He invented the wheel barometer, discussed the application of barometrical indications to meteorological forecasting, suggested a system of optical telegraphy, anticipated E.F.F.
P. 258), besides constructing satisfactory formulae for the barometrical determination of heights (Mec. cel.
(including his earliest publication, "On the Arithmetic of Impossible Quantities," 1779, and an "Account of the Lithological Survey of Schehallion," 1811) and in the Transactions of the Royal Society of Edinburgh ("On the Causes which affect the Accuracy of Barometrical Measurements," &c.), also the articles "Aepinus" and "Physical Astronomy," and a "Dissertation on the Progress of Mathematical and Physical Science since the Revival of Learning in Europe," in the Encyclopaedia Britannica (Supplement to fourth, fifth and sixth editions).
Playfair's contributions to pure mathematics were not considerable, his paper "On the Arithmetic of Impossible Quantities," that "On the Causes which affect the Accuracy of Barometrical Measurements," and his Elements of Geometry, all already referred to, being the most important.