KEILL, JOHN, an eminent mathematician and natural philosopher, the elder brother of the preceding, was born in Edinburgh, on the 1st of December, 1671. [Martin’s Biographia Philosophica, 457.] He received the rudiments of education in the schools of his native city, and remained at the Edinburgh university until he was enabled to take the degree of master of arts. He early displayed a genius and predilection for mathematics, and had the good fortune to study the science, along with the Newtonian system of philosophy, under Dr Gregory. When, in the year 1694, Gregory went to try his fortune in England, Keill followed him, and contrived along with him to find admission to Oxford, where he held one of the Scottish exhibitions in Baliol college. Keill made his first appearance before the scientific world in his "Examination of Dr Burnet’s Theory of the Earth, together with some remarks on Mr Whiston’s new Theory of the Earth," published at Oxford in the year 1698. Any "Theory of the Earth," or account of its formation and state, in anticipation of the discovery of facts to support it, always formed a fruitful subject of debate; but Burnet’s Theory afforded more ample field for censure than any other which pretended to support from the enlightened doctrines of modern philosophy. The grand outlines of his theory were of themselves sufficiently imaginative, and their effect was increased by the curious speculations with which he filled up the minor details of his edifice. He supposes the earth to have been originally a heterogeneous mass of fluid matter, of which the heavier portions fell to the centre, forming there a dense body, surrounded and coated by lighter bodies, while the water—the lightest of all the heterogeneous mass, remained on the outside of the whole. The air and other celestial fluids floated round this body: while between it and the water was gradually formed a coat of unctuous or oily matter, higher than water. Upon this unctuous coat, certain impure particles which had at first been mingled with the air, descended, and floating about covered the surface, forming a shell over the water, which became the crust of the earth. The crust thus formed was level and uniform, without hill or vale; so it remained for about sixteen centuries, until the heat of the sun having cracked it in divers places, the water rushed forth, causing the general deluge. This water found, however, a means of partially subsiding, betwixt the broken masses of the crust, and thus leaving the globe in the state of ocean, hill, and valley.

Keill, who, besides being a man of accurate science, was a person of clear good sense and critical acumen, saw clearly the evil done to science, by the admission of suppositions which have a fully greater chance of being wrong than of being right, while the richness of the doctor’s imagination, and the poetic beauty of his language and illustration, did not protect his principles from a subjection to the strict rules of logic. Keill’s book is full of the clear argumentation of a man who is rather formed to correct and check the discoveries of others, than to allow his invention to stray so far as to make any of his own. He occasionally condescends to use demonstration, while, well knowing that there may be positions against which the gravity of an argument is misapplied, he makes very frequent use of sarcasm, a power of which he is an accomplished and apt handler. Most of the vigour of the attack is derived from the manner in which the different parts of the theory are found inconsistent with each other, without any very extensive reference to other authority. "After this fashion," says Keill, after giving an outline of Burnet’s first formation of the earth, "has the theorist formed his antediluvian habitable world, which doth not much differ from the Cartesian method of making the earth: only Des Cartes, being somewhat wiser than the theorist, would not allow the outward crust, within whose bowels the waters were shut up, to be a habitable earth, knowing well that neither man nor beast could live long without water. But he made the crust first be broken, and the waters flow out, before he placed any inhabitants on it. Another small difference betwixt the two hypotheses is, that Monsieur Des Cartes never thought of making the exterior orb of oily liquids, which the theorist asserts to be absolutely necessary towards the formation of the crust; for if it were not, says he, for the oily liquor which swims upon the surface of the abyss, the particles of earth which fell through the air had sunk to the bottom, and had never formed the exterior orb of earth. But notwithstanding this, I believe it may be easily made evident (though neither of these systems is true), that the theorist’s hypothesis is the worse of the two, which I will prove from his own concessions: for he has already owned that the oily liquor is much lighter than the watery orb. He has mentioned also, that the terrestrial particles when falling from the air, if the orb were only water, would sink to the bottom; and therefore these particles must be heavier than water. From thence I think it does necessarily follow, that these terrestrial particles must also be heavier than the oily fluid, which is lighter than water, and therefore they will more easily descend through it than they did through water, it being well known that there are several bodies which will swim in water, but sink in oil." [Examination 37, 38,]

Proceeding on such positions, Keill destroys what has been raised by his adversary, wisely substituting nothing in its stead, except what experiment and demonstration support; the general aim of the principles he espouses being, that, excepting in so far as we know by experiment the operation of nature, we must take the cosmogony of the earth, either literally as we find it laid down in holy writ, or, admitting our inability to penetrate into its secrets, be content with what is afforded us by experience, demonstration, and rational or certain deduction. Whiston, in his "New Theory of the Earth, from its original to the consummation of all things," maintained, that the Mosaic account of the creation did not give a philosophical account of the formation of the universe, but that it was merely intended, in the most simple and intelligible manner, to give a history of the formation of the globe we inhabit; that before being brought into existence as an inhabited world, it had been a comet, which being subject to perpetual reverses from heat to cold, became by the alternate congealing and melting of its surface, covered with a coat of heterogeneous matter or a chaos, within which the solid nucleus formed a great burning globe. This great mass of matter, as the eccentricities of its orbit decreased, became more nearly circular, and the materials ranging themselves according to their gravities, assumed at the period of the "creation" the forms of earth, water, and air. If this theory does not possess any recommendation to our belief superior to that claimed by Burnet, its author had at least the art, to found a greater number of his conclusions on experiments, and to deduce others in a less imaginative manner. Keill treats this adversary with more respect than he affords to the theoretic Burnet, seldom proving his positions "impossible," and generally contenting himself with being sceptical; he allows that the author "has made greater discoveries, and proceeded on more philosophical principles than all the theorists before him have done."

Keill’s small work is often referred to as authority by geologists and natural philosophers; it contains many experimental calculations, among which is that estimate of the depth of the sea, on which Breislak in later times founded his celebrated calculation, that there never could have been a sufficient quantity of water in and about our globe to have kept the matter of it at any time in solution. It was considered by many, that Keill had used the venerable doctor Burnet, much his elder in years, a scholar, and a man esteemed for his private virtues, with too much asperity and unbecoming sarcasm. It appears that the respective theorists answered the attack, although in what manner we have been unable to discover.

In 1699, Keill published a rejoinder, entitled "An Examination of the Reflections on the Theory of the Earth, together with a defence of the Remarks on Mr Whiston’s New Theory." The Defence of the Theory appears by no means to have infused into Keill a greater spirit of politeness. He proceeds with the impatience of a man of sense and knowledge interrupted, terminating with an advice to Burnet to study "numbers and magnitude, astronomy and statics; that," he continues, "he may be the better able to understand the force of my arguments against his Theory, after which I doubt not but that he will easily perceive its errors, and have the ingenuity to acknowledge them. But till then, all farther disputation between him and me must needs be vain and frivolous, since true reasoning on natural philosophy depends on such principles as are demonstrated in those sciences, the knowledge of which he has not yet attained." To his other opponent, Whiston, Keill has in this work, probably owing to the manner in which he was answered, forgot his former courtesy, treating him with no more deference than he has used toward Burnet.

In 1700, Dr Thomas Millington, Sedelian professor of natural philosophy in Oxford, on his appointment as physician in ordinary to the king, substituted Keill as his assistant, to read his public lectures; and the term for enjoying the Scottish exhibition at Baliol college then expiring, he accepted an invitation from Dr Aldrich, dean of Christ’s church, to reside there. As his master Gregory was the first who introduced the Newtonian philosophy to the universities, Keill himself possesses the reputation of having been the first to demonstrate its principles on experiment; a task he is said to have performed through machinery of his own invention, but of what description, or to what extent he proceeded in his proofs, we are not informed.

In 1701, Keill published his "Introductio ad Veram Physicam," a useful and popular treatise on the Newtonian Philosophy. It is considered as an excellent introduction to Sir Isaac Newton’s Principia, and has frequently been reprinted in England, and in a French translation. About the year 1708, Keill was chosen a fellow of the Royal Society, and after his admission he published in the Philosophical Transactions a pretty lengthy paper, "in which the laws of attraction, and other principles of physic are shown." At this period, the scientific world became disturbed by the dispute which had assumed the aspect of a national question, whether Leibnitz formed his idea of the doctrine of fluxions from some unpublished discoveries of Sir Isaac Newton, and which of these two great men could properly be considered the inventor of that sublime addition to the power of the human intellect. In the Acta Eruditorum published at Leipsic, it was maintained that Leibnitz was the sole inventor, all right on the part of Newton being denied. To this Keill answered in a paper which he communicated to the Royal Society, defending his friend without much regard to the accusations which he brought against his opponent.

In 1711, Leibnitz complained to the Royal Society, that Keill had accused him of obtaining and publishing his knowledge in a manner not reputable to a philosopher, or even exactly consistent with honesty; he appealed to Sir Isaac himself as a witness of his integrity, and required that Keill should publicly disavow the offensive construction which might be applicable to his words. The Royal Society being appealed to as philosophical judges in the matter, appointed a committee to examine the papers and documents connected with the dispute, who did not find it difficult to produce a report rather unfavourable to the continental philosopher, bearing "That Mr Leibnitz was in London in 1673, and kept a correspondence with Mr Collins, by means of Mr Oldenburgh, till September, 1676, when he returned from Paris to Hanover, by way of London and Amsterdam; that it did not appear that M. Leibnitz knew anything of the differential calculus before his letter of the 21st June, 1677, which was a year after a copy of a letter wrote by Sir Isaac Newton, in the year 1672, had been sent to Paris to be communicated to him, and about four years after Mr Collins began to communicate that letter to his correspondents; wherein the method of fluxions was sufficiently explained to let a man of his sagacity into the whole matter: and that Sir I. Newton had even invented his method before the year 1669, and of consequence fifteen years before Mr Leibnitz had given anything on the subject in the Leipsic acts;" from which train of circumstances they concluded that Keill was justified in his imputations. The censure of the society, and the papers connected with it, were published apart from the Transactions in 1712, under the title "Commercium Epistolicum de Analysi Promota." For some time the philosopher appears not to have answered this array against him, until the Abbe Conti, in the year 1716, addressed him, calling on him, if he did not choose to answer Keill, at least to vindicate himself from the non-admission of his claim on the part of Newton; [Published in the Phil. Trans., xxx. 924.] and he just commenced the work of vindication at a period when death prevented him from completing it.

In the year 1709, Keill was appointed treasurer to the Palatines, and in performance of his duties, attended them in their passage to New England. On his return in 1710, he was appointed successor to Dr Caswell, Savilian professor of astronomy at Oxford. At this period, he again entered the field of controversy, in support of his friend Sir Isaac Newton, whose philosophy had been attacked on the foundation of Des Cartes’s theory of a plenum; and he published in the Philosophical Transactions for 1713, a communication to the society, on the rarity of matter and the tenuity of its composition. In this controversy, he was, however, interrupted by his appointment to the situation of decypherer to the queen, and he was soon afterwards presented with the degree of doctor of medicine, by the university of Oxford. About this period we find him gratefully remembered by that unfortunate scholar Simon Oakley, for having permitted him the use of the Savilian study. [Nichol’s Literary Anecdotes.]