Hi Mike,
My side of the family is one of the other branches of the family starting with William & Agnes.
Andrew Rutherford (1785-1855) & Agnes Sibbald (1788-1870)
John Rutherford (1818-1905) & Helen Middlemas (1828-1913)
William Middlemas Rutherford (1849-1929) & Alison Gray (1857-1907)
John Rutherford (1883-1943) & Jane White Dunn (1876-1960)
John and Jane were my grandparents, John immigrated from Kelso, Scotland to the US in 1912 and Jane from Gourock, Scotland in 1907.
The Rutherford lineage from William & Agnes is quite large. I have descendant lines from their sons Andrew, Thomas, George and John but nothing on William, James and Betty. The census numbers for Rutherford's in Roxburghshire between 1841 thru 1901 range from 516 to 728. I'm thinking that the family may have ranged up to 10% of the census totals. I have 35 grandchildren, 20 male and 15 female, of William & Agnes living in Roxburghshire in the early 1800's.
I would like to get more information on William, James & Betty. Also, I have always thought that it would be good to look in Bamburgh for an Elizabeth or Betty Mills, a possibility for Agnes's mother.
Jack