I want to thank everyone for their help and suggestions. This is what I know so far. According to the 1900 U.S. Census Rudolph Benz and Louisa (Fartherson) had a total of 10 children of which only three lived. They include the following:
Jacob Benz
DOB - March, 1878 DOD – October, 1939 Age – 62 Mt. Peace Cem.
Catherine (Katie) Benz
DOB – November, 1883 DOD – October, 1953 Age – 69 Mt. Peace Cem.
William Benz
DOB - June, 1887 DOD – May, 1954 Age - 66 Mt. Peace Cem.
Most of the other children I have been unable to identify with the exception of the following:
John Benz ?
DOB – January, 1875
Emma Benz
DOB – April, 1883 DOD – January, 1884 Age – 5 mo. Mt. Peace Cem.
Rudolph Benz served roughly ten years in both the Union Army (1862-65) and the US Navy (1866 to 72). Based upon his recorded age and the listed length of marriage contained in the 1910 U.S. Census it would appear that the couple was married around 1885. This seems like a rather late marriage for Benz considering the number of child he sired (unless Louisa had been previously married).
I wonder if the name Fartherson could, in fact, be Scandinavian in origin as has been suggested. Most of the variations I have tried - Featherson, Fatherson, Featherstone, etc. seem to be more common English surnames rather than German.
Another possibility is that although Rudolph Benz lists Philadelphia as his place of birth it may not be the place that he met Louisa. In Reading, PA in 1844 a male child by the name of Rudolph Bence was born; his father's name is listed as John (1860 U.S. Census). Both the birth date and the name of the father match although the surname is slightly different. In addition, when John Benz enlisted in the Union Army in 1862 he did so in Reading, PA - not Philadelphia which seems rather odd since Reading would be a substantial distance from Philadelphia.
I wonder if Louisa Fartherson could have been originally from Reading, Berks County, Pennsylvania. Berks County, as well as much of central Pennsylvania, contains large populations of Amish, Mennonite, and Moravian dissenters. Today they are collectively referred to as Pennsylvania "Dutch" but not all of these groups were from Germany. I wonder is Louisa Fartherson could be a common name is some other region of central Europe that I have not yet considered?