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Dr. Peter Mark Roget (1779-1869)
1838 P. M. Roget, London Secretary to the Royal Society, became a member of the Institution of Civil Engineers.
1870 Obituary 
DR. PETER MARK ROGET, F.R.S., was born in London, on the 18th of January, 1779, and was the only son of the Rev. John Roget, a Genevese clergyman at that time settled in London as minister of a French Protestant church in the City. His mother was the sister of Sir Samuel Romilly, who not only held her husband in the warmest esteem, but was wont to attribute to Roget’s early prediction of his professional success the choice of that path in life which he afterwards trod with such distinction.
Mr. Roget did not live to superintend his son’s education. He died in Switzerland when his son was but four years old, and the task devolved upon his widow, who appears to have brought to it an exceptional degree o€ intelligence and judgment. Some of the rudiments of learning were acquired at a private school kept by a Genevese friend, M. Chauvet, in Kensington Square; and, at the age of fourteen, the boy commenced his studies at the University of Edinburgh. He had already shown a decided taste for mathematics, and had begun to teach himself the elements of science.
The choice of medicine as his profession did not impose a limit upon his range of study, and he listened with as lively an interest to the discourses of Dugald Stewart, as to the lectures which he attended, with equal diligence, in the medical school. At the age of nineteen, he took his degree of M.D., and showed his predilection for scientific re3earch by selecting, as the subject of his thesis, the laws of chemical affinity. His name appears before the beginning of the century as a writer on medical subjects, for there is a letter from him on pulmonary consumption, published in 1799 in Dr. Beddoes’s Essay on that disease. Another letter of his was published in the following year by Davy, on the respiration of nitrous oxide.
Among the friends and instructors of his youth, there was perhaps no one to whom he confessed greater oblations than his uncle’s esteemed friend Dumont, and it was probably through t81mt channel that Dr. Roget made the acquaintance of the philosopher Jeremy Bentham. In the autumn of 1800 he was, at Bentham’s invitation, an inmate in his house for six weeks, for the purpose of assisting him with advice in a project described in Bentham’s words as a Frigidarium; a sort of ice house for the purpose of preserving fermentable substances of all sorts from prejudicial fermentation, by excluding the degree of heat necessary to that process.” The scheme does not however appear to have led to any practica1 result.
During the short peace of Amiens, he accepted an engagement to travel on the Continent, in charge of two young men, the sons of Mr. John Philips, of Manchester, In the spring of 1803 the three travellers were enjoying themselves at Geneva, when Dr. Roget suddenly found himself a French prisoner, being included under Napoleon’s order to arrest all the English within his dominions; from which liability the two young Philips’s were held exempt, as being under eighteen. Dr. Roget was on the point of being sent with the other prisoners to Verdun (there to remain till the restoration of 1814), when he claimed and obtained his release by insisting that, as the son of a citizen of Geneva, he was entitled to the rights of a French subject. These rights did not, however, include that of quitting the country, and they moreover involved a liability to the conscription. Dr. Roget therefore seized the opportunity afforded him by the grant of a passport for Paris, to escape with his young friends across Switzerland, and get them back to England as best he could, through Germany and Denmark.
After attending the Marquis of Lansdowne for some months as his private physician, he wag, in October, 1804, appointed one of the physicians to the Manchester Infirmary, which office he held for four years. Encouraged by success there, particularly in awakening an interest, by means of lectures, in the then dawning science of comparative physiology, he removed to London, where, on the 3rd of March, 1809, he was admitted a licentiate of the College of Physicians (of which he became a fellow in 1831), and entered into a practice which in a few years became considerable.
He soon established himself also as an able expositor of his favourite science of animal physiology, in a series of courses of public lectures, which extended over a period of more than thirty years.
He also at that time took a leading part in the establishment of the following institutions connected with his profession-the Northern Dispensary, of which he was acting physician for eighteen years; the Great Windmill Street School of Medicine, where he lectured ’ for five years on the Practice of Physic; and the Medico-Chirurgical Society, of which he was secretary for seventeen years, and president for two years. He also held for many years the post of physician to the Spanish Embassy.
Dr. Roget became known as a practical mathematician by his invention, in 1814, of a sliding rule for performing the operations of involution and evolution of numbers, on principles similar to those of the common sliding-rule for obtaining products and quotients. In Dr. Roget’s instrument, the rule or fixed line is marked in degrees proportioned to the second logarithms (or logarithms of logarithms), while the slider retains its graduation on the scale of simple logarithms, of the natural numbers. On a single setting €or a given number, the rule or fixed line exhibits the whole series of powers of that number corresponding to the exponents marked on the slider. That this must be the case may be seen in the general formula, log. log a + log m = log. log a nb.
By reversing the slider, the series of roots may be similarly displayed; and the rule may also be used to find the exponent of a given power, and to solve other problems, such as the interpolation of mean terms of a geometric series. Among the various applications of which it is susceptible may be mentioned the calculation of compound interest, the solution of questions relating to the increase of population, the doctrine of chances, the radiation of heat, the transmission of light, and the density of gases under pressure. A full description of the instrument, with suggestions of other modes in which the logo-logarithmic scale may be employed mechanically for similar purposes, is contained in Dr. Roget’s paper on the subject in the “Philosophical Transactions” for 1825, with which body his name was afterwards long associated as one of its secretaries. He held that office from 1827 to 1848.
In 1823 Dr. Roget and Dr. Latham were appointed physicians to the Millbank Penitentiary on the occasion of epidemic dysentery which had broken out there. The result of their labours appeared in a Report to the House of Commons in the following year.
In 1824 Dr. Roget married Miss Hobson, daughter of a Liverpool merchant. He was left a widower with two children in 1833.
On the 25th of June, 1827, a Royal Commission was issued to Dr. Roget, Mr. Brande, and Mr. Telford, to inquire into the state of the supply of water in the metropolis, it being already evident, from the disappearance of fish and other symptoms, that the river Thames was suffering a gradual deterioration. The result of their inquiries, and of a series of analyses performed under their direction by Dr. Bostock, was, that the water was susceptible of improvement by filtration, but that it ought to be supplied from other sources than the tidal portion of the Thames. To their report, dated 21st April, 1828, is also appended a mass of information collected with a view to providing a remedy for the state of things then existing, which shows that the commissioners were fully prepared to prosecute an inquiry in that direction had the Government of the day thought fit to afford them the means of doing so.
Their recorded opinion led, however, to the adoption of a system of filtration, and subsequently to the Act of 1852, forbidding the water companies to draw their supplies below Teddington Lock.
On the 27th of March, 1838, Dr. Roget, being at the time Secretary to the Royal Society, was elected an Honorary Member of the Institution of Civil Engineers “on account of his high scientific attainments.” He was also an Honorary Member of the Smeatonian Society of Civil Engineers. At this time he was actively employed on the senate of the University of London, in the foundation of which body he took great interest, and for which he was for some years examiner in physiology and comparative anatomy. He was a member of nearly all the learned societies of London, and of numerous foreign academies.
Dr. Roget’s published works, the dates of which are scattered over a period of no leas than seventy years, embrace subjects so distinct from one another, that they afford a measure of his versatility of mind as well as extent of information. Although, during his life, his reputation as a writer was mainly founded on his admirable “Bridgewater Treatise,” on “Animal and Vegetable Physiology,” the first edition of which came out in 1834, it seems probable that his name will be better known to future generations by the work of his old age, his “Thesaurus of English Words and Phrases.” This is a philosophical arrangement of words so disposed as to exhibit, in their appropriate groups, the resources of the language which arc available for the expression of any given idea. Very early in life Dr. Roget had assured himself of the utility of such a work, by compiling for his own use a small vocabulary on the same system. His retirement from professional practice, and from the secretaryship of the Royal Society, at length gave him time to take up this design and carry it into effect.
The work was first published in 1852, since which time the demand for it has steadily increased, and its value is becoming more and more widely acknowledged. Of his other writings, the major part are on subjects connected with his profession, viewed in all cases under the light of science and philosophy. He contributed various articles to the “Encyclopaedia Britannica,” the most important of which is a treatise on “Physiology,” which was also published separately, together with his article on “Phrenology,” in which ‘pseudo’ science he was a declared unbeliever. In 1827-31, he wrote a series of treatises on “Electricity, Galvanism, Magnetism, and Electro-magnetism,” for the Society for the Promotion of Useful Knowledge, of which he was an active member. His familiarity with these branches of science had already appeared in his article in the “Quarterly Review” for 1826, on “Electromagnetism,” and in that entitled “Galvanism ” in the “Encyclopedia Metropolitana.” Of Dr. Roget’s minor writings, the following may with propriety be here noticed:-The article “Kaleidoscope,” in the supplement to the sixth edition of the “Encyclopaedia Britannica;” and a letter on the same subject, dated 3rd April, 1818, published in the “Annals of Philosophy,” vol. xi., p. 375, in which the writer draws attention to the advantages of that form of the instrument in which three mirrors are employed, and determines the conditions of its manufacture. An appendix to Larkin’s “Solid Geometry and Crystallography” (l820), in which Dr. Roget demonstrates the ratios subsisting between the volumes of the solids composing the artificial series, together with the inclinations of their faces.
In the “Annals of Philosophy,” N.S., vol. i., p. 135, is a letter dated 25th Jan., l821, from Dr. Roget, in which the writer points out a material error in Mr. Perkins’s account of his experiments on the compressibility of water. In the “Philosophical Transactions” for 1825, p. 131, is a curious paper by Dr. Roget on “An Optical Deception in the Appearance of the Spokes of a Wheel seen through Vertical Apertures.” To the “Scientific Gazette” for 1825, pp. 259, 277, Dr. Roget contributed a paper “On an Apparent Violation of the Law of Continuity,” in which he proposed the following paradox: If an elliptic hoop be supposed to be subjected to a force of compression in the direction of the major axis, and the action of this force be continued until the curve, passing through the form of a circle, opens out in a transverse direction, the major axis becoming the minor, the motion of each of the two foci would seem to be discontinuous, its direction changing suddenly at a right angle, after the foci have merged in the centre, at the moment when the ellipse takes the form of a circle. In the “Journal of the Royal Institution” for l831 is an article by Dr. Roget “On the Geometric Properties of the Magnetic Curve, with an account of an Instrument for its Mechanical Description.” The writer gives simple demonstrations of the fundamental propositions belonging to the curve, derived directly from the law of magnetic forces, and shows how it may be traced on paper by means of the property that the difference of the cosines of the angles made by the radii with the axis is a constant quantity. The “London and Edinburgh Philosophical Magazine” for April, 15-10 (vol. xvi.), Article li., is a “Description of a method of moving the Knight over every square of the Chess-board, without going twice over any one; commenting at any given square, and ending at any other given square of a different colour. By P. M. Roget, M.D., Sec. R.S.” It is an ingenious and complete solution of a problem which had exercised the ingenuity of mathematicians for a hundred years without a like success.
Dr. Roget also contrived, in 1845, a chess-board with movable cad men, which admits of being folded up and carried in the pocket without disturbing the state of the game. It bears the name of the “Economic Chess-board,” and is particularly adapted to the use of amateurs of chess problems. In contrivances such as this Dr. Roget’s ingenuity was continually at work. He had a natural taste for mechanism. At the meetings of the British Association his favourite section was that devoted to mechanical science, and it must be in the remembrance of many Fellows of the Royal Society with what interest he regarded the Swedish calculating machine when it was exhibited at Somerset House by the late Mr. Gravatt. Few persons mere then aware that he had himself projected and made some progress in constructing the model of an engine designed with the same object.
Although, in Dr. Roget’s scientific researches, the doctrine of utility, which had been impressed upon him in early life by his friends, Dumont and Bentham, was ever present to his mind, he was also incited to their pursuit by an innate and ardent love of his subject for its own sake. He would exhibit the same keen relish for analysis undertaken in the construction of a toy as when employed in the establishment of a physical principle; the same lively interest in mechanical contrivance, when amusing his friends with an optical illusion, as when working in the same field m&h Babbage and with Scheut’z. In his mode of describing the kaleidoscope of Sir David Brewster, for example, one may easily detect an acquaintance with the niceties of its construction, which was gained by personal experiments in its manufacture. His mind, thus constituted, was never at a loss for resources, and an habitual industry characterised him to his last day. In old age, when debarred by deafness from the enjoyment of society, and when external events ride less impression upon him than in former days, he long derived amusement from work which would demand from most men considerable application of mind; investigating difficult problems in optics, playing with permutations and combinations, and composing four-move stratagems of chess of acknowledged beauty and merit. A few years before his death he made considerable progress with a set of tangible or ocular demonstrations in plane geometry, such as proving the Forty-seventh Proposition of the First Book of Euclid by means of three pieces of card, which, differently placed together, would form either the square on the hypotenuse or the sum of the squares on the sides.
It was chiefly in such employments as these, pursued during his serene retirement from the n-world, that an indication remained o? what he had been in the prime of life, at a period which few of his many friends are now living to recall. Those among them who knew him best can say with confidence that no man was more benevolent at heart, more unaffected in word or deed, or more steadfast in the simple following of what he held to be right.
These qualities were accompanied by an unvarying gentleness of demeanour, a natural courtesy that was no respecter of persons, and an unselfish spirit that ever restrained him from imposing upon others the task he was himself able to perform.
Dr. Roget’s general writings are much esteemed for elegance of style; and his treatment of subjects which do not afford scope for literary ornament is no less remarkable for perspicuity and correctness.
He took a real pleasure in the mere neatness of execution of any work in hand, however trivial; and his firm, clear handwriting, invaluable to a mathematician, was the delight of compositors.
When he applied himself to a task, he strove to accomplish it thoroughly; never sparing himself trouble, though ever fertile of resources for the economy of labour; but apparently following out the principle, that what is worth doing at all is worth doing well.
Dr. Roget’s death was unattended by suffering. It occurred on the 12th of September, 1869, at West Malvern, where he had been spending the summer. A grey granite slab in the country churchyard now marks his resting-place, and records the great age of ninety years, to which he lived.