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On the 1860 Iowa Census, I found an Abraham Baughman, aged 46, married to Levina, aged 38. However, the census shows the following children (ages at the time): Elias (18), Henry (11), Elizabeth (14), Rebecca (9), David (5), and Melissa (2). The census shows Abraham's place of birth as Iowa. I think that Abe must be a child from his second wife. I believe I am a descendent of Willias Baughman. I found an article (can give details of book if interested)that W.H. (Billy) had come to Cambridge NE in 1888 and bought half interest in his brother Abe's store.
I hope this may helped some.