Maclaurin, Coun

, an eminent mathematician and philosopher, was the son of a clergyman, and born at Kilmodan, near Inverary, in Scotland, Feb. 1698. His family was originally from Tirey, one of the western islands. He was sent to the university of Glasgow in 1709, where he continued five years, and applied himself to study in a most intense manner, particularly to the mathematics. His great genius for this science discovered itself so early as at | twelve years of age; when, having accidentally met with a copy of Euclid’s Elements in a friend’s chamber, he became in a few days master of the first six books without any assistance: and it is certain, that in his sixteenth year he had invented many of the propositions, which were afterwards published as part of his work entitled “Geometria Organica.” In his fifteenth year, he took the degree of master of arts; on which occasion he composed and publicly defended a thesis “On the power of gravity,” with great applause. After this he quitted the university, and retired to a country-seat of his uncle, who had the care of his education, his parents being dead some time. Here he spent two or three years in pursuing his favourite studies; and such was his acknowledged merit, that having in 1717 offered himself a candidate for the professorship of mathematics in the Marischal college of Aberdeen, he obtained it after a ten days trial against a very able competitor. In 1719 he went to London, where he left his “Geometria Organica” in the press, and where he became acquainted with Dr. Hoadly, bishop of Bangor, Dr. Clarke, sir Isaac Newton, and other eminent men. At the same time he was admitted a member of the royal society; and in another journey in 1721, he contracted an intimacy with Martin Folkes, esq. the president of it, which lasted to his death.

In 1722, lord Polwarth, plenipotentiary of the king of Great Britain at the congress of Cambray, engaged him to go as tutor and companion to his eldest son, who was then to set out on his travels. After a short stay at Paris,“and visiting other cities in France, they fixed in Lorrain; where Maclaurin wrote his treatise” On the percussion of Bodies,“which gained the prize of the royal academy of sciences, for 1724; but his pupil dying soon after at Montpelier, he returned immediately to his professorship at Aberdeen. He was hardly settled here when he received an invitation to Edinburgh; the patrons of that university being desirous that he should supply the place of Mr. James Gregory, whose great age and infirmities had rendered him incapable of teaching. On this occasion he had some difficulties to encounter, arising from competitors, who had great interest with the patrons of the university, and also from the want of an additional fund for the new professor; all which, however, at length were surmounted, in consequence of two letters from sir Isaac Newton. In one, addressed to himself, with allowance to shew it to | the patrons of the university, sir Isaac expresses himself thus:I am very glad to hear that you have a prospect of being joined to Mr. James Gregory, in the professorship of the mathematics at Edinburgh, not only because you are my friend, but principally because of your abilities; you being acquainted as well with the new improvements of mathematics, as with the former state of those sciences. I heartily wish*you good success, and shall be very glad to hear of your being elected.“In a second letter to the lord provost of Edinburgh, he writes thus:I am glad to understand that Mr. Maclaurin is in good repute amongst you for his skill in mathematics, for I think he deserves it very well; and to satisfy you that I do not flatter him, and also to encourage him to accept the place of assisting Mr. Gregory, in order to succeed him, I am ready, if you please to give me leave, to contribute 20l. per annum towards a provision for him, till Mr Gregory’s place becomes void, if I live so long, and I will pay it to his order in London."

In Nov. 1725, he was introduced into the university at the same time with his learned colleague and intimate friend, Dr. Alexander Monro, professor of anatomy. After this, the mathematical classes soon became very numerous, there being generally upwards of 100 students attending his lectures every year. These being of different standing and proficiency, he was obliged to divide them into four or five classes, in each of which he employed a full hour every day, from the first of Nov. to the first of June. In the first class he taught the first six books of “Euclid’s Elements,” plain trigonometry, practical geometry, the elements of fortification, and an introduction to algebra. The second studied algebra, the llth and 12th books of Euclid, spherical trigonometry, conic sections, and the general principles of astronomy. The third went on in astronomy and perspective, read a part of sir Isaac Newton’s “Priricipia,” and saw a course of experiments for illustrating them performed: he afterwards read and demonstrated the elements of fluxions. Those in the fourth class read a system of fluxions, the doctrine of chances, and the rest of Newton’s “Principia.” Besides these labours belonging to his professorship, he had frequently other employments and avocations. If an uncommon experiment was said to have been made any where, the feurious were desirous of having it repeated by him; and if | an eclipse or comet was to be observed, his telescopes were always in readiness.

He lived a bachelor to the year 1733; but being formed for society, as well as contemplation, he then married Anne, the daughter of Mr. Walter Stewart, solicitor-general to his late majesty for Scotland. By this lady he had seven children, of which, two sons and three daughters, together with his wife, survived him. In 1734, Berkeley, bishop of Cloyne, published a piece called “The Analyst;” in which he took occasion, from some disputes that had arisen concerning the grounds of the fluxionary method, to explode the method itself, and also to charge mathematicians in general with infidelity in religion. Maclaurin thought himself included in this charge, and began an answer to Berkeley’s book: but, as he proceeded, so many discoveries, so many new theories and problems occurred to him, that, instead of a vindicatory pamphlet, it increased to “A complete system of Fluxions, with their application to the most considerable problems in geometry and natural philosophy.” This work, which was published at Edinburgh in 1742, 2 vols. 4to, cost him infinite pains, and will do him immortal honour, being indeed the most complete treatise on that science that has yet appeared *. In the mean time, he was continually gratifying the public with some performance or observation of his own, many of which were published in the fifth and sixth volumes of the “Medical Essays,” at Edinburgh. Some of them appeared likewise in “The Philosophical Transactions” as the following: 1. “Of the construction and measure of Curves.” 2. “A new method of describing all kinds of Curves.” 3. “A letter to Martin Folkes, esq. on Equations with impossible Roots, May 1726.” 4. “Coiir tinuation of the same, March 1729.” 5. “December the 21st, 1732, On the description of Curves; with an account of farther improvements, and a paper dated at Nancy,


Dr. Thomson, however, remarks that his demonstrations are often so long and complicated, and require such severe attention to follow them, that he believes they are seldom perused by the mathematicians of the present day, who, having turned almost the whole of their attention to the analytical method, are not so capable as their predecessors of following long synthetical demonstrations. But it will be acknowledged by every person who peruses the book, that all the objeotions of Dr. Berkeley against the doctrine of fluxions are completely refuted, and whatever doubts the most captious metaphysicians may think proper hereafter to start about the nature of infinities, the mathematician has no more concern with them than with the famous sophisms about space and motion, Thomson’s Hist, of the Royal Society.

| Nov. 27, 1722.” 6. “An account of the treatise of Fluxions, Jan. 27, 1742.” 7. “The same continued, March 10, 1742” 8. “A Rule for finding the meridional parts of a Spheroid with the same exactness as of a Sphere, Aug. 1741.” 9. “Of the Basis of the Cells wherein the Bees deposit their honey, Nov. 3, 1734.

In the midst of these studies he was always ready to promote any scheme xvhich might contribute to the service of his country. When the earl of Morton set out, in 1739, for Orkney and Shetland, to visit his estates there, he desired Mr. Maclaurjn to assist him in settling the geography of those countries, which is very erroneous in all our maps, to examine their natural history, to survey the coasts, and to take the measure of a degree of the meridian. Maclaurin’s family affairs, and other connections, however, not allowing of his absence, he drew up a memorial of what he thought necessary to be observed, furnished the proper instruments, and recommended Mr. Short, the famous optician, as a fit operator for the management of them. He had still another scheme for the improvement of geography and navigation, of a more extensive nature; which was, the opening a passage from Greenland to the South Sea by the North pole. That such a passage might be found, he was so fully persuaded, that he has been heard to say, if his situation could admit of such adventures, he would undertake the voyage, even at his own charge. But when schemes for finding it were laid before the parliament in 1744, and himself consulted by several persons of high rank concerning them, before he could finish the memorials he proposed to send, the premium was limited to the discovery of a North-West passage and he used to regret, that the word West was inserted, because he thought that passage, if at all to be found, must lie not far from the pole.

In 1745, having been very active in fortifying the city of Edinburgh against the rebel army, he was obliged to fly to the north of England; where he was invited by Herring, then archbishop of York, to reside with him during his stay in this country. “Here,” says he, in a letter to one of his friends, “I live as happy as a man can do, who is ignorant of the state of his family, and who sees the ruin of his country.” We regret to add, that in this expedition being exposed to cold and hardships, and naturally of a weak and tender constitution, he laid the foundation of a | dropsical disorder, which put an end to his life June 14, 1746, aged 48. There is a circumstance recorded of him during his last moments, which shows that he was the inquiring philosopher to the last: He desired his friend Dr. Monro to account for a phenomenon he then observed in himself, viz. flashes of fire seeming to dart from his eyes, while in the mean time his sight was failing, so that he could scarcely distinguish one object from another."

Mr. Maclaurin is said to have been a very good, as well as a ver^y great man, and worthy of affection as well as admiration. His peculiar merit as a philosopher was, that all his studies were accommodated to general utility; and we find, in many places of his works, an application even of the most abstruse theories, to the perfection of mechanical arts. He had resolved, for the same purpose, to compose a course of practical mathematics, and to rescue several useful branches of the science from the bad treatment they often meet with in less skilful hands. But all this his death prevented; unless we should reckon, as a part of his intended work, the translation of Dr. David Gregory’s “Practical Geometry,” which he revised, and published with additions, 1745. He had, however, frequent opportunities of serving his friends and his country by his great skill. Whatever difficulty occurred concerning the constructing or perfecting of machines, the working of mines, the improving of manufactures, the conveying of water, or the execution of any other public work, he was at hand to resolve it. He was likewise employed to terminate some disputes of consequence that had arisen at Glasgow concerning the gauging of vessels; and for that purpose presented to the commissioners of excise two elaborate memorials, with their demonstrations, containing rules by which the officers now act. He made also calculations relating to the provision, now established by law, for the children and widows of the Scotch clergy, and of the professors in the universities, entitling them to certain annuities and sums, upon the voluntary annual payment of a certain sum by the incumbent. In contriving and adjusting this wise and useful scheme, he bestowed a great deal of labour, and contributed, not a little, towards bringing it to perfection.

Among his works, we have mentioned his “Geometria Organica,” in which he treats of the description of curve lines by continued motion: and that which gained the prize of the royal academy of sciences in 1724. In 1740, | he likewise shared the prize of the same academy, with the celebrated Bernouilli and Euler, for resolving the motion of the tides from the theory of gravity; a question which had been given out the former year, without receiving any solution. He had only ten days for composing this paper, and could not find leisure to transcribe a fair copy; so that the Paris edition of it is incorrect. He afterwards revised the whole, and inserted it in his “Treatise of Fluxions,” as he did also the substance of the former piece. These, with the “Treatise of Fluxions,” and the pieces printed in the “Philosophical Transactions,” of which we have given a list, are all the writings which he lived to publish. Since his death, two volumes more have appeared his “Algebra,” and his “Account of sir Isaac Newton’s Philosophical discoveries.” His “Algebra,” though not finished by himself, is yet allowed to be excellent in its kind; containing, in no large volume, a complete elementary treatise of that science, as far as it has hitherto been carried; besides some neat analytical papers on curve lines. His “Account of sir Isaac Newton’s Philosophy” was occasioned by the following circumstances: sir Isaac dying in the beginning of 1728, his nephew, Mr, Conduitt, proposed to publish an account of his life, and desired Mr. Maclaurin’s assistance. The latter, out of gratitude to his great benefactor, chearfully undertook, and soon finished, the history of the progress which philosophy had made before sir Isaac’s time: and this was the first draught of the work in hand, which not going forward, on account of Mr. Conduitt’s death, was returned to Mr. Maclaurin. To this he afterwards made great additions, and left it in the state in which it now appears. His main design seems to have been, to explain only those parts of sir Isaac’s philosophy which have been, and still are, controverted: and this is supposed to be the reason, why his grand discoveries concerning light and colours are but transiently and generally touched. For it is known, that ever since the experiments on which his doctrine of light and colours is founded, have been repeated with due care, this doctrine had not been contested; whereas his theory of celestial phaenomena, founded on gravitation, had been misunderstood, and even ridiculed. The weak charge of introducing occult qualities has been frequently repeated; foreign professors still amuse themselves with imaginary triumphs; and even the polite and ingenious | cardinal de Polignac has been seduced to lend them the harmony of his numbers.

To the last mentioned of his works is prefixed “An Account of the Life and Writings of Mr. Maclaurin:” from which we have taken the substance of the present memoir. 1


Life as above. Tytler’s Life of KarflCS. Biog. Brit.