According to research I have done for the last 30 years on the Parchman ancestry, William Perchment (born 1925) had the following lineage:
George William Perchment (born ~1893)
Henry Leonard Perchment (born 1871)
William Perchment (born ~1830)
Peter Perchment (born 1801)
Peter Parchman/Perchment (born 1755)
Nicholas Parchman/ Parchment (born about 1730-1735 presumably in Germany)

Nicholas presumably had 4 sons. John and Philip (with the name Parchman) moved to middle Tennesse about 1789. Jacob was scalped by Indians in West Virginia in 1785, and Peter (named Parchman and Perchment in war records and pension applications) remained behind in Pittsburgh, where he was a pioneer of the city, having fought for Virginia (which claimed Fort Pitt) in the Revolution. One of Peter's daughters (Mary Perchment Forsythe) was an ancestor of the Mellons apparently. The Perchment family was on the social register in Pittsburgh around 1870 to 1900. One of Peter's grandsons married the daughter of the owner of the largest department store in Pittsburgh.

Gerry Parchman