The 1850 census image shows Jane's age as 64-years old as of the census date of 20 Sept 1850.Jane could NOT be the daughter of Mathew Acheson and Jane K. Thompson, because Jane (the mother of Mary Alexander) was born in 1826.She would have only been 10 years old at the time of birth of a child that would have been 14 years old during the 1850 census.Closer reading of the census image shows the age 64 for Jane Acheson.She is probably the mother of Mathew.Please see: 1850 census, Ohio, Muskingum Co., Blue Rock Twp. Image 14 of 36, Page 89.
I cannot prove it, but this Mathew is likely the son of Matthew Reed Acheson and Nancy Smith(or perhaps a second wife).I have 13 Mathews in my database with birth dates for all but two, and this is the only one that fits (birth date).I will be adding two more Mathew Achesons next month when some 1722 imigration papers arrive that I have ordered copies of.You and Stanley are both correct about the confusion, but much of that has been propogated by FTM and the LDS because of the random distribution of home-brewed family trees with bad info.
I will be writing treatise this Spring on the likely patriarchs of this family.There are more than one.John's close-by neighbor in Lancaster County is Mathew Atchison, and after the death of John Atchison (b. 1710), the "Widow Atchison" moved into the other family's home, according to tax records for Lancaster Co., PA.This Mathew is of an older generation who died intestate, and he is close to John's age (b. 1710). Elder Mathew had a son named John who lived there also. There is an older generation Humphrey and Robert Atchison too that show up in the early records. The two immigration records I have ordered are both for "Mathew Atchisons" that came to America in 1722. The are no other Mathew Achesons(Atchisons, etc.) that have show up in immigration records for the 18th century thus far. To further complicate this family, this older Mathew had at least two sons, John and Mathew, and all of the latter generations moved to Washington County, PA.I am pretty certain the extra set of Humphrey and Mathew Atchison/Achesons that show up in the 1790 census for Washington Co., PA is out of elder Mathew's family.I have a copy John Atchison's Will.I wish elder Mathew had written one as well!
Lastly, another discrepency comes from a paragraph from "History of Washington County, Pennsylvania", Mt. Pleasant Twp. (pp. 850-865) says, "Matthew Atcheson's name appears first on record in a bill of sale made by David Rankin to him on the 10th of April, 1778, in which Rankin sells "unto Matthew Atcheson, of said county, a tract of land situate on the head-waters of Raccoon Creek, adjoining lands of William Rankin, Thomas Cherry, and John Reed." Matthew Atcheson was a native of Ireland, who emigrated to this country with his wife and four sons, David, Matthew, Humphrey, and Robert. Matthew Atcheson, Sr., died about 1814, leaving sons, David, Matthew R., Humphrey, John, and a daughter Jean (Mrs. Moses Cherry). The original farm is now owned by Robert and Matthew Atcheson and John Henderson."This Matthew is clearly of an older generation.The conventional wisdom was that these offspring were born in Pennsylvania, NOT Ireland.
In "The History of the Achesons in America", 1912, John Leon Acheson found precisely the same problem differentiating between these two similar-named, but different generations of these Acheson patriarchs.
Good luck with your search!
Regards, James William Acheson