An update to my request for information on these books:
I obtained a copy of Dr. Porteus' book via inter-library loan. It would be impossible to properly review it here. The book is a detailed account of the 400 plus year history of the Mell's in England, particularly the Yorkshire area. He presents a case for the derivation of the name from the Teutonic root for mixing or the product of milling grain. As to continental origins, he states that there may be northern German or Danish connections and the name was probably brought to the North coast of England by traders or marauders. He also mentions briefly a Mell branch in the south of England.
Through the courtesy of a member of this forum, I also obtained a copy of P. H. Mell's "Genealogy of the Mell Family in the Southern States". This book, which was begun in 1880 and published in 1897, contains a tree which traces the Mell name to Normandy, France in 1070 to Roberto Comes de Mellenti, thence to England. This branch may well be the southern England one mentioned by Porteus. The basis for this book was from personal recollections of Thomas James Mell of Savannah GA, the oldest living Mell there in 1880. The story came down to him from his father, Thomas Sumner Mell , who"liked to talk about the family, and knew many things that have come down to us imperfectly" This Mell family was descended from John Mellwho was in Charleston SC in 1677.