Penshaw All Saints:
John Cowper, born 20 Dec 1801, baptised 18 Apr 1802 1st son of Thomas Cowper, pitman, native of Flixbrough, Lancashire by his wife Eleanor Smith, native of Houghton Parish
Maybe they really meant Thomas was the third child instead of third son? Or there could have been another son between John and Thomas that died before he was baptised.
Janis