Col. John Williams is descended from Robert Williams of Roxbury, MA and the family genealogies written about this family disagree quite a bit.
The first genealogy is now in the public domain at Google Books. Written by Dr. Stephen West Williams, MD. in 1847, it is a classic example of the family genealogies written (and mostly self published or locally published) in the 1800s. It is also available by subrsciption at Ancestry.com and Genealogy.com. Please note that Dr. Williams was a physician and because of his livelihood he could afford to publish a genealogy.
In 1891, Edward H. Williams, Jr. [of Bethlehem, PA)wrote another family history about the family of Robert Williams which is available at Ancestry.com. It is an old copy and it faded and not easily searchable, has a loss of text (means it is unreadable, I guess) and only covers four generations.
In 1897, a small combined genealogy of the families of Williams and Gallup was produced by Charles Fish Williams. It is of interest to me as I am decended from both Robert Williams and John Gallup. It is available at Google Books and at Ancestry.com.
But, wait! In 1934 another descendant of Robert Williams, Harrison Williams, LLB, another person with professional standing as a lawyer, published yet another Williams genealogy. He remarkes several times that earlier genealogies did not take information from the vital records. It has taken a lot of reading on my part to go through this at Ancestry.com and glean the information from it an compare the data to what the other sources have given.
This is a great learning adventure and one everyone should take heed. You can't just rely on on print resource when researching your ancestors. I continue to look for vital records associated with this family and add that information to my records.