She mentioned that she and her cousin had done the autosomal DNA testing and offered to compare our results to see if we were a match. Me, my mother, and Grandfather tested through ftDNA. She tested with 23AndMe, so she had to upload her test results to Gedmatch.com for us to compare our DNA results since we tested with different companies. We also compared my family’s DNA results to her cousin, the granddaughter of Elijah Peters and great-granddaughter of James and Martha. Their grandmothers were double-cousins (mothers were sisters, fathers were brothers).
Although her cousin tested through ftDNA, she did not show up as a match to my family. I still did a comparision with Gedmatch.com just in case there was a small match that was not big enough to reach the threshold to be considered a match. 
In doing the Gedmatch.com comparison, we ran a one-to-one comparison between the first descendant's kit and mine, her kit and my mother, her kit and my grandfather. Then we did the same for her cousin's kit. We set the minimum cM value equal to 1.
- Descendant vs Me - 0
- Descendant vs my Mother - 0
- Descendant vs my Grandfather - 0
- Descendant's cousin vs me - 4.3cM
- Descendant's cousin vs Mother - 4.9cM
- Descendant's cousin vs my Grandfather - 4.7cM
- X chromosome comparison between Descendant's cousin and my Grandfather - 0
- X chromosome comparison between Descendant and my Grandfather - 0
- Continue looking for the Martha Peters family represented on the 1880 Oregon Co., MO census report. She was in the right place at the right time and is a good candidate to be the mother of my ancestor, William Edward Peters.
- Continue combing through the DNA results of me, my mother, and grandfather to look for matches with Peters in their list of surnames and connections to Oregon or Howell Counties, MO.
- Investigate the X matches of my grandfather, since William Peters has been identified as one of his X ancestors.
- Apply this exercise to other "suspicious" ancestors: It would be nice to find some descendants of Wilzey King’s family to test and compare to as well. This is another line that I am hypothetically connecting my line to, but am not quite sure of.