Of course there are some obvious differences between these two stories: the main character in The Sherwood Ring is a girl of 17, Peggy Grahame; the main character in The Riddle of Penncroft Farm is a boy of 12 named Lars Olafson. Peggy goes to her ancestral home in upper New York State as an orphan; Lars is with his mother and father when they go to their ancestral home in Pennsylvania. The Sherwood Ring tells a fictional story about Tory guerrilla activity in New York state led by a fictional character, the amazingly competent British officer, Peaceable Sherwood. The Riddle of Penncroft Farm focuses on true events of the American Revolution in and around Philadelphia (the Battle of Brandywine, the occupation of Philadelphia by the British, Whitemarsh, and Valley Forge, etc.) as experienced by the fictional character, Geordie Hargreaves.
There are still plenty of "reverberations" that link these two stories, however.
1. Both Peggy and Lars are told by a parent that the ancestral family home (Rest-and-be-Thankful in SR and Penncroft Farm in RPF) might be haunted. Neither Peggy's father nor Lars's mother claims to have seen any ghosts, but each reports that others in the family have claimed that they have. (Peggy's father says his aunt and sister both said they had met ghosts at Rest-and-be-Thankful; Lars's mother says her late brother had said that he had done so.)
2. Peggy is lonely and unhappy going to Rest-and-be-Thankful. She misses her father who has died and she does not know anyone in New York State. Lars is lonely and unhappy because he misses his friends and his brother and does not want to move to Pennsylvania.
3. Peggy meets her first ghost in the woods on the way to Rest-and-be-Thankful. Lars sees his first ghost in the window of the house as he is arriving at Penncroft Farm. He then meets Geordie on the road home from school, where he has managed to alienate most of the students in his new classroom.
4. When Peggy first sees Rest-and-be-Thankful, it is surrounded by blossoming apple trees. Aunt Cass tells Lars that Penncroft Farm was originally a fruit orchard, and describes how beautiful it is when the apple trees bloom.