This line begins with Thomas Appleby, a labourer of Neasham in County Durham, where the River Tees marks the border with Yorkshire. Thomas was a great-grandson of Henry Appleby of Kirkby Malzeard, Yorkshire.
Thomas' only son, also Thomas, was a florist who moved from Neasham, firstly to York, then London before (seemingly after his wife died) migrating to San Francisco where he died.
Thomas the florist's sons William and Charles followed him to San Francisco as nurserymen, but judging by the US census, both seem to have died bachelors. Thomas eldest son, Thomas Henry, emigrated with his wife and children to Texas. He initially worked in Weatherford as a nurseryman and later in Dallas as an account and auditor. Thomas' other son Edwin and stayed in England.