William Hardy aged 32 married 25 Nov 1878 at St Saviours Church, Clarborough, his wife was Rosanna SAXILBY (could this be where the Saxilby reference came in?)
Children of William and Rosanna
John D Q 1879 Doncaster 9c/656 MMS Saxilby
Sarah S Q 1884 East Retford 7b/16 MMS Saxilby
Charlotte D Q 1886 East Retford 7b/15 MMS Saxilby
Emily D Q 1891 East Retford 7b/15 MMS Saxilby
Mary Jane J Q Worksop 7b/26 MMS Saxilby.
Apart from John the rest of their children are daughters.
Now for your great grandfather William to be the cousin of Thomas Hardy (1935) put simply, their fathers must have been brothers. So they share a set of grandparents.
There is a Robert Hardy and his wife Sarah baptising children in Newark.
3 Nov 1846 William Hardy father a labourer
8 Apr 1851 Thomas Hardy father a labourer abode Baldertongate.
28 Apr 1861 Henry Bower Hardy father a potter abode Cross guns Yard
22 July 1856 Frederick father a Tramps and? Abode Nottingham.
so you need to look at the sons marriages and their children and see if there is a cousin connection. Of course there is also the added complication if a daughter had a child!!
