Foster: Periam, William, s. Edw., of London, gent. Christ Church, matric. 10 July 1697, aged 18; BA 1701, MA 1704, proctor 1712, BD 20 Apr 1713, DD 25 June 1713, rectorof Fuggleston-with-Bemerton, Wilts, 1712, canon of Salisbury 1738, until his death 1743. See Al. West. 233; Foster's Index Eccl.
I think that the two ordination records must relate to the same person; certainly there is no JP in Foster for the appropriate date.