John Playfair

John Playfair (1748-1819), mathematician and physicist, was born on the 10th of March 1748 at Benvie, Forfarshire, in Scotland where his father was parish minister. He was taught at home until he was fourteen, when he entered the University of St Andrews. In 1766, when only eighteen, he applied for the chair of mathematics in Marischal College, Aberdeen, but unsuccessfully. Six years later he applied for the chair of natural philosophy in St Andrews, but again without success, and in 1773 he accepted the living of the united parishes of Liff and Benvie, which had become vacant on the death of his father. He continued, however, to carry on his mathematical studies, and in 1782 he resigned to become the tutor of Ferguson of Raith. This enabled him to be frequently in Edinburgh, and to join the literary and scientific circles for which it was then famous. Moreover, through Maskelyne, the astronomer royal, whose acquaintance he had made in the course of the Schiehallion experiments in 1774, (to illustrate the principles of gravitation, from the effect of mountains in disturbing the plumb line) he also gained access to the scientific circles of London. ("I met," wrote Playfair, "with a very cordial reception from him (Dr Maskelyne), and found that an acquaintance contracted among wilds and mountains is much more likely to be durable than one made up in the bustle of a great city: nor would I, by living in London for many years, have become so well acquainted with this astronomer, as I did by partaking of his hardships and labours on Schehallien for a few days.")

In 1785, Adam Ferguson exchanged the moral chair in the University of Edinburgh for that of mathematics, taught by professor Dugald Stewart, and, being in bad health, chose Playfair as his assistant. He continued, however, to attend his two pupils until 1787, when he took up his residence with his mother, who had for some time lived in Edinburgh. He now commenced a series of papers which appeared in the Transactions of the Royal Society of Edinburgh. The first of these was the life of Dr Matthew Stewart, the late professor of mathematics in the university of Edinburgh. A second was on the causes which affect the accuracy of Barometrical Measurements. A third was Remarks on the Astronomy of the Brahmins.

The death of his brother James, in 1793, interrupted his philosophical pursuits, by forcing on his management some complicated business, along with the education of his brother’s son. In 1795, he published an edition of Euclid’s elements for the use of his class. In this work he adopted the plan of using algebraic signs instead of words, to render the proportions more compact and apparent, and "Playfair’s Euclid" became well known to the boys in most mathematical schools. In 1797 he suffered a severe attack of rheumatism, during which he sketched an essay on the accidental discoveries which have been made by men of science whilst in pursuit of something else, or when they had no determinate object in view; and wrote the observations on the trigonometrical tables of the Brahmins, and the theorems relating to the figure of the earth, which were afterwards published in the Transactions of the Royal Society of Edinburgh. About the same time, his friend James Hutton died, and Playfair, who intended to have written his memoir, found in the study of his works a vast field in which he afterwards distinguished himself, by the preparation of the "Illustrations of the Huttonian Theory of the Earth.". Playfair today is remembered most not for his contributions to mathematics, but for the formidable role that he played in bringing the work of Hutton to prominence.

In 1802, Playfair published Illustrations of the Huttonian Theory of the Earth. To its publication the influence exerted by Hutton on the progress of geological knowledge is largely due. In 1805 he exchanged the chair of mathematics for that of natural philosophy in succession to Dr John Robison, whom also he succeeded as general secretary to the Royal Society of Edinburgh. He took a prominent part, on the Liberal side, in the ecclesiastical controversy which arose in connexion with Leslie's appointment to the post he had vacated, and published a satirical Letter (1806). He was elected a Fellow of the Royal Society in 1807. He died in Edinburgh on 20th July 1819.

A collected edition of Playfair's works, with a memoir by James G. Playfair, appeared at Edinburgh in 4 volumes. His writings include a number of essays contributed to the Edinburgh Review from 1804 onwards, various papers in the Phil. Trans. His Elements of Geometry appeared in 1795 and passed through many editions; his Outlines of Natural Philosophy (1812-1816) consist of the propositions and formulae which were the basis of his class lectures. 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. His lives of Matthew Stewart, Hutton, Robison, many of his reviews, and above all his "Dissertation" are of the utmost value.

Illustrations of the Huttonian Theory of the Earth

Playfair's "Illustrations of the Huttonian Theory of the Earth" expressed Hutton's evidence and conclusions in a crisp, tightly organised logical form, making it easy to follow the flow of the argument and very hard to refute it lightly. A critical step in Hutton's case was his argument that granite was a rock formed under great heat and pressure which in places had been forced upwards to displace overlying strata, and occasionally to infiltrate those strata

"... in Dr. Hutton’s theory, granite is regarded as a stone of more recent formation that the strata incumbent on it; as a substance which has been melted by heat, and which, when forced up from the mineral regions, has elevated the strata at the same time."

Playfair laid out the observational facts simply and clearly

"...It has been observed in many instances, that where granite and stratified rocks, such as primary schistus, are in contact, the latter are penetrated by veins of the former, which traverse them in various directions."

He systematically dismantled the conventional view, that granite was formed by mixtures of minerals dissolved in water (and produced at the time of the supposed Flood)

"These phenomena, which were first distinctly observed by Dr. Hutton, are of great importance in geology, and afford a clear solution of the two chief questions concerning the relation between granite and schistus. As every vein must be of a date posterior to the body in which it is contained, it follows, that the schistus was not superimposed on the granite, after the formation of this last. If it be argued, that these veins, though posterior to the schisti, are also posterior to the granite, and were formed by the infiltration of water in which the granite was dissolved or suspended; it may be replied, [first], That the power of water to dissolve granite, is a postulatum of the same kind that we have so often, and for such good reason, refused to concede; and [second], That in many instances the veins proceed from the main body of the granite upwards into the schistus; so that they are in planes much elevated in respect of the horizon, and have a direction quite opposite to that which the hypothesis of infiltration requires. It remains certain, therefore, that the whole mass of granite, and the veins proceeding from it, are coeval, and both of later formation than the strata."

Thus his conclusions were direct and forensic.

"the fluidity which preceded the consolidation of mineral substances was simple, that is, it did not arise from the combination of these substances with any solvent; and next, that after consolidation, these bodies have been raised up by an expansive force acting from below, and have by that means been brought into their present situation."

References

• Significant Scots John Playfair Electricscotland.com
• John_Playfair Encyclopedia Britannica 1911