Thanks anyway. I have actually been looking further into the census and tax lists. If Capt. Leonard is indeed son of John Adcock, then presumably this is "John Adcock Sr" of 1761 tax lists and 1790 census. John Sr. is possibly "John Adcock" named in 1780 will of Leonard Adcock.
I intend to pay a visit to State Archives in January. I hope to look at the 1780 will of Leonard Adcock and the 1786 state census for Adcocks (which gives better household info than does the 1790 Federal Census). I will let you know what I find.