The parish register for St. Dogwells, Pembrokeshire has the following entry for 1799:
There is no burial record in this or an adjacent parish church in Wales for an infant John James between 1799 and 1802 with the correct parents.
In the 10 year period in this parish from 1791 - 1800, 9 out of 53 baptisms were recorded as "privately baptised"; the other 44 were recorded as "publickly baptised" or "baptised". Of the private baptisms, 3 were followed within a few months by public baptisms.
So: what is the meaning of the phrase "private baptism"?
A little family context: Thomas James (circa 1768 - 1851) born Llanfair Nant Y Gof, Pembrokeshire and his wife Anne Scourfield (circa 1778 - 1852) born St. Dogwells were married on 3rd April 1798 in St. Dogwells. I know of at least three children (including this one) but this is the only baptism record I can find for one of the children, which is probably because they were Baptists. There is a supposed 4th -- or rather 1st -- child: Joseph James born 21 June 1798 but I'll raise another question about him!