Hi! I realize that you are looking for descendants of your Katherina Appel but I thought you might be interested to know that my name is Katharina and I inherited that name from a succession of Katharinas'. In fact my Grandmother was named Katharina Appel though it was her married name, her maiden name being Kaltenschnee. Both the Appel's and the Kaltenschnee's were from Leisenwald, Germany. My grandfather Jacob Johannes Appel was born Jan.2, 1887, son of Konrad Appel and Wilhelmine nee Lohreg, while Katharina was the daughter of Heinrich Kaltenschnee and Katharina nee Neidhardt. I have inherited a very old picture which I was told was also a Katharina but it is unclear which side of the family she was on. I, myself was born in Göttingen and emigrated to Canada with my parents in the 50's. Perhaps you will find that this ties in with your search. Good luck either way!