I have been traveling so did not see your reply wntil now. THANKS SO MUCH! One of the places I traveled to was Loudoun Co, VA and I found some of the information that you have. As to William Silcott Alder I only know what I have found on their marriage record and in the census records. You are right about her name being spelled Burkett on her Church marriage record, and her father (or some relative that signed for her proof of age) wrote his name William Birkitt.The record I had orginially seen was from "Loudoun County Marriages" Compiled by Mary Alice Wertz,p. 3, which has her name Margaret E. Birkitt (Birkett). So I'm just staying open on her name.
William & Margret are living in Anderson Co, KS in 1870 census and "Lattinock age 87" is living with them. I thought this was probably Latimore. It's p. 138, PO Garnett, Reeder Dist, Anderson Co, KS. William is listed as a teacher in this census. The 1860 census of Barnsille, Warren Twp., Belmont, Ohio list him as a Prof.of Mathematics.
William died before 1900 and is buried in Greenwood Cemetery, Council Grove, Morris Co, KS. There are no dates on his stone. His daughter Eva Sarah (Alder) Brunts is also buried in this cemetery which was how we located him. Margaret is also buried here - no dates. Family members probably put makers on their graves years after their deaths, so didn't know the dates. I'm just gussing.