Gillian
Your best chance of a response is to place a request on the appropriate Yorkshire county board, making sure that you give all known information and making it clear what you hope to find. For a man born in 1862, you can check the 1881 census on the FHS website and then perhaps armed with the address, post requests for lookups at that same address in 1871 and 1861. If you are lucky, you may be able to find a grandparent living with the family to give you further clues.
Check FreeBMD for details of marriages and births (especially when you have census data). Sometimes it seems to be easier to trace families back through the maternal line, but harder to trace the desendants of female ancestors due to their name changing. Once you have accumulated a base of information from censuses, you'll be amazed what that tells you. Of course, if you supplement this with the acquisition of certificates, it becomes even easier. Some people buy a lot of certificates that subequently turn out not to belong to their family, but there should generally be enough information available to avoid this unfortunate turn of events.
Good luck
Nick
