SIMPSON (Thomas)
, F. R. S. a very eminent mathematician, and professor of Mathematics in the Royal Military Academy at Woolwich, was born at Market Bosworth, in the county of Leicester, the 20th of August 1710. His father was a stuff-weaver in that town; and though in tolerable circumstances, yet, intending to bring up his son Thomas to his own business, he took so little care of his education, that he was only taught to read English. But nature had furnished him with talents and a genius for far other pursuits; which led him afterwards to the highest rank in the mathematical and philosophical sciences.
Young Simpson very soon gave indications of his turn for study in general, by eagerly reading all books he could meet with, teaching himself to write, and embracing every opportunity he could find of deriving knowledge from other persons. His father observing him thus to neglect his business, by spending his time in reading what he thought useless books, and following other such like pursuits, used all his endeavours to check such proceedings, and to induce him to follow his profession with steadiness and better effect. But after many struggles for this purpose, the differences thus produced between them at length rose to such a height, that our author quitted his father's house entirely.
Upon this occasion he repaired to Nuneaton, a town at a small distance from Bosworth, where he went to lodge at the house of a taylor's widow, of the name of Swinfield, who had been left with two children, a daughter and a son, by her husband, of whom the son, who was the younger, being but about two years older than Simpson, had become his intimate friend and companion. And here he continued some time, working at his trade, and improving his knowledge by reading such books as he could procure.
Among several other circumstances which, long before this, gave occasion to shew our author's early thirst for knowledge, as well as proving a fresh incitement to acquire it, was that of a large solar eclipse, which took place on the 11th day of May, 1724. This phenomenon, so awful to many who are ignorant of the cause of it, struck the mind of young Simpson with a strong curiosity to discover the reason of it, and to be able to predict the like surprising events. It was however several years before he could obtain his desire, which at length was gratified by the following accident. After he had been some time at Mrs. Swinfield's, at Nuneaton, a travelling pedlar came that way, and took a lodging at the same house, according to his usual custom. This man, to his profession of an itinerant merchant, had joined the more profitable one of a fortune-teller, which he performed by means of judicial astrology. Every one knows with what regard persons of such a cast are treated by the inhabitants of country villages; it cannot be surprising therefore that an untutored lad of nineteen should look upon this man as a prodigy, and, regarding him in this light, should endeavour to ingratiate himself into his favour; in which he succeeded so well, that the sage was no less taken with the quick natural parts and genius of his new acquaintance. The pedlar, intending a journey to Bristol fair, lest in the hands of young Simpson an old edition of Cocker's Arithmetic, to which was subjoined a short Appendix on Algebra, and a book upon Genitures, by Partridge the almanac maker. These books he had perused to so good purpose, during the absence of his | friend, as to excite his amazement upon his return; in consequence of which he set himself about erecting a genethliacal figure, in order to a presage of Thomas's future fortune.
This position of the heavens having been maturely considered secundum artem, the wizard, with great confidence, pronounced, that, “within two years time Simpson would turn out a greater man than himself!”
In fact, our author profited so well by the encouragement and assistance of the pedlar, afforded him from time to time when he occasionally came to Nuneaton, that, by the advice of his friend, he at length made an open profession of casting nativities himself; from which, together with teaching an evening school, he derived a pretty pittance, so that he greatly neglected his weaving, to which indeed he had never manifested any great attachment, and soon became the oracle of Nuneaton, Bosworth, and the environs. Scarce a courtship advanced to a match, or a bargain to a sale, without previously consulting the infallible Simpson about the consequences. But as to helping people to stolen goods, he always declared that above his skill; and over life and death he declared he had no power: all those called lawful questions he readily resolved, provided the persons were certain as to the horary data of the horoscope: and, he has often declared, with such success, that if from very cogent reasons he had not been thoroughly convinced of the vain foundation and fallaciousness of his art, he never should have dropt it, as he afterwards found himself in conscience bound to do.
About this time he married the widow Swinfield, in whose house he lodged, though she was then almost old enough to be his grandmother, being upwards of fifty years of age. After this the family lived comfortably enough together for some short time, Simpson occasionally working at his business of a weaver in the daytime, and teaching an evening school or telling fortunes at night; the family being also farther assisted by the labours of young Swinfield, who had been brought up in the profession of his father.
But this tranquillity was soon interrupted, and our author driven at once from his home and the profession of astrology, by the following accident. A young woman in the neighbourhood had long wished to hear or know something of her lover, who had been gone to sea; but Simpson had put her off from time to time, till the girl grew at last so importunate, that he could deny her no longer. He asked her if she would be afraid if he should raise the devil, thinking to deter her; but she declared she feared neither ghost nor devil: so he was obliged to comply. The scene of action pitched upon was a barn, and young Swinfield was to act the devil or ghost; who being concealed under some straw in a corner of the barn, was, at a signal given, to rise slowly out from among the straw, with his face marked so that the girl might not know him. Every thing being in order, the girl came at the time appointed; when Simpson, after cautioning her not to be afraid, began muttering some mystical words, and chalking round about them, till, on the signal given, up rises the taylor slow and solemn, to the great terror of the poor girl, who, before she had seen half his shoulders, fell into violent fits, crying out it was the very image of her lover; and the effect upon her was so dreadful, that it was thought either death or madness must be the consequence. So that poor Simpson was obliged immediately to abandon at once both his home and the profession of a conjuror.
Upon this occasion it would seem he fled to Derby, where he remained some two or three years, viz, from 1733 till 1735 or 1736; instructing pupils in an evening school, and working at his trade by day.
It would seem that Simpson had an early turn for versifying, both from the circumstance of a song written here in favour of the Cavendish family, on occasion of the parliamentary election at that place, in the year 1733; and from his first two mathematical questions that were published in the Ladies Diary, which were both in a set of verses, not ill written for the occasion. These were printed in the Diary for 1736, and therefore must at latest have been written in the year 1735. These two questions, being at that time pretty difficult ones, shew the great progress he had even then made in the mathematics; and from an expression in the first of them, viz, where he mentions his residence as being in latitude 52°, it appears he was not then come up to London, though he must have done so very soon after.
Together with his astrology, he had soon furnished himself with arithmetic, algebra, and geometry sufficient to be qualified for looking into the Ladies Diary (of which he had afterwards for several years the direction), by which he came to understand that there was a still higher branch of the mathematical knowledge than any he had yet been acquainted with; and this was the method of Fluxions. But our young analyst was quite at a loss to discover any English author who had written on the subject, except Mr. Hayes; and his work being a folio, and then pretty scarce, exceeded his ability of purchasing: however an acquaintance lent him Mr. Stone's Fluxions, which is a translation of the Marquis de l'Hospital's Analyse des Infiniment Petits: by this one book, and his own penetrating talents, he was, as we shall see presently, enabled in a very few years to compose a much more accurate treatise on this subject than any that had before appeared in our language.
After he had quitted astrology and its emoluments, he was driven to hardships for the subsistence of his family, while at Derby, notwithstanding his other industrious endeavours in his own trade by day, and teaching pupils at evenings. This determined him to repair to London, which he did in 1735 or 1736.
On his first coming to London, Mr. Simpson wrought for some time at his business in Spitalfields, and taught mathematics at evenings, or any spare hours. His industry turned to so good account, that he returned down into the country, and brought up his wife and three children, she having produced her first child to him in his absence. The number of his scholars increasing, and his abilities becoming in some measure known to the public, he was encouraged to make proposals for publishing by subscription, A new Treatise of Fluxions: wherein the Direct and Inverse Methods are demonstrated after a new, clear, and concise Manner, with their Application to Physics and Astronomy: also the Doctrine of Infinite Series and Reverting Series universally, are amply explained, Fluxionary and Exponential Equations solved: together with a variety of new and curious Problems. |
When Mr. Simpson first proposed his intentions of publishing such a work, he did not know of any English book, founded on the true principles of Fluxions, that contained any thing material, especially the practical part; and though there had been some very curious things done by several learned and ingenious gentlemen, the principles were nevertheless left obscure and defective, and all that had been done by any of them in infinite series, very inconsiderable.
The book was published in 4to, in the year 1737, although the author had been frequently interrupted from furnishing the press so fast as he could have wished, through his unavoidable attention to his pupils for his immediate support. The principles of fluxions treated of in this work, are demonstrated in a method accurately true and genuine, not essentially different from that of their great inventor, being entirely expounded by finite quantities.
In 1740, Mr. Simpson published a Treatise on The Nature and Laws of Chance, in 4to. To which are annexed, Full and clear Investigations of two important Problems added in the 2d Edition of Mr. De Moivre's Book on Chances, as also two New Methods for the Summation of Series.
Our author's next publication was a 4to volume of Essays on several curious and interesting Subjects in Speculative and Mixed Mathhmatics; printed in the same year 1740: dedicated to Francis Blake, Esq. since Fellow of the Royal Society, and our author's good friend and patron.—Soon after the publication of this book, he was chosen a member of the Royal Academy at Stockholm.
Our author's next work was, The Doctrine of Annuities and Reversions, deduced from general and evident Principles: with useful Tables, shewing the Values of Single and Joint Lives, &c. in 8vo, 1742. This was followed in 1743, by an Appendix containing some Remarks on a late book on the same Subject (by Mr. Abr. De Moivre, F. R. S.) with Answers to some personal and malignant Representations in the Preface thereof. To this answer Mr. De Moivre never thought fit to reply. A new edition of this work has lately been published, augmented with the tract upon the same subject that was printed in our author's Select Exercises.
In 1743 also was published his Mathematical Dissertations on a variety of Physical and Analytical Subjects, in 4to; containing, among other particulars,
A Demonstration of the true Figure which the Earth, or any Planet, must acquire from its rotation about an Axis. A general Investigation of the Attraction at the Surfaces of Bodies nearly spherical. A Determination of the Meridional Parts, and the Lengths of the several Degrees of the Meridian, according to the true Figure of the Earth. An Investigation of the Height of the Tides in the Ocean. A new Theory of Astronomical Refractions, with exact Tables deduced from the same. A new and very exact Method for approximating the Roots of Equations in Numbers; which quintuples the number of Places at each Operation. Several new Methods for the Summation of Series. Some new and very useful Improvements in the Inverse Method of Fluxions. The work being dedicated to Martin Folkes, Esq. President of the Royal Society.
His next book was A Treatise of Algebra, wherein the fundamental Principles are demonstrated, and applied to the Solution of a variety of Problems. To which he added, The Construction of a great Number of Geometrical Problems, with the Method of resolving them numerically.
This work, which was designed for the use of young beginners, was inscribed to William Jones, Esq. F. R. S. and printed in 8vo, 1745. And a new edition appeared in 1755, with additions and improvements; among which was a new and general method of resolving all Biquadratic Equations, that are complete, or having all their terms. This edition was dedicated to James Earl of Morton, F. R. S. Mr. Jones being then dead. The work has gone through several other editions since that time: the 6th, or last, was in 1790.
His next work was, “Elements of Geometry, with their Application to the Mensuration of Superficies and Solids, to the Determination of Maxima and Minima, and to the Construction of a great Variety of geometrical Problems:” first published in 1747, in 8vo. And a second edition of the same came out in 1760, with great alterations and additions, being in a manner a new work, designed for young beginners, particularly for the gentlemen educated at the Royal Military Academy at Woolwich, and dedicated to Charles Frederick, Esq. Surveyor General of the Ordnance. And other editions have appeared since.
Mr. Simpson met with some trouble and vexation in consequence of the first edition of his Geometry. First, from some reflections made upon it, as to the accuracy of certain parts of it, by Dr. Robert Simson, the learned professor of mathematicks in the university of Glasgow, in the notes subjoined to his edition of Euclid's Elements. This brought an answer to those remarks from Mr. Simpson, in the notes added to the 2d edition as above; to some parts of which Dr. Simson again replied in his notes on the next edition of the said Elements of Euclid.
The second was by an illiberal charge of having stolen his Elements from Mr. Muller, the professor of fortification and artillery at the same academy at Woolwich, where our author was professor of geometry and mathematics. This charge was made at the end of the preface to Mr. Muller's Elements of Mathematics, in two volumes, printed in 1748; which was fully refuted by Mr. Simpson in the preface to the 2d edition of his Geometry.
In 1748 came out Mr. Simpson's Trigonometry, Plane and Spherical, with the Construction and Application of Logarithms, 8vo. This little book contains several things new and useful.
In 1750 came out, in two volumes, 8vo, The Doctrine and Application of Fluxions, containing, besides what is common on the Subject, a Number of new Improvements in the Theory, and the Solution of a Variety of new and very interesting Problems in different Branches of the Mathematics.—In the preface the author offers this to the world as a new book, rather than a second edition of that which was published in 1737, in which he acknowledges, that, besides errors of the press, there are several obscurities and defects, for want of experience, and the many disadvantages he then laboured under, in his first sally. |
The idea and explanation here given of the first principles of Fluxions, are not essentially different from what they are in his former treatise, though expressed in other terms. The consideration of time introduced into the general definition, will, he says, perhaps be disliked by those who would have fluxions to be mere velocities: but the advantage of considering them otherwise, viz, not as the velocities themselves, but as magnitudes they would uniformly generate in a given time, appears to obviate any objection on that head. By taking fluxions as mere velocities, the imagination is confined as it were to a point, and without proper care insensibly involved in metaphysical difficulties. But according to this other mode of explaining the matter, less caution in the learner is necessary, and the higher orders of fluxions are rendered much more easy and intelligible. Besides, though Sir Isaac Newton defines fluxions to be the velocities of motions, yet he has recourse to the increments or moments generated in equal particles of time, in order to determine those velocities; which he afterwards teaches to expound by finite magnitudes of other kinds. This work was dedicated to George earl of Macclesfield.
In 1752 appeared, in 8vo, the Select Exercises for young Preficients in the Mathematics. This neat volume contains, A great Variety of algebraical Problems, with their Solutions. A select Number of Geometrical Problems, with their Solutions, both algebraical and geometrical. The Theory of Gunnery, independent of the Conic Sections. A new and very comprehensive Method for finding the Roots of Equations in Numbers. A short Account of the first Principles of Fluxions. Also the Valuation of Annuities for single and joint Lives, with a Set of new Tables, far more extensive than any extant. This last part was designed as a supplement to his Doctrine of Annuities and Reversions; but being thought too small to be published alone, it was inserted here at the end of the Select Exercises; from whence however it has been removed in the last editions, and referred to its proper place, the end of the Annuities, as before mentioned. The examples that are given to each problem in this last piece, are according to the London bills of mortality; but the solutions are general, and may be applied with equal facility and advantage to any other table of observations. The volume is dedicated to John Bacon, Esq. F. R. S.
Mr. Simpson's Miscellaneous Tracts, printed in 4to, 1757, were his last legacy to the public: a most valuable bequest, whether we consider the dignity and importance of the subjects, or his sublime and accurate manner of treating them.
The first of these papers is concerned in determining the Precession of the Equinox, and the different Motions of the Earth's Axis, arising from the Attraction of the Sun and Moon. It was drawn up about the year 1752, in consequence of another on the same subject, by M. de Sylvabelle, a French gentleman. Though this gentleman had gone through one part of the subject with success and perspicuity, and his conclusions were perfectly conformable to Dr. Bradley's observations; it nevertheless appeared to Mr. Simpson, that he had greatly failed in a very material part, and that indeed the only very difficult one; that is, in the determination of the momentary alteration of the po- sition of the earth's axis, caused by the forces of the sun and moon; of which forces, the quantities, but not the effects, are truly investigated. The second paper contains the Investigation of a very exact Method or Rule for finding the Place of a Planet in its Orbit, from a Correction of Bishop Ward's circular Hypothesis, by Means of certain Equations applied to the Motion about the upper Focus of the Ellipse. By this Method the Result, even in the Orbit of Mercury, may be found within a Second of the Truth, and that without repeating the Operation. The third shews the Manner of transferring the Motion of a Comet from a parabolic Orbit, to an elliptic one; being of great Use, when the observed Places of a (new) Comet are sound to differ sensibly from those computed on the Hypothesis of a parabolic Orbit. The fourth is an Attempt to shew, from mathematical Principles, the Advantage arising from taking the Mean of a Number of Observations, in practical Astronomy; wherein the Odds that the Result in this Way, is more exact than from one single Observation, is evinced, and the Utility of the Method in Practice clearly made appear. The fifth contains the Determination of certain Fluents, and the Resolution of some very useful Equations, in the higher Orders of Fluxions, by Means of the Measures of Angles and Ratios, and the right and versed Sines of circular Arcs. The 6th treats of the Resolution of algebraical Equations, by the Method of Surd-divisors; in which the Grounds of that Method, as laid down by Sir Isaac Newton, are investigated and explained. The 7th exhibits the Investigation of a general Rule for the Resolution of Isoperimetrical Problems of all Orders, with some Examples of the Use and Application of the said Rule. The 8th, or last part, comprehends the Resolution of some general and very important Problems in Mechanics and Physical Astronomy; in which, among other Things, the principal Parts of the 3d and 9th Sections of the first Book of Newton's Principia are demonstrated in a new and concise Manner. But what may perhaps best recommend this excellent tract, is the application of the general equations, thus derived, to the determination of the Lunar Orbit.
According to what Mr. Simpson had intimated at the conclusion of his Doctrine of Fluxions, the greatest part of this arduous undertaking was drawn up in the year 1750. About that time M. Clairaut, a very eminent mathematician of the French Academy, had started an objection against Newton's general law of gravitation. This was a motive to induce Mr. Simpson (among some others) to endeavour to discover whether the motion of the moon's apogee, on which that objection had its whole weight and foundation, could not be truly accounted for, without supposing a change in the received law of gravitation, from the inverse ratio of the squares of the distances. The success answered his hopes, and induced him to look farther into other parts of the theory of the moon's motion, than he had at first intended: but before he had completed his design, M. Clairaut arrived in England, and made Mr. Simpson a visit; from whom he learnt, that he had a little before printed a piece on that subject, a copy of which Mr. Simpson asterwards received as a present, and found in it the same things demonstrated, to which he himself had directed his enquiry, besides several others. |
The facility of the method Mr. Simpson fell upon, and the extensiveness of it, will in some measure appear from this, that it not only determines the motion of the apogee, in the same manner, and with the same ease, as the other equations, but utterly excludes all that dangerous kind of terms that had embarrassed the greatest mathematicians, and would, after a great number of revolutions, entirely change the figure of the moon's orbit. From whence this important consequence is derived, that the moon's mean motion, and the greatest quantities of the several equations, will remain unchanged, unless disturbed by the intervention of some foreign or accidental cause. These tracts are inscribed to the Earl of Macclesfield, President of the Royal Society.
Besides the foregoing, which are the whole of the regular books or treatises that were published by Mr. Simpson, he wrote and composed several other papers and fugitive pieces, as follow:
Several papers of his were read at the meetings of the Royal Society, and printed in their Transactions: but as most, if not all of them, were afterwards inserted, with alterations or additions, in his printed volumes, it is needless to take any farther notice of them here.
He proposed, and resolved many questions in the Ladies Diaries, &c; sometimes under his own name, as in the years 1735 and 1736; and sometimes under feigned or fictitious names; such as, it is thought, Hurlothrumbo, Kubernetes, Patrick O'Cavenah, Marmaduke Hodgson, Anthony Shallow, Esq, and probably several others; see the Diaries for the years 1735, 1736, 42, 43, 53, 54, 55, 56, 57, 58, 59, and 60. Mr. Simpson was also the editor or compiler of the Diaries from the year 1754 till the year 1760, both inclusive, during which time he raised that work to the highest degree of respect. He was succeeded in the Editorship by Mr. Edw. Rollinson. See my Diarian Miscellany, vol. 3.
It has also been commonly supposed that he was the real editor of, or had a principal share in; two other periodical works of a miscellaneous mathematical nature; viz, the Mathematician, and Turner's Mathematical Exercises, two volumes, in 8vo, which came out in periodical numbers, in the years 1750 and 1751, &c. The latter of these seems especially to have been set on foot to afford a proper place for exposing the errors and absurdities of Mr. Robert Heath, the then conductor of the Ladies Diary and the Palladium; and which controversy between them ended in the disgrace of Mr. Heath, and expulsion from his office of editor to the Ladies Diary, and the substitution of Mr. Simpson in his stead, in the year 1753.
In the year 1760, when the plans proposed for erecting a new bridge at Blackfriars were in agitation, Mr. Simpson, among other gentlemen, was consulted upon the best form for the arches, by the New-bridge Committee. Upon this occasion he gave a preference to the semicircular form; and, besides his report to the Committee, some letters also appeared, by himself and others, on the same subject, in the public newspapers, particularly in the Daily Advertiser, and in Lloyd's Evening Post. The same were also collected in the Gentleman's Magazine for that year, page 143 and 144.
It is probable that this reference to him, gave occasion to the turning his thoughts more seriously to this subject, so as to form the design of composing a regular treatise upon it: for his family have often informed me, that he laboured hard upon this work for some time before his death, and was very anxious to have completed it, frequently remarking to them, that this work, when published, would procure him more credit than any of his former publications. But he lived not to put the finishing hand to it. Whatever he wrote upon this subject, probably fell, together with all his other remaining papers, into the hands of major Henry Watson, of the engineers, in the service of the India Company, being in all a large chest full of papers. This gentleman had been a pupil of Mr. Simpson's, and had lodged in his house. After Mr. Simpson's death, Mr. Watson prevailed upon the widow to let him have the papers, promising either to give her a sum of money for them, or else to print and publish them for her benefit. But neither of these was ever done; this gentleman always declaring, when urged on this point by myself and others, that no use could be made of any of the papers, owing to the very imperfect slate in which he said they were left. And yet he persisted in his refusal to give them up again.
From Mr. Simpson's writings, I now return to himself. Through the interest and solicitations of the beforementioned William Jones, Esq, he was, in 1743, appointed professor of mathematics, then vacant by the death of Mr. Derham, in the Royal Academy at Woolwich; his warrant bearing date August 25th. And in 1745 he was admitted a fellow of the Royal Society, having been proposed as a candidate by Martin Folkes, Esq. President, William Jones, Esq. Mr. George Graham, and Mr. John Machin, Secretary; all very eminent mathematicians. The president and council, in consideration of his very moderate circumstances, were pleased to excuse his admission fees, and likewise his giving bond for the settled future payments.
At the academy he exerted his faculties to the utmost, in instructing the pupils who were the immediate objects of his duty, as well as others, whom the superior officers of the ordnance permitted to be boarded and lodged in his house. In his manner of teaching, he had a peculiar and happy address; a certain dignity and perspicuity, tempered with such a degree of mildness, as engaged both the attention, esteem and friendship of his scholars; of which the good of the service, as well as of the community, was a necessary consequence.
It must be acknowledged however, that his mildness and easiness of temper, united with a more inactive state of mind, in the latter years of his life, rendered his services less useful; and the same very easy disposition, with an innocent, unsuspecting simplicity, and playfulness of mind, rendered him often the dupe of the little tricks of his pupils. Having discovered that he was fond of listening to little amusing stories, they took care to furnish themselves with a stock; so that, having neglected to learn their lessons perfect, they would get round him in a crowd, and, instead of demonstrating a proposition, would amuse him with some comical story, at which he would laugh and shake very heartily, especially if it were tinctured with somewhat of the | ludicrous or smutty; by which device they would contrive imperceptibly to wear out the hours allotted for instruction, and so avoid the trouble of learning and repeating their lesson. They tell also of various tricks that were practised upon him in consequence of the loss of his memory in a great degree, in the latter stage of his life.
It has been said that Mr. Simpson frequented low company, with whom he used to guzzle porter and gin: but it must be observed that the misconduct of his family put it out of his power to keep the company of of gentlemen, as well as to procure better liquor.
In the latter stage of his existence, when his life was in danger, exercise and a proper regimen were prescribed him, but to little purpose; for he sunk gradually into such a lowness of spirits, as often in a manner deprived him of his mental faculties, and at last rendered him incapable of performing his duty, or even of reading the letters of his friends; and so trifling an accident as the dropping of a tea-cup would flurry him as much as if a house had tumbled down.
The physicians advised his native air for his recovery; and in February, 1761, he set out, with much reluctance (believing he should never return) for Bosworth, along with some relations. The journey fatigued him to such a degree, that upon his arrival he betook himself to his chamber, where he grew continually worse and worse, to the day of his death, which happened the 14th of May, in the fiftyfirst year of his age.
