he applied himself with great industry and success to the study of the mathematical sciences. The late Principal Hill, who was his fellowstudent, says of him in one of his letters from college: "Playfair has very great merit, and more knowledge and a better judgment than any of his class-fellows. I make no exceptions; my parts might be more showy, and the kind of reading to which my inclination led me, was calculated to enable me to make a better figure at St Andrews; but, in judgment and understanding, I am greatly inferior to him."

In 1766 he became a candidate for the professorship of mathematics, in the Marischal college of Aberdeen, vacant by the death of Dr Stewart. He had six competitors to contend with; who, according to the terms of the foundation, were subject to an examination, to which, it was considered, none but the most able mathematicians would be equal. The examination lasted a fortnight, and terminated in favour of Dr Trail; who, however, afterwards confessed that he attributed his own success solely to the fact of his being two years older than Mr Playfair. He quitted the university in 1769; and, for the next year or two, spent most of his time in Edinburgh, where he became intimate with Dr Robertson, Adam Smith, Dr Black, and Dr Hutton.

In 1772, on the decease of his father, he was presented to the parish of Benvie. He continued, however, to cultivate the exact sciences, and in 1779 we find him communicating to the Royal society of London, an essay on the Arithmetic of Impossible quantities, "pointing out the insufficiency of the doctrine of negative quantities given by John Bernouilli and Maclaurin, viz. that the imaginary characters which are involved in the expression, compensate or destroy each other. He attempted, also, to show, in this ingenious paper, that the arithmetic of impossible quantities is nothing more than a particular method of tracing the affinity of the measures of ratios and of angles; and that they can never be of any use as instruments of discovery, unless when the subject of investigation is a property common to the measure of ratios and of angles."

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In 1782 he accepted the tutorship of the two eldest sons of Mr Ferguson of Raith; in consequence of which he resigned his clerical office, but was soon after appointed to the mathematical chair in the university of Edinburgh. In the meantime he became a member of the Royal society, lately instituted in the Scottish metropolis, and communicated to their Transactions a paper On the causes which affect the Accuracy of Barometrical Measurements,' and a Biographical Account of the Rev. Dr Matthew Stewart.' In 1789 he succeeded Dr Gregory as secretary to the physical class of the Royal society. In the same year, a paper of his was read to this society, entitled Remarks on the Astronomy of the Brahmins,' written in furtherance and explanation of the views of M. Bailly, in his Traité de l'Astronomie Indienne et Orientale.' His next communication was in 1792, On the Origin and Investigation of Porisms.'

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In 1796 he published his 'Elements of Geometry;' and in 1802, his Illustrations of the Huttonian theory,' of which an able writer says: "Though brought out under the modest appellation of a commentary, it is unquestionably entitled to be regarded as an original work; and though the theory which it expounds must always retain the name of the philosopher who first suggested it. yet Mr Playfair has, in a great

measure, made it his own, by the philosophical generalization which he has thrown around it; by the numerous phenomena which he has enabled it to embrace; by the able defences with which its weakest parts have been sustained; and by the relation which he has shown it to bear to some of the best established doctrines, both in chemistry and astronomy."

In 1805 he was appointed secretary to the Royal society, on the death of Dr Robison, whom he also succeeded in the chair of Natural Philosophy in the university of Edinburgh. In 1807 he was elected a fellow of the Royal society of London, to which he communicated an Account of the Lithological Survey of Schehallien.' In 1809 his paper On the Progress of Heat when communicated to Spherical bodies,' was read before the society of Edinburgh. In 1814 he published, for the use of his students, 'Outlines of Natural Philosophy,' in two volumes, the first relating to dynamics, mechanics, hydrostatics, hydraulics, aërostatics, and pneumatics,-the second to astronomy. A third was to have been added, treating of optics, electricity, and magnetism; but he never finished the volume.

Mr Playfair's next work was his splendid Discourse on the Progress of the Physical and Mathematical sciences,' which appeared in the supplement to the Encyclopædia Britannica.' Of this essay, Sir James Mackintosh says: "There is no composition on the history of the Physical and Exact sciences, in our language, which can be compared to that of Mr Playfair in philosophical eloquence, except the noble work of his great predecessor Mr Maclaurin on the Newtonian discoveries, which in some places rises to a true sublimity, without ever losing the serenity and clearness of philosophy. The manner of these two great mathematicians, however, is very different; and indicates a difference in their habitual mode of contemplating science. Mr Maclaurin seems to have admired most the grandeur of nature as disclosed by philosophy; Mr Playfair to have fixed his admiration on the energy with which human reason lays open nature to our view. The manner of thinking of the former was most naturally favourable to eloquence. The second, in a more advanced state of progress, when outward nature began to be viewed with abated wonder, found a new object of admiration in those intellectual victories and conquests which had long before inspired the genius of his master, Bacon.'

In 1816 Mr Play fair visited the continent. Soon after his return to Edinburgh, his health began to decline. He died on the 20th of July, 1819, and was honoured with a public funeral. Soon after his death an 'Account of the Character and Merits of the late Professor Playfair,' evidently from the pen of an intimate and highly accomplished friend, appeared in a periodical publication. The following is an extract from this able elogé :

"If he did not signalise himself by any brilliant or original invention, he must, at least, be allowed to have been a most generous and intelligent judge of the achievements of others, as well as the most eloquent expounder of that great and magnificent system of knowledge which has been gradually evolved by the successive labours of so many gifted individuals. He possessed, indeed, in the highest degree, all the characteristics both of a fine and powerful understanding, at once penetrating and vigilant, but more distinguished, perhaps, for the caution and

sureness of its march, than for the brilliancy or rapidity of its movements, and guided and adorned through all its progress by the most genuine enthusiasm for all that is grand, and the justest taste for all that is beautiful in the truth or the intellectual energy with which he was habitually conversant. To what account these rare qualities might have been turned, and what more brilliant or lasting fruits they might have produced, if his whole life had been dedicated to the solitary cultivation of science, it is not for us to conjecture; but it cannot be doubted that they added incalculably to his eminence and utility as a teacher; both by enabling him to direct his pupils to the most simple and luminous methods of inquiry, and to imbue their minds, from the very commencement of the study, with that fine relish for the truths it disclosed, and that high sense of the majesty with which they were invested, that predominated in his own bosom. While he left nothing unexplained or unreduced to its proper place in the system, he took care that they should never be perplexed by petty difficulties, or bewildered in useless details, and formed them betimes to that clear, masculine, and direct method of investigation, by which, with the least labour, the greatest advances might be accomplished.

"Mr Playfair, however, was not merely a teacher; and has fortunately left behind him a variety of works, from which other generations may be enabled to judge of some of those qualifications which so powerfully recommended and endeared him to his contemporaries. It is, perhaps, to be regretted, that so much of his time, and so large a proportion of his publications, should have been devoted to the subjects of the Indian astronomy, and the Huttonian theory of the earth. For, though nothing can be more beautiful or instructive than his speculations on those curious topics, it cannot be dissembled that their results are less conclusive and satisfactory than might have been desired; and that his doctrines, from the very nature of the subjects, are more questionable than we believe they could possibly have been on any other topic in the whole circle of the sciences. To the first, indeed, he came under the great disadvantages of being unacquainted with the Eastern tongues, and without the means of judging of the authenticity of the documents which he was obliged to assume as the elements of his reasonings; and as to the other, though he ended, we believe, with being a very able and skilful mineralogist, we think it is now generally admitted, that that science does not yet afford sufficient materials for any positive conclusion; and that all attempts to establish a theory of the earth must, for many years to come, be regarded as premature. Though it is impossible, therefore, to think too highly of the ingenuity, the vigour, and the eloquence of those publications, we are of opinion, that a juster estimate of Mr Playfair's talent, and a truer picture of his genius and understanding, is to be found in his other writings; in the papers, both biographical and scientific, with which he has enriched the transactions of our Royal society; his account of De Laplace, and other articles which he is understood to have contributed to the Edinburgh Review; the outlines of his lectures on natural philosophy; and, above all, his introductory discourse to the supplement to the Encyclopædia Britannica,' with the final correction of which he was occupied up to the last moments that the progress of his disease allowed him to dedicate to any intellectual exertion.

"With reference to these works, we do not think we are influenced by any national or other partiality, when we say that he was certainly one of the best writers of his age; and even that we do not now recollect any one of his contemporaries who was so great a master of composition. There is a certain mellowness and richness about his style, which adorns without disguising the weight and nervousness which is its other great characteristic; a sedate gracefulness and manly simplicity in the more level passages, and a mild majesty and considerate enthusiasm where he rises above them, of which we scarcely know where to find any other example. There is great equability too, and sustained force in every part of his writings. He never exhausts himself in flashes and epigrams, nor languishes into tameness or insipidity; at first sight you would say that plainness and good sense were the predominating qualities; but, by and by, this simplicity is enriched with the delicate and vivid colours of a fine imagination; the free and forcible touches of a most powerful intellect; and the lights and shades of an unerring and harmonizing taste. In comparing it with the styles of his most celebrated contemporaries, we would say that it was more purely and peculiarly a written style, and therefore rejected those ornaments that more properly belong to oratory. It had no impetuosity, hurry, or vehemence-no bursts or sudden turns or abruptions, like that of Burke; and though eminently smooth and melodious, it was not modulated to an uniform system of solemn declamation like that of Johnson, nor spread out in the richer and more voluminous elocution of Stewart; nor still less broken into the patchwork of scholastic pedantry and conversational smartness which has found its admirers in Gibbon. It is a style, in short, of great freedom, force, and beauty; but the deliberate style of a man of thought and of learning; and neither that of a wit throwing out his extempores with an affectation of careless grace, nor of a rhetorician, thinking more of his manner than his matter, and determined to be admired for his expression, whatever may be the fate of his sentiments.

"His habits of composition, as we have understood, were not, perhaps, exactly what might have been expected from their results. He wrote rather slowly, and his first sketches were often very slight and imperfect, like the rude chalking of a masterly picture. His chief effort and greatest pleasure was in their revisal and correction; and there were no limits to the improvement which resulted from this application. It was not the style merely, nor indeed chiefly, that gained by it. The whole reasoning, and sentiment, and illustration, were enlarged and new-modelled in the course of it, and a naked outline became gradually informed with life, colour, and expression. It was not at all like the common finishing and polishing to which careful authors generally subject the first draughts of their compositions, nor even like the fastidious and tentative alterations with which some more anxious writers essay their choicer passages. It was, in fact, the great filling in of the picture, the working up of the figured weft on the naked and meagre woof that had been stretched to receive it; and the singular thing in this case was, not only that he left this most material part of his work to be performed after the whole outline had been finished, but that he could proceed with it to an indefinite extent, and enrich and improve as long as he thought fit, without any risk either of destroying the proportions of that outline, or injuring the harmony and unity of the design.

He

was perfectly aware, too, of the possession of this extraordinary power, and it was partly, we presume, in consequence of it, that he was not only at all times ready to go on with any work in which he was engaged without waiting for favourable moments or hours of greater alacrity, but that he never felt any of those doubts and misgivings, as to his being able to get creditably through with his undertaking, to which, we believe, most authors are occasionally liable. As he never wrote upon any subject of which he was not perfectly master, he was secure against all blunders in the substance of what he had to say, and felt quite assured, that if he was only allowed time enough, he should finally come to say it in the very best way of which he was capable. He had no anxiety, therefore, either in undertaking or proceeding with his tasks, and intermitted and resumed them at his convenience, with the comfortable certainty that all the time he bestowed on them was turned to good account, and that what was left imperfect at one sitting might be finished with equal ease and advantage at another. Being thus perfectly sure both of his ends and his means, he experienced in the course of his compositions none of that little fever of the spirits with which that operation is so apt to be accompanied. He had no capricious visitings of fancy, which it was necessary to fix on the spot, or to lose for ever; no casual inspiration to invoke and to wait for; no transitory and evanescent lights to catch before they faded. All that was in his mind was subject to his control, and amenable to his call, though it might not obey at the moment; and while his taste was so sure, that he was in no danger of overworking any thing that he had designed, all his thoughts and sentiments had that unity and congruity, that they fell almost spontaneously into harmony and order; and the last added, incorporated, and assimilated with the first, as if they had sprung simultaneously from the same happy conception."

James Watt.

BORN A. D. 1736.-DIED A. D. 1819.

JAMES WATT was born at Greenock, on the 19th of January, 1736. His grandfather was a good mathematician, and educated one of his sons as a surveyor; his other son, the father of the celebrated man whose life we are now attempting to sketch, followed the business of a mer chant at Greenock, and was one of the magistrates of that town. James was from infancy of a very delicate constitution, so that his attendance at school was often interrupted; but he was fond of study, and by private diligence amply made up for what he lost by his repeated absence from school. To the mechanical sciences especially, he devoted much of his attention; and at the age of eighteen was apprenticed to a maker of mathematical instruments in London. The weak state of his health, however, soon compelled him to return to his native place; but he had acquired so much knowledge of his art, as warranted his friends to advise him to establish himself in Glasgow, where he was appointed instrument-maker to the university, with apartments in the college.

In 1763 he commenced practice as a general engineer, and was soon extensively employed in his native country, in making surveys, and es