Replying to both Jennifer and Carol: I don't have any of these particular people in my files, but I think they are certainly of my Acheson family, as the first names that you mentioned were used repeatedly in the family.
This line starts with John Acheson (1710-1778) who was born in Northern Ireland and came to America about 1735, settling in Little Britain, Lancaster Co., PA. He had sons Matthew (1734-1814), Humphrey (1740-1814), and John (1745-1749), as well as four daughters. Matthew and Humphrey both moved to Washington County, PA. (Their wives were also sisters.)
Matthew b. 1734 had sons named David, John, Matthew, Humphrey, and Robert. Humphrey b. 1740 had sons named David, John, Matthew, and Humphrey. (Do you begin to see possible sources of confusion?) I think several of them moved to Muskingum County, OH, but I only have information on David the son of Matthew. He had sons named--you guessed it--David, John, Humphrey, and Matthew. I should also mention that at least two of the above families also had daughters named Jane. I expect that the same pattern was followed in the families of his brothers and cousins.
All of this is not made any simpler by the fact that there were numerous marriages of cousins. The above-mentioned David son of Matthew married his first cousin Ann daughter of his father's brother Humphrey. Then the last David's son Humphrey married Mary, a daughter of his father's brother Robert.
Lots of luck!
Carol, as for the family you found in the 1850 census, I would venture a guess that perhaps Matthew Acheson married Jane Alexander, and the younger girls are their sisters.