MEMOIR OF THOMAS KEITH, ESQ. THOMAS KEITH, Esquire, the subject of the present brief Memoir, professor of Mathematics, and Author of many distinguished works, was born in 1759, at Brandsburton, near Beverley, in the county of York. His parents bestowed on him a respectable education; but by the death of his father he was thrown on the world with but slender pecuniary means, and left to make his way in it by his talents and industry. He first engaged himself in a family, as private tutor; and after spending a few years in this employ, he was induced, from the precarious and scanty subsistence which was to be obtained in the country, as well as from the favourable opinion which his friends entertained of his abilities and acquirements, to seek his fortune in London. He arrived in the metropolis in the year 1781, where he soon became known, and his merits as a mathematician duly appreciated, from the many works which his indefatigable industry produced. In 1789 he published "The Complete Practical Arithmetician," to which " A Key" was added in 1790, for the use of students. In 1791, an Abridgement of "The Complete Practical Arithmetician *," for the use of young students, appeared; but after passing through one edition, it was suppressed. Shortly afterwards he published an "In * In an advertisement at the end of this work Mr. Keith announced for publication, "The New Universal Spelling Book, or Young Gentlemen and Ladies' Preceptor." But whether it appeared in print or not we have not been able to ascertain. a troduction to the Science of Geography." Besides these works, Mr. Keith published, in 1801, "An Introduction to the Theory and Practice of Plane and Spherical Trigonometry;" "A Treatise on the Use of the Globes," in 1805; and "The Elements of Geometry," in 1814. He likewise sent many contributions to the various mathematical periodicals which were published towards the end of the latter, and at the commencement of the present, century. Mr. Keith superintended several editions of "Hawney's Complete Measurer," "Paterson's Roads," "Geography and History, by a Lady, for the Use of her Pupils," &c. The mathematical works of Mr. Keith have been long known and esteemed in this country. His great experience as a mathematical teacher, and his persevering habits of mind, well qualified him for the task of supplying our schools with a good practical course of mathematical instruction. All his works bear incontestable marks of having been produced with much care and considerable labour. Not, indeed, that he developed fresh discoveries, or even laid out new views with old materials, for his productions have little or no pretensions to this kind of originality. But the labour displayed in his writings consists in the fulness and completeness with which he has discussed every subject to which he directed his mind, never evading any topic legitimately connected with the matter of inquiry merely on the score of its difficulty. His work on the Globes, his The first edition of Mr. William Hawney's " Complete Measurer" was published in London in the year 1717; and was recommended to the public as a very useful work by Dr. John Harris, secretary and vice-president of the Royal Society, an eminent mathematician, and author of several mathematical works. (The "Lexicon Technicum, or a Universal Dictionary of Arts and Sciences, 2 vols. folio, 1708," afterwards augmented to 3 vols. folio, was Dr. Harris's principal literary labour: this work was the foundation of all our Cyclopædias.) It appears, from an advertisement which is printed on the fly-leaf at the commencement of the first edition of the "Complete Measurer," that Mr. W. Hawney kept a school, and was private teacher of the mathematics at Lydd, or Lidd, in the county of Kent. The last edition of this work, which Mr. Keith superintended, was published in January, 1824; and since the editor's decease, two editions of it, and also two editions of his own " Arithmetic " and "Key" have appeared, considerably enlarged, by Samuel Maynard. Arithmetic, his Trigonometry, &c., are all examples of this comprehensiveness of plan, and together form a body of information which cannot be too strongly recommended to the study of those who value science more for its practical utility than for its merely speculative beauties. Although we cannot claim for Mr. Keith the merit of originality, yet he has praise of another kind, that of usefulness, which those who tread the same path of science will not fail to accord to him. And this is a distinction which, if not the most eminent, is certainly among the most honourable; for it will be readily acknowledged, that those who smooth the road to science or literature, and facilitate to others the attainment of knowledge, are often more permanently useful than such as are endowed with original genius. The greatest personal or mental acquirements die with their possessors; but they who labour that others may be wise benefit all posterity. The writers of good introductory treatises on the sciences are therefore entitled to no mean praise; and their fame deserves to live in the genius which they have excited, and in the facilities which they have afforded to the acquisition of knowledge. Mr. Keith's reputation as an accountant led to his being appointed by George III., in 1804, to the situation of Secretary to the Master of his Majesty's Household. As a teacher, too, Mr. Keith was very successful, being engaged in families of the first distinction, as well as in some of the most respectable ladies' establishments in the vicinity of the metropolis. As a proof of his eminence in this department, and the estimation in which he was held, it is only necessary to mention his appointment, in 1810, to the Professorship of Geography and the Sciences to her Royal Highness the Princess Charlotte of Wales; from whom, as well as from her Royal Highness the Princess Sophia Matilda, (who, with many other distinguished personages, had the benefit of his instruction,) he received the most flattering marks of attention and respect. In 1814 he was nominated by the Speaker of the House of Commons, the Right Honourable C. Abbot, afterwards a 2 Lord Colchester, to the then vacant situation of Accountant to the British Museum, the duties of which he performed to the time of his death. In the month of November, 1822, he was afflicted with an internal disorder, which ultimately caused his death, on the 29th of June, 1824, at No. 1. York Buildings, New Road, St. Mary-le-bone, London, in his 65th year. He ended his life with perfect composure and resignation, and retained almost to his last hour the exercise of those strong mental faculties, and of those kind and gentle manners, which had so much endeared him to his family and friends. Mr. Keith left behind him, nearly completed, a new work on the science of Geography, intended for the use of schools, which was published in 1826. Such is a short account of this useful and valuable man. Though the incidents of his life, like those of most other laborious students, afford very scanty materials for biography, being little more than a journal of studies and a catalogue of publications, curiosity may find ample compensation by surveying in his works the character of his mind. And to such of our readers as ardently desire to be useful in their day and generation, we would say, that though they may feel the impossibility of immortalising their names by great or splendid achievements, they may at least imitate the industry and perseverance of Mr. Keith, and emulate his usefulness. THE CONTENTS. Page 1 PROP. 1. To find the logarithm of any whole number, or mixed decimal, consisting of one, two, three, or four figures 3. To find the logarithm of a pure decimal 4. To find the logarithm of a vulgar fraction 5. To find the number answering to any logarithm, to 136 10. To extract the square or cube root, &c. of any number 10 12. To find a fourth proportional to three given num- 4. To find the natural or logarithmic versed sine of an |