Your great-grandfather would be my four times great uncle.
Your great-grandfather also had a sister, Anne Elizabeth.She was born in 1854 and died in 1935. When she was twelve she and her family came to the U.S. from Notingham England. I am related (in a distant way) to you through her.She married Rhuban Troutman and they had a child, Mary Elizabeth Troutman.Mary married Maurice Edward Mckay and they had a daughter, Ruth H. Ruth was born September 30, 1901 and died October 11, 1992.I was only two at the time, so I never knew her. She married Waldo Leroy Myers, my great-grandfather. He was born November 3, 1897 and died March 16, 1965.Waldo served in WWI in the Navy, and Ruth was an aircraft spotter and parachute packer.I have Waldo's dress blue uniform, artifacts from the war he brought home, and pictures. If you are interested in the Myers line, please tell me and I will be glad to type it out for you.
Back to your great-grandfather.My records conflict with yours. I have an original document that states that he had a brother Joseph, not Thomas.There is no record of a Thomas coming to the U.S. with the family, although Thomas could have died as a child in England. I am positive that William had a brother Joseph though, because of the original document.
I also have a picture of your great aunt Aunt Anne Elizabeth when she was about twenty-two years old.
This information is mostly about my line of ancestors, but I hope it helps you.