Hello Sandy...
The second certificate certainly looks promising with it mentioning BURNS.
Does the certificate give the name of James BURNS' wife. Or of their residence.
And, just to clarify, apart from the 1901 ROGERS-MCGRATH marriage certificate is this 1874 baptism certificate the only other mention of the surname BURNS that you've come across (excluding on-line family trees)
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For what it's worth, keep in the back of your mind the Patrick and Margaret McGRATH of Doyleston that I mentioned in an earlier post. I think I'm right in saying that Doyleston is within the Lincoln registration district (but I may be wrong :-)
Have also added probate links to earlier post. Possibly think of asking for a look-up.
EDIT:
Another probate that may be connected. Maybe not :-)
Note surname is BURN, not BURNS. But Doyleston gets a mention.
BURN James (R23028836) 1918 - 1918 - Doyleston - Farmer
http://archway.archives.govt.nz/ViewFullItem.do?code=23028836May be BDM NZ Deaths - 1918/1178 - BURNS, James - 69Y - d.o.d 14 Jun 1918
Need to check fiche for location
Regards
Beg