farmer in the neighbourhood, to learn the farming business where he remained several years. Having obtained some knowledge therein, he removed to the distance of about thirty miles, to be superintendant to a farm near Kendal. After being there some time, and arrived at the age of about 17 or 18, he was informed that his father had been possessed of a tolerable estate, in landed property; and that, in the beginning of the last century, he had descended from the same family with Dr. Edmund Gibson, then bishop of London. He spent the little money he had acquired by his industry to come at the truth of the business; when he found, to his sorrow, that the estate was mortgaged to its full value and upwards. He therefore continued his occupation, and soon afterwards rented and managed a little farm of his own, at a place called Hollins, in Cartmell Fell, not far from Cartmell, where he applied himself vigorously to study. A little time previous to this, he had admired the operation of figures; but laboured under every disadvantage, for want of education. As he had not been taught either to read or write he turned his thoughts to reading English,and enabled himself to read and comprehend a plain author. He therefore purchased a treatise on arithmetic; and, though he could not write, he soon went through common arithmetic, vulgar and decimal fractions, the extraction of the square and cube roots, &c. by his memory only, and became so expert therein, that he could tell, without setting down a figure, the product of any two numbers multiplied together, although the multiplier and multiplicand, each of them, consisted of nine places of

figures: and it was equally astonish ing how he could answer, in the same manner, questions in division, in decimal fractions, or in the extraction of the square or cube roots, where such a multiplicity of figures is often required in the operation: Yet at this time he did not know that any merit was due to himself, conceiving other people's capacity like his own; but being a sociable companion, and when in company taking a particular pride in puzzling his companions with proposing different questions to them, they gave him others in return, which, from the certain and expeditious manner he had in answering them, made him first noticed as an arithmetician, and a man of most wonderful memory. Finding himself still labouring under further difficulties, for want of a knowledge in writing, he taught himself to write a tolerable hand. As he did not know the meaning of the word mathematics, he had no idea of any thing beyond what he had learned. He thought himself a masterpiece in figures, and challenged all his companions, and the society he attended. Something, however, was proposed to him concerning Euclid; but as he did not understand the meaning of the word he was silent, but afterwards found it meant a book, containing the elements of geometry, which he purchased, and applied himself very diligently to the study of, and against the next meeting, in this new science he was prepared with an answer. He now found himself launching out into a field of which, before, he had no conception. He continued his geometrical studies; and as the demonstration of the different propositions in Euclid depend entirely upon a recollection of some

of

of those preceding, his memory was of the utmost service to him; and as it did not require much knowledge in classical education, but principally the management of straight lines, it was a study just to his mind; for while he was attending the business of his farm, and humming over some tune or other, with a sort of whistle, his attention was certain to be solely engaged upon some of his geometrical propositions, and, with the assistance of a piece of chalk, upon the lap of his breeches-knee, or any other convenient spot, would clear up the most difficult parts of the science in a most masterly manner. His mind being now open a little to the works of nature, he paid particular attention to the theory of the earth, the moon, and the rest of the planets belonging to this system, of which the sun is the centre; and, consider ing the distance and magnitude of the different bodies belonging to it, and the distance of the fixed stars, he soon conceived each to be the centre of a different system. He well considered the laws of gravity, and that of the centripetal and centrifugal forces, and the cause of the ebbing and flowing of the tides; also, the projection of the sphere, stereographic, orthographic, and gnomonical; also, trigonometry and astronomy. He paid particular at tention to, and was never better pleased than when he found his calculations agree with observation: and being well acquainted with the projection of the sphere, he was fond of describing all astronomical questions geometrically, and of projecting the eclipses of the sun and moon that way. By this time he was possessed of a small library. He next turned his thoughts to algebra,

and took up Emerson's treatise on that subject; and though the most difficult, and that, with Simpson's, are the best authors yet published, he went through it with great success, and the management of surd quantities, and the clearing equations of high powers, were amusement to him while at work in the fields, as he generally could perform them by his memory; and if he met with any thing very intricate, he had recourse to a piece of chalk, as in his geometrical propositions. The arithmetic of infinites, and the diffe rential method, he made himself master of, and found out that algebra and geometry were the very soul of the mathematics. He therefore paid a particular attention to them, and used to apply the former to almost every branch of the different sciences. The art of navigation, the principles of mechanics, also, the doctrine of motion, of falling bodies, and the elements of optics, he grounded himself in; and, as a preliminary to fluxions, which had only been lately discovered by sir Isaac Newton, as the boundary-of the mathematics, he went through conic sections, &c. to make a trial of this last and finishing branch. Though he expressed some difficulty at his first entrance, yet he did not rest till he made himself master of both a fluxion and a flowing quantity. As he had paid a similar attention to all the intermediate parts, he was become so conversant in every branch of the mathematics, that no question was ever proposed to him which he did not answer, nor any rational question in the mathematics, that he ever thought of, which he did not comprehend. He used to answer all the questions in the Gentleman and Lady's Diaries,

the

the Palladium, and other annual publications, for several years; but his answers was seldom inserted, except by, or in the name of some other persons, for he had no ambition in making his abilities known, further than satisfying himself that nothing passed him which he did not understand. He frequently has had questions from his pupils and other gentlemen in London, the universities, and different parts of the country, as well as from the university of Gottingen, in Germany, sent him to solve, which he never failed to answer; and, from the minute enquiry he made into natural philosophy, there was scarcely a phenomenon in nature, that ever came to his knowledge or observation, but he could in some measure or other, reasonably account for it. He went by the name of Willy o' th' Hollins for many years after he left the place. He removed to Tarngreen, where he lived about fifteen years, and from thence into the neighbourhood of Cartmell, and was best known by the name of Willy Gibson, still continuing his occupation as before. For the last forty years of his life, he kept a school of about eight or ten gentlemen, who boarded and lodged at his own farmhouse; and having a happy turn of explaining his ideas, he has turned out a great many very able mathematicians, and a great many more gentlemen he has instructed in accompts, for the counting-house, as well as for the sea, and for landsurveying, which profession he followed himself for these last forty years and upwards. In the course of his life he had had very great practice that way; and, having acquired a little knowledge of draw ing, could finish plans in a very

pretty manner. He has been several times appointed, by acts of parliament, a commissioner for the inclosing of commons, and was a very proper person for that purpose; for, as well as his practice in land surveying, he had equal experience and judgement in the quality of land, as well as the quantity; also in levelling or conveying of water from one place to another, for he was well acquainted with the curvature of the earth's surface. He used to study incessantly, during the greatest part of the night; and inthe day-time, when in the fields, his pupils frequently went to him, to have their different difficulties removed. He was fond of society, and his company was courted by all who knew him. He left a widow. They had been married, and lived together in the purest harmony and friendship, for near fifty years; and in all probability, if it had not been for an accident, from their apparent health and constitution, they might have lived together many years longer; as before the melancholy accident, he had never been out of health an hour in all his life. He has also left ten children living. He was well known and respected by a numerous acquaintance, by several eminent gentlemen in the city of London, and in other parts of the kingdom, and particularly so for a considerable distance round his place of residence. He had but four days illness; and though he was in the greatest agony, from a bruise he had got in his inside by a fall from a cart, he bore it with the greatest patience and died in the greatest composure, aged 71 years, at his house at Blawith, near Cartmell, the 4th of October, 1791.

Anecdotes