Dear Sue: The census image for the 1901 census has been sent to you. The transcription of their surname was: HAGNES. The reference numbers are RG13/4471, folio 23, p.3. I was hoping that the 1901 census may have shown Ann and/or Arthur back with their parents which may have helped you but that wasn't the case. John (age 62), William (23) and Charles (21) are all listed as market gardeners. Perhaps Ann and Arthur are daughter Gertrude's children. I would suggest ordering the baptism films from LDS for these two. It's amazing just how many ministers added comments in the registers. If the two are illegitimate, just the mother's name would be listed and most likely the word "illegitimate' written. I have found a death in the December Quarter of 1891 (www.freebmd.org.uk) of Arthur HAGUES, age 3, in the Sculcoates district (Ref. Vol. 9d. p.91) and it would seem to be your Arthur and would explain why he is not in the 1901 census. Perhaps you might like to order his death certificate to see who the parents are.....or, order the film of the burial register from LDS. By the way, have you looked at the 1881 census (available free on www.familysearch.org) where the family are listed and several other children not mentioned above? As the family appear to have remained in Cottingham for many years, it would be very worthwhile ordering the baptism, marriage and burial registers for this family. Kind regards, Barbara, NZ