lifes and Play Balls have off white stock. Even 1910s news photos have colors to the the images. If you reproduced these cards or photos in strictly black on white ink, they wouldn't look right-- they'd look like dime store Xerox copies and experienced collector's wouldn't believe for a second they were originals. This is why they often recommend you reproduce your old b & w family photos using color not black and white film-- if you look at the originals, you will see they aren't strictly black and white. Yes, they're called "black and white," but your family photos look will a lot better when you use color film.