I too have had a good look for William and most William Rants on the 1881 cen' and FreeBMD seem to come from the Norfolk or Lincoln areas of England. Have you looked under a variant or a mis-transcription : Rand, Grant or simular? Did William have other forenames ? As people often used their second or even their third name all their lives. In my own tree I have a Miriam Ivy known all her life as Ivy, Beeley's transcribed on one census as Bailey. Also James Quew my G/Granddad, was known as James Jubber for most of his life before he married. This was because his father (James Quew) died when he was a baby and his mother remarried Jonathon Jubber Just a few idea's Chris P NZ :-)