Maternal DNA testing
Mothers pass genetic material to their children. Some of it, the mitochondrial DNA (mtDNA), is passed intact. In other words, this mtDNA it is not recombined with the father's DNA. Daughters pass it further to their children, creating a genetic signature of the maternal line that continues from generation to generation. An occasional random mutation occurs, perhaps every 5 to 22 generations, marking a "branch" in the mtDNA tree.
If two persons have matching mtDNA, it is fairly certain they have a common maternal ancestor in the past 5 to 22 generations. [FamilyTreeDNA estimates a 95% confidence of a common ancestor at 22 generations (or to about the year 1500.)]
If the test results from a known maternal descendant of Jemima's mother matched that of another person whose genealogy was known back to the village of Newark, New Jersey in the early 1700s, one could be fairly certain that Jemima's mother was related to that Newark resident as perhaps a sister, daughter, maternal niece, etc. At the least, it would give additional leads on where to focus genealogical searches.
The next article in the series will tell of the search for a living maternal descendant of Jemima's mother (Joel's wife). Such a descendant would carry the same mtDNA as mother of Joel Campbell's children.