During the course of the year 1772, the death of his father suddenly devolved upon Playfair the burden of supporting his family, and compelled him in a measure to seek a livelihood by entering the Church. Although he had been educated with a view to his entering this profession, for which he was in every way qualified, his decided predilection for science had hitherto made him hesitate about engaging in a vocation, the duties of which, he felt, if conscientiously discharged, would necessarily interfere greatly with the studies he was loath to abandon. In this emergency, however, he considered himself no longer entitled to indulge in these predilections, and therefore made an application, which proved successful, to Lord Gray, the patron, for a presentation to the livings of Liff and Benvie, which had been previously held by his father. From this period until 1782, he was constantly resident at Liff, occupied almost exclusively with the pastoral duties of his office, and with the education of his younger brothers. In the year 1779 Playfair contributed to the 'Transactions' of the Royal Society of London a paper on the 'Arithmetic of Impossible Quantities,' which exhibits, within a very small compass, a striking example of the rare and admirable talent of detaching the sound spirit of science from what may be termed its mysticism. In the year 1782 he was induced by very advantageous offers to resign his charge, and to superintend the education of Ferguson of Raith, and his brother Sir Ronald; an arrangement which restored him in a great measure to the literary and scientific society of Edinburgh, and enabled him to visit London, where he was gratified by a personal introduction to several of the most eminent cultivators of science in that city. Playfair was received into the University of Edinburgh during the course of the year 1785, and, in consequence of an arrangement made between Dr. Adam Ferguson and Mr. Dugald Stewart, was appointed joint-professor of mathematics with Dr. Ferguson, whose delicate state of health prevented him from discharging the active duties of the professorship; Mr. Stewart filling the chair of moral philosophy, previously held by Dr. Ferguson. Previous to this, like Leslie, Playfair had been twice a candidate for a similar honour, but unsuccessfully. On the first occasion, when only eighteen years old, he had offered himself, with the approbation of his instructors at St. Andrew's, as candidate for the professorship of mathematics in Marischal College, Aberdeen, and had sustained with much credit a competitive examination which lasted eleven days, and embraced nearly the whole range of the exact sciences. Out of six competitors, two only were judged to have surpassed him--the Rev. Dr. Trail, who was appointed to the office, and Dr. Hamilton, who afterwards succeeded to and long filled it with much reputation.