Reverend James Graham (pictured above) is often cited as the father of our ancestor William Graham. While we believe they are probably related (they are from Cumberland Valley, Pennsylvania and, as Dwight pointed out, he resembles Theodore (William's son) pictured below), there are several reasons Rev. James Graham can not be our ancestor.
The documents that say Rev. James Graham is William Graham's father also say that Rev. James Graham was born in 1756 (which worked out great since William Graham was born in 1784), but Rev. James Graham, first full-time pastor to Beulah Presbyterian Church in Pittsburgh was born in 1775. I feel pretty certain this is a correct date since I found a great deal of information about him in Annals of Old Wilkinsburg and Vicinity, with much of the information from his grand-daughter Martha Graham. According to her, his installation as pastor of the Beulah Church, "took place October 16, 1804. This was James Graham's twenty-ninth birthday." His installation date is a matter of church record.
The year of his death is also inaccurate---it's often stated as 5 June 1848, but again this book Annals of Old Wikinsburg and Vicinity, describes his death:
Riding home from a visit to a parishioner June 12, 1845, James Graham's horse was frightened and he was thrown, receiving injuries on head and knee from which he never recovered. He rested at the house of John Shaeffer near which the accident occurred. . .
After riding home to reassure his family he was all right, he fell asleep and never regained consciousness. He is buried in the Beulah Cemetery and his tombstone has the date June 12, 1845.
In fact, Reverend James Graham had no sons named William. By his first wife Elizabeth Martin: Mary, Robert, Matilda, Eliza, James and Priscilla. By his second wife Rachel Glenn: Rebecca and "a little son Thomas."(I assume that means he died young. Although he is not in that cemetery, there is nothing more about him in the chapter. But, someone had to be Martha Graham's father. . . ). By Rev. James Graham's third wife, Martha McCullough (often named as the mother of William Graham), he had two daughters Margaret and Rachel---no sons. His only sons were James, Robert and Thomas.
His son James died in 1849; this same document states that, "Eliza and James Graham, Jr. had four daughters, Martha, Evaline, Elizabeth and Margaretta. James died of typhoid fever when his youngest daughter was 6 weeks old. And, his son Robert "never married."
To read this document, click here. Then, search "Rev. James Graham", you can see what pages look interesting and can go to those pages. Or, you can simply scroll down to the chapters on "Beulah Church II", "Graham Family", "The Death of Reverend James Graham."
There may well be a James Graham (1756-1848) who had a son named William, but it wasn't this James Graham. And, this Martha McCullough was not his mother, either.
I wish I could say poor research led genealogists down this wrong path, but I've gone down that path, too. The internet and digitizing old documents has changed research tremendously---I'm excited to be able to find new and interesting information about my family each day on the internet.