This pamphlet attracted the attention of Charles Cathcart, 8th Lord Cathcart, who appointed Robertson his chaplain. In 1766 Robertson published anonymously "An Attempt to explain the Words, Reason, Substance". This was written earlier. He describes himself as "a presbyter of the church of England", says nothing of his resignation but only of his refusal of further preferment, and propounds the plan of a comprehensive establishment, based on a subscription to the Bible only, and with a service book silent on all controverted points. To an edition issued in March 1767 is appended the letter of 1760 signed "W. Robertson"; another issue, with the same appendix, is dated 1768. Robertson presented a copy to the University of Glasgow, and received from the senatus the degree of D.D. (21 January 1768). Philip Skelton, after criticising the 'Attempt' from an evangelical point of view in his "Observations", offered Robertson a provision for life under his own roof, or a separate income at his option; the offer was declined, but an intimate correspondence was maintained till Robertson's death. The "Attempt" was also answered in a "Confutation" (Dublin, 1769, 2 vols.) by Smyth Loftus. John Disney assigned to him "Eleutheria", 1768, a poem dedicated to Catharine Macaulay, and stated that in 1767–8 he contributed to the "Monthly Review". Robertson married, in 1728, Elizabeth (d. 1758), daughter of Major William Baxter, and had twenty-one children, but survived them all, leaving only a grandson.