I'm not entirely sure when the first games of double-headers started. It might very well have been 3:00 as well. Keep in mind that the average length of a game during the deadball era was around 90 minutes or so. A two-hour game would have been long, and a three-hour game would have caused rioting in the stands. Pete Alexander, a notoriously fast worker on the mound, could finish a game in under an hour. So it would have been possible to start the first game at 3:00 and end the second game before nightfall.
In the schedules that I've done for this period, I usually start the first game at noon and the second game at 3:00. That's more of a guess than anything else. Also, I like to keep a three-hour gap between start times, just to make it more likely that the first game won't overlap with the second (not that it matters in terms of the game, but I'm sure some people care about that sort of thing).
Also, in this time period, it wasn't unusual for clubs to agree beforehand to play only seven innings if it looked like a regulation game wouldn't finish before dark, or if one of the teams had a train to catch. I'm not sure when they stopped doing that, but I've seen several newspaper reports from that era that specifically mention that the teams agreed to play seven innings.
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