Speaker 1: Chapter eighteen, Part four of A Short Account of the
Speaker 1: History of Mathematics by W. W. Rowsball. This is a
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Speaker 1: This is a reading by Paul King PJK dot scripts
Speaker 1: that I might t dot e d U forward slash
Speaker 1: p j K. A Short account of the History of
Speaker 1: mathematics by W. W. Rowsball, Chapter eighteen Leibniz and the
Speaker 1: Mathematicians of the first half of the eighteenth century, Part four. Cavendish,
Speaker 1: the Honorable Henry Cavendish was born at Nice on October tenth,
Speaker 1: seventeen thirty one, and died in London on February twenty fourth,
Speaker 1: eighteen ten. His tastes for scientific research and mathematics were
Speaker 1: formed at Cambridge, where he resided from seventeen forty nine
Speaker 1: to seventeen fifty three. He created experimental electricity and was
Speaker 1: one of the earliest writers to treat chemistry as an
Speaker 1: exact science. I mention him here on account of his
Speaker 1: experiment in seventeen ninety eight to determine the density of
Speaker 1: the Earth by estimating its attraction as compared with that
Speaker 1: of two given lead balls. The result is that the
Speaker 1: mean density of the Earth is about five and a
Speaker 1: half times that of water. This experiment was carried out
Speaker 1: in accordance with a suggestion which had been first made
Speaker 1: by John Mitchell, a fellow of Queen's College, Cambridge, who
Speaker 1: had died before he was able to carry it into effect. Rumford,
Speaker 1: Sir Benjamin Thompson, Count Rumford, born at Concord on March
Speaker 1: twenty sixth, seventeen fifty three and died at Auteil on
Speaker 1: August twenty first, eighteen fifteen. Was of English descent and
Speaker 1: fought on the side of the lawyer Illis in the
Speaker 1: American War of Secession. On the conclusion of peace, he
Speaker 1: settled in England, but subsequently entered the service of Bavaria,
Speaker 1: where his military and civil powers of organization proved of
Speaker 1: great value. At a later period he again resided in England,
Speaker 1: and when there he founded the Royal Institution. The majority
Speaker 1: of his papers were communicated to the Royal Society of London.
Speaker 1: Of these, the most important is his memoir, in which
Speaker 1: he shewed that heat and work are mutually convertible. Young.
Speaker 1: Among the most eminent physicists of his time was Thomas Young,
Speaker 1: who was born in Milverton on June thirteenth, seventeen seventy
Speaker 1: three and died in London on May tenth, eighteen twenty nine.
Speaker 1: He seems as a boy to have been somewhat of
Speaker 1: a prodigy, being well read in modern languages and literature
Speaker 1: as well as in science. He always kept up his
Speaker 1: literary tastes, and it was he who first furnished the
Speaker 1: key to decipher the Egyptian hieroglyphics. He was destined to
Speaker 1: be a doctor, and after attending lectures at Edinburgh and Gottingen,
Speaker 1: entered im Manual College, Cambridge, from which he took his
Speaker 1: degree in seventeen ninety nine, and to his stay at
Speaker 1: the university he attributed much of his future distinction. His
Speaker 1: medical career was not particularly successful, and his favorable maxim
Speaker 1: that a medical diagnosis is only a balance of probabilities
Speaker 1: was not appreciated by his patients, who looked for certainty
Speaker 1: and returned for their fee. Fortunately, his private means were ample.
Speaker 1: Several papers contributed to various learned societies from seventeen ninety
Speaker 1: eight onwards prove him to have been a mathematician of
Speaker 1: considerable power. But the researches which have immortalized his name
Speaker 1: are those by which he laid down the laws of
Speaker 1: interference of waves and light, and was thus able to
Speaker 1: suggest the means by which the chief difficulties in the
Speaker 1: way of acceptance of the undulatory theory of light could
Speaker 1: be overcome. Wallaston. Another experimental physicist of the same time
Speaker 1: in school was William Hyde Wallaston, who was born at
Speaker 1: Dereham on August sixth, seventeen sixty six and died in
Speaker 1: London on December twenty second, eighteen twenty eight. He was
Speaker 1: educated at Caius College, Cambridge, of which society he was
Speaker 1: a fellow. Besides his well known chemical experiments, he has
Speaker 1: celebrated for his researches on experimental optics and for the
Speaker 1: improvements which he affected in astronomical instruments. Dalton. Another distinguished
Speaker 1: writer of the same period was John Dalton, who was
Speaker 1: born in Cumberland on September fifth, seventeen sixty six and
Speaker 1: died at Manchester on July twenty seventh, eighteen forty four.
Speaker 1: Dalton investigated the tension of vapors and the law of
Speaker 1: the expansion of a gas under changes of temperature. He
Speaker 1: also found the atomic theory in chemistry. It will be
Speaker 1: gathered from these notes that the English school of physicists
Speaker 1: at the beginning of this century were mostly concerned with
Speaker 1: the experimental side of the subject, but in fact no
Speaker 1: satisfactory theory could be formed without some similar careful determination
Speaker 1: of the facts. The most eminent French physicists of the
Speaker 1: same time were Fourier, Poissin Ampere, and Fresnol. Their method
Speaker 1: of treating the subject is more mathematical than that of
Speaker 1: their English contemporaries, and the two first named were distinguished
Speaker 1: for general mathematical ability. Fourier. The first of these French
Speaker 1: physicists was Jean Baptiste Joseph Fourier, who was born at
Speaker 1: Auterre on March twenty first, seventeen sixty eight and died
Speaker 1: at Paris on May sixteenth, eighteen thirty. He was the
Speaker 1: son of a tailor and was educated by the Benedictines.
Speaker 1: The commissions in the scientific corps of the army was,
Speaker 1: as still the case in Russia, reserved for those of
Speaker 1: good birth, and being thus ineligible, he accepted a military
Speaker 1: lectureship on mathematics. He took a prominent part in his
Speaker 1: own district in promoting the revolution, and was rewarded by
Speaker 1: an appointment in seventeen ninety five in the normal school,
Speaker 1: and subsequently by a chair at the Polytechnic School. He
Speaker 1: went with Napoleon on his Eastern expedition in seventeen ninety
Speaker 1: eight and was made governor of Lower Egypt, cut off
Speaker 1: from France by the English fleet, he organized the workshops
Speaker 1: on which the French army had to rely for their
Speaker 1: munitions of war. He also contributed several mathematical papers to
Speaker 1: the Agiat Institute, which Napoleon founded at Cairo with a
Speaker 1: view of weakening English influence in the East. After the
Speaker 1: British victories and the capitulation of the French under General
Speaker 1: Manon in eighteen oh one, he returned to France and
Speaker 1: was made prefect of Grenoble, and it was while there
Speaker 1: that he made his experiments on the propagation of heat.
Speaker 1: He moved to Paris in eighteen sixteen. In eighteen twenty
Speaker 1: two he publishes Theory and a Letigue les chere, in
Speaker 1: which he bases his reasoning on Newton's law of cooling,
Speaker 1: namely that the flow of heat between two adjacent molecules
Speaker 1: is proportional to the infinitely small difference of their temperatures.
Speaker 1: He states that the theory demands that the temperatures of
Speaker 1: stellar space should be between minus fifty degrees celsius and
Speaker 1: minus sixty degrees celsius, a conclusion which it has been
Speaker 1: as yet impossible to prove or disproof. In this work
Speaker 1: issues that any function of a variable, whether continuous or discontinuous,
Speaker 1: can be expanded in a series of signs of multiples
Speaker 1: of the variable, a result which is constantly used in
Speaker 1: modern analysis. Lagrange had given particular cases of the theorem
Speaker 1: and had implied that the method was general, but he
Speaker 1: had not pursued the subject. Fourier left an unfinished work
Speaker 1: on determinate equations, which was edited by Navier and published
Speaker 1: in eighteen thirty one. This contains much original matter. In particular,
Speaker 1: there is a demonstration of Fourier's theorem on the position
Speaker 1: of the roots of an algebraic equation. Lagrange had shown
Speaker 1: how the roots of an algebraical equation might be separated
Speaker 1: by means of another equation whose roots were the squares
Speaker 1: of the differences of the roots of the original equation.
Speaker 1: Budan in eighteen o seven and X eighteen eleven had
Speaker 1: enunciated the theorem generally known by the name of Fourier,
Speaker 1: but the demonstration was clumsy and not altogether satisfactory. Fourier's
Speaker 1: proof is the same as that usually given in textbooks
Speaker 1: on the theory of equations. The final solution of the
Speaker 1: problem was given in eighteen twenty nine by Jacques Chain,
Speaker 1: Francois Sturm Saudiq Calnou. Among Fourier's contemporaries who were interested
Speaker 1: in the theory of heat, the most eminent was Saldi Calno,
Speaker 1: son of the eminent geometrician mentioned previously. Saudi Calno was
Speaker 1: born at Paris in seventeen ninety six and died there
Speaker 1: of cholera in August eighteen thirty two. He was an
Speaker 1: officer in the French army. In eighteen twenty four he
Speaker 1: issued a short work entitled Reflection selepresence montris deu feu,
Speaker 1: in which he attempted to determine in what way heat
Speaker 1: produced its mechanical effect. He made the mistake of assuming
Speaker 1: that heat was material, but his essay was the commencement
Speaker 1: of the modern theory of thermodynamics. Poissant Semeon. Denis Poisson
Speaker 1: born at Pithiviers on June twenty first, seventeen eighty one
Speaker 1: and died at Paris on April twenty fifth, eighteen forty
Speaker 1: is almost equally distinguished for his application of mathematics to
Speaker 1: mechanics and to physics. His father had been a common soldier,
Speaker 1: and on his retirement was given some small administrative post
Speaker 1: in his native village. When the revolution broke out, he
Speaker 1: appears to have assumed the government of the place, and,
Speaker 1: being left undisturbed, became a person of some local importance.
Speaker 1: The boy was put out to nurse, and he used
Speaker 1: to tell how one day his father, coming to see him,
Speaker 1: found that the nurse had gone out on pleasure bent
Speaker 1: while she had left him suspended by a small cord
Speaker 1: to a nail fixed in the wall. This, she explained,
Speaker 1: was a necessary precaution to prevent him from perishing under
Speaker 1: the teeth of the various animals and animicula that roamed
Speaker 1: on the floor. Poissin used to add that his gymnastic
Speaker 1: efforts carried him incessantly from one side to the other,
Speaker 1: and it was thus in his tenderest infancy that he
Speaker 1: commenced those studies on the pendulum that were there to
Speaker 1: occupy so large a part of his mature age. He
Speaker 1: was educated by his father and destined, much against his will,
Speaker 1: to be a doctor. His uncle offered to teach him
Speaker 1: the art, and began by making him prick the veins
Speaker 1: of cabbage leaves with a lancet. When perfect in this
Speaker 1: he was allowed to put on blisters, but in almost
Speaker 1: the first case he did this by himself. The patient
Speaker 1: died in a few hours, and though all the medical
Speaker 1: practitioners of the place assured him that the event was
Speaker 1: a very common one, he vowed he would have nothing
Speaker 1: more to do with the profession. Returning home, he found
Speaker 1: amongst the official papers sent to his father a copy
Speaker 1: of the Questions set at the Polytechnic School, and at
Speaker 1: once found his career. At the age of seventeen, he
Speaker 1: entered the Polytechnic, and his abilities excited the interests of
Speaker 1: Lagrange and Laplace, whose friendship he retained to the end
Speaker 1: of their lives. A memoir on Finite Differences, which he
Speaker 1: wrote when only eighteen, was reported on so favorably by
Speaker 1: Legendre that it was ordered to be published in the
Speaker 1: Recuere des Sevante et cage. Directly he had finished the course,
Speaker 1: he was made a lecturer at the school, and he
Speaker 1: continued through his life to hold various government, scientific posts
Speaker 1: and professorships. He was somewhat of a socialist, and remained
Speaker 1: a rigid Republican till eighteen fifteen. With a view to
Speaker 1: me making another empire impossible, he joined the Legitimists. He took, however,
Speaker 1: no active part in politics, and made the study of
Speaker 1: mathematics his amusement as well as his business. His works
Speaker 1: and memoirs are between three and four hundred in number.
Speaker 1: The chief treatises which he wrote were as Treates de
Speaker 1: Mechanique two volumes, eighteen eleven and eighteen thirty three, which
Speaker 1: was long a standard work, His Theory nouver de laxion
Speaker 1: Capelli in eighteen thirty one, his Theory mathematic de lecheur
Speaker 1: in eighteen thirty five, to which a supplement was added
Speaker 1: in eighteen thirty seven, and is recherche les probability de
Speaker 1: jugement in eighteen thirty seven. He had intended, if he
Speaker 1: had lived, to write a work which should cover all
Speaker 1: mathematical physics, and in which these would have been incorporated
Speaker 1: of his memoirs on the subject of pure mathematics, the
Speaker 1: most important are those on definite integrals and the Fourier's series.
Speaker 1: These are to be found on the Jenel Polytechnique from
Speaker 1: eighteen thirteen to eighteen twenty three and in the Memoir
Speaker 1: de Lacademie for eighteen twenty three. Their application to physical
Speaker 1: problems constituting one of his chief claims to distinction his
Speaker 1: essay on the Calculus of variations Mamou de Lacademie eighteen
Speaker 1: thirty three and his papers on the Probability of the
Speaker 1: mean results of observations Connaissance de Tempe eighteen twenty seven
Speaker 1: and following years. Most of his memoirs were published in
Speaker 1: the three periodicals here mentioned. Perhaps the most remarkable of
Speaker 1: his memoirs and applied mathematics are those on the theory
Speaker 1: of electrostatics and magnetism, which originated a new branch of
Speaker 1: mathematical physics. He supposed that the results were due to
Speaker 1: the attractions and repulsions of imponderable part of the most
Speaker 1: important of those on physical astronomy are the two re
Speaker 1: read in eighteen oh six printed in eighteen oh nine
Speaker 1: on the secular inequalities of the mean motions of the planets,
Speaker 1: and on the variations of arbitrary constants introduced into the
Speaker 1: solutions of questions on mechanics. In those Poissan discusses the
Speaker 1: question of the stability of the planetary orbits, which Legendre
Speaker 1: had already proved to the first degree of approximation for
Speaker 1: the distributing forces. Enchows that the result can be extended
Speaker 1: to the third order of small quantities. These were the
Speaker 1: memoirs which led to Lagrange's famous memoir of eighteen oh eight.
Speaker 1: Poissan also published a paper in eighteen twenty one on
Speaker 1: the libration of the Moon, and another in eighteen twenty
Speaker 1: seven on the motion of the Earth about its center
Speaker 1: of gravity. His most important memoirs and the theory of
Speaker 1: attraction are one in eighteen twenty nine on the attraction
Speaker 1: of spheroids, and another in eighteen thirty five on the
Speaker 1: attraction of a homogeneous ellipsoid. The substitution of the correct
Speaker 1: equation involving the potential, namely grad squared v equals negative
Speaker 1: four pi row for Laplace's form of it, Pi squared
Speaker 1: v equals zero was first published in eighteen thirteen in
Speaker 1: De Bouditaine des science of the society Phiromatique. Lastly, I
Speaker 1: may mention his memoir in eighteen twenty five on the
Speaker 1: theory of waves. Empeire Andre Marie Ampere was born at
Speaker 1: Leon in January twenty second, seventeen seventy five, and died
Speaker 1: at Marseilles on June tenth, eighteen thirty six. He was
Speaker 1: widely read in all branches of learning, and lectured and
Speaker 1: wrote on many of them. But after the year eighteen
Speaker 1: o nine, when he was made professor of analysis at
Speaker 1: the Polytechnic School in Paris, he confined himself almost entirely
Speaker 1: to mathematics and science. His papers on the connection between
Speaker 1: electricity and magnetism were written in eighteen twenty. According to
Speaker 1: his theory propounded in eighteen twenty six, a molecule of
Speaker 1: matter which can be magnetized is traversed by a cloud
Speaker 1: of electric current, and a magnetization is produced by any
Speaker 1: cause which makes the direction of these currents in the
Speaker 1: different molecules of the body approach parallelism. Fresnel Augustin Jean
Speaker 1: Fresnel born at Broglie on May tenth, seventeen eighty eight
Speaker 1: and died at Verderey on July fourteenth, eighteen twenty seven.
Speaker 1: Was a civil engineer by profession, but he devoted his
Speaker 1: leisure to the study of physical optics. The undulatory theory
Speaker 1: of light, which huck Reugens and Euler had supported on
Speaker 1: a priori grounds, had been based on experiment by the
Speaker 1: researches of Fresnel deduced the mathematical consequences of these experiments
Speaker 1: and explained the phenomenon of the interference of both ordinary
Speaker 1: and polarized light. Billout Fresnel's friend and contemporary, Jean Baptiste Biot,
Speaker 1: who was born at Paris on April twenty first, seventeen
Speaker 1: seventy four and died there in eighteen sixty two, requires
Speaker 1: a word or two in passing. Most of his mathematical
Speaker 1: work was in connection with the subject of optics, and
Speaker 1: especially with the polarization of light. His systematic works were
Speaker 1: produced within the years eighteen o five. In eighteen seventeen,
Speaker 1: a selection of his more valuable memoirs was published in
Speaker 1: Paris in eighteen fifty eight. Arago Francois Jean Dominique Arago
Speaker 1: was born at Estangel in the Pyrenees on February twenty
Speaker 1: sixth seventeen eighty six and died in Paris on October second,
Speaker 1: eighteen fifty three. He was educated at the Polytechnic School, Paris,
Speaker 1: and we gather from his autobiography that, however distinguished were
Speaker 1: the professors of that institution, they were remarkably incapable of
Speaker 1: imparting their knowledge or maintaining discipline. In eighteen o four
Speaker 1: he was made secretary to the Observatory, and then from
Speaker 1: eighteen o six to eighteen o nine he was engaged
Speaker 1: in measuring a meridian arc in order to determine the
Speaker 1: exact length of a meter. He was then made one
Speaker 1: of the astronomers at Paris, given a residence there, and
Speaker 1: made a professor at the Polytechnic School, where he enjoyed
Speaker 1: a marked success as a lecturer. He subsequently gave popular
Speaker 1: lectures on astronomy, which were both lucid and accurate, a
Speaker 1: combination of qualities which was rarer than now. He reorganized
Speaker 1: the National Observatory, the management of which had long been inefficient.
Speaker 1: But in doing this he shewed himself dictatorial and passionate,
Speaker 1: and the same defaul efects of character revealed themselves in
Speaker 1: many of the events of his life. He remained to
Speaker 1: the end a consistent Republican, and after the Coup d'ettas
Speaker 1: of eighteen fifty two, though half blind and dying, he
Speaker 1: resigned his post as an astronomer rather than take the
Speaker 1: oath of allegiance. It is to the credit of Napoleon
Speaker 1: the Third that he gave directions that the old man
Speaker 1: should be in no way disturbed, and that he should
Speaker 1: be left free to say and do what he liked.
Speaker 1: His earliest physical researches were on the pressure of steam
Speaker 1: at different temperatures and the velocity of sound eighteen eighteen
Speaker 1: to eighteen twenty two. His magnetic observations mostly took place
Speaker 1: from eighteen twenty three to eighteen twenty six. He discovered
Speaker 1: what had been called rotary magnetism and the fact that
Speaker 1: most bodies could be magnetized. These discoveries were completed and
Speaker 1: explained by Faraday. He warmly supported Fresnel's optical theories, and
Speaker 1: the two philosophers conducted together those experiments on the polarization
Speaker 1: of light, which led to the interference that the vibrations
Speaker 1: of the luminiferous ether were transverse to the direction of motion,
Speaker 1: and that the polarization consisted in a resolution of rectilinear
Speaker 1: motion into components at right angles to each other. The
Speaker 1: subsequent invention of the polariscope and the discovery of rotatory
Speaker 1: polarization are due to Arago. The general idea of the
Speaker 1: experimental determination of the velocity of light in the manner
Speaker 1: subsequently affected by Faisot and Foucot, was suggested by him
Speaker 1: in eighteen thirty eight, but his failing eyesight prevented his
Speaker 1: arranging the details or making the experiments. It will be
Speaker 1: noticed that some of the last members of the French
Speaker 1: school were alive at a comparatively recent date, but nearly
Speaker 1: all mathematical work was done before the year eighteen thirty.
Speaker 1: They are the direct successors of the French writers who
Speaker 1: flourished at the commencement of this century, and seem to
Speaker 1: have been out of touch with the great German mathematicians
Speaker 1: of the early part of it, on whose researches much
Speaker 1: of the best work of this century is based. They
Speaker 1: are thus placed here, though their writings are in some
Speaker 1: cases of a later date than those of gauss Abel,
Speaker 1: Jacobi and other mathematicians of recent times. The introduction of
Speaker 1: analysis into England, the complete isolation of the English school
Speaker 1: and its devotion to geometrical methods are the most marked
Speaker 1: features in its history during the latter half of the
Speaker 1: eighteenth century, and the absence of any considerable and valuable
Speaker 1: contributions to the advancement of mathematical science was a natural consequence.
Speaker 1: One result of this was that the energy of the
Speaker 1: englishmen of science was largely devoted to practical physics and
Speaker 1: practical astronomy, which were in consequence studied in Britain, perhaps
Speaker 1: more than elsewhere. Almost the only English mathematician at the
Speaker 1: beginning of this century who used analytical methods and whose
Speaker 1: work requires mentioned here is Ivory, to whom the celebrated
Speaker 1: theorem of attractions is due. James Ivory was born in
Speaker 1: Dundee in seventeen sixty five and died at Douglastown on
Speaker 1: September twenty first, eighteen forty five. After graduating at Saint Andrews,
Speaker 1: he became the managing partner in a flax spinning company
Speaker 1: in Forfardshire, but continued to devote most of his leisure
Speaker 1: to mathematics. In eighteen o four he was made professor
Speaker 1: at the Royal Military College at Marlow, which has now
Speaker 1: moved to Sandhurst. He contributed numerous papers to the Philosophical Transactions,
Speaker 1: the most remarkable being those on attractions. In one of these,
Speaker 1: in eighteen he shewed how the attraction of a homogeneous
Speaker 1: ellipsoid on an external point is a multiple of that
Speaker 1: of another ellipsoid on an internal point, the latter can
Speaker 1: be easily obtained. He criticized Laplace's solution of the method
Speaker 1: of Lee squares with unnecessary bitterness and in terms which
Speaker 1: proved his incompetence to understand it. The Cambridge Analytical school.
Speaker 1: Toward the close of the last century, the more thoughtful
Speaker 1: members of the Cambridge School of Mathematics began to recognize
Speaker 1: that their isolation from the continental contemporaries was a serious evil.
Speaker 1: The earliest attempt in England to explain the notation and
Speaker 1: methods of the calculus as used on the continent was
Speaker 1: due to Woodhouse, who stands out as the apostle of
Speaker 1: the new movement. It is doubtful if he could have
Speaker 1: brought the analytical methods into vogue by himself, but his
Speaker 1: views were enthusiastically adopted by three undergraduates, Babbage, Peacock and Herschel,
Speaker 1: who he succeeded in carrying out reforms that he had
Speaker 1: suggested in a book which will fall into the hands
Speaker 1: of few but English readers. I may be pardoned for
Speaker 1: making space for a few remarks on these four mathematicians.
Speaker 1: The original stimulus came from French sources, and I therefore
Speaker 1: placed these remarks at the close of my account of
Speaker 1: the French school. But I should add that the English
Speaker 1: mathematicians of this century at once struck out a line
Speaker 1: independent of their French contemporaries. Woodhouse Robert Woodhouse was born
Speaker 1: at Norwich on April twenty eighth, seventeen seventy three. Was
Speaker 1: educated at Caius College, Cambridge, of which society he was
Speaker 1: subsequently a fellow, was Plumian Professor in the university, and
Speaker 1: continued to live at Cambridge till his death on December
Speaker 1: twenty third, eighteen twenty seven. His earliest work, entitled The
Speaker 1: Principles of Analytical Calculation, was published at Cambridge in An
Speaker 1: eighteen o three. In this he explained the differential notation
Speaker 1: and strongly pressed the employment of it, but he severely
Speaker 1: criticized the methods used by Continental writers and their constant
Speaker 1: assumption of non evident principles. This was followed in eighteen
Speaker 1: o nine by a trigonometry Plain and Spherical, and in
Speaker 1: eighteen ten by historical treatise on the Calculus of variations
Speaker 1: and isoparametrical problems. He next produced an Astronomy, the first
Speaker 1: volume usually bound in two on practical and Descriptive Astronomy,
Speaker 1: being issued in eighteen twelve, the second volume, containing an
Speaker 1: account of the treatment of physical astronomy by Laplace and
Speaker 1: other Continental writers, being issued in eighteen eighteen. All these
Speaker 1: works deal critically with the scientific foundation of the subjects considered,
Speaker 1: a point which is not unfrequently neglected in modern textbook boks.
Speaker 1: A man like Woodhouse, of scrupulous honor, universally respected, a
Speaker 1: trained logician, and with a caustic wit, was well fitted
Speaker 1: to introduce a new system. And the fact that when
Speaker 1: he first called attention to the Continental analysis, he exposed
Speaker 1: the unsoundness of some of the usual methods of establishing it.
Speaker 1: More like an opponent than a partisan, and was politic
Speaker 1: as it was honest. Woodhouse did not exercise much influence
Speaker 1: on the majority of his contemporaries, and the movement might
Speaker 1: have died away for the time being had it not
Speaker 1: been for the advocacy of Peacock, Herschel and Babbage, who
Speaker 1: formed an analytical Society with the object of advocating the
Speaker 1: general use in the University of analytical methods and of
Speaker 1: the differential notation. Peacock George Peacock, who was the most
Speaker 1: influential of the early members of the New School, was
Speaker 1: born at Denton on April ninth, seventeen ninety one. He
Speaker 1: was educated at Trinity College, Cambridge, of which society he
Speaker 1: was subsequently a fellow and tutor. The establishment of the
Speaker 1: University Observatory was mainly due to his efforts, and in
Speaker 1: eighteen thirty six he was appointed to the Loundean Professorship
Speaker 1: of Astronomy and Geometry. In eighteen thirty nine he was
Speaker 1: made Dean of Eli and resided there until his death
Speaker 1: in November eighth, eighteen fifty eight. Although Peacock's influence on
Speaker 1: English mathematicians was considerable, he has left but few memorials
Speaker 1: to his work. But I may note that his Report
Speaker 1: on Recent Progress and Analysis eighteen thirty three commenced those
Speaker 1: valuable summaries of scientific progress which enriched many of the
Speaker 1: annual volumes of the transactions of the British Association Babbage.
Speaker 1: Another important member of the Analyticalsis Society was Charles Babbage,
Speaker 1: who was born at Totna's in December twenty sixth, seventeen
Speaker 1: ninety two. He entered Trinity College, Cambridge in eighteen ten,
Speaker 1: subsequently became Lucasian Professor in the university, and died in
Speaker 1: London on October eighteenth, eighteen seventy one. It was he
Speaker 1: who gave the name to the Analytical Society, which he
Speaker 1: stated was formed to advocate the principles of pure Deism
Speaker 1: as opposed to the dottage of the university. In eighteen
Speaker 1: twenty the Astronomical Society was founded mainly through his efforts,
Speaker 1: and at a later time eighteen thirty to eighteen thirty
Speaker 1: two he took a prominent part in the foundation of
Speaker 1: the British Association. He will be remembered for his mathematical
Speaker 1: memoirs on the calculus of functions, and in the invention
Speaker 1: of analytical machines which could not only perform ordinary processes
Speaker 1: of a ru arithmetic, but could tabulate the values of
Speaker 1: any functions and print the results. Herschel the third of
Speaker 1: those who helped bring analytical methods into general use in England.
Speaker 1: Was the son of Sir William Herschel seventeen thirty eight
Speaker 1: to eighteen twenty two, the most illustrious astronomer of the
Speaker 1: latter half of the last century, and the creator, it
Speaker 1: may be fairly said, of stellar astronomy. Sir John Frederick
Speaker 1: William Herschel was born on March seventh, seventeen ninety two
Speaker 1: and educated at Saint John's College, Cambridge, and died on
Speaker 1: May eleventh, eighteen seventy one. His earliest original work was
Speaker 1: a paper on Coates's theorem, and it was followed by
Speaker 1: others on mathematical analysis, but his desire to complete his
Speaker 1: father's work led ultimately to his taking up astronomy. His
Speaker 1: papers on light and astronomy contain a clear exposition of
Speaker 1: the principles which underline the mathematical treatment of those subjects.
Speaker 1: In eighteen thirteen, the Analytical Society published a volume of memoirs,
Speaker 1: of which the preface and the first paper on continued
Speaker 1: products are due to Babbage and the Three years later
Speaker 1: they issued a translation of Lacrois tret des elementaire to
Speaker 1: calcur differentier et du calcur integral in eighteen seventeen and
Speaker 1: again in eighteen nineteen. The differential notation was used in
Speaker 1: the university examinations, and after eighteen twenty its use was
Speaker 1: well established. The Analytical Society followed up this rapid victory
Speaker 1: by the issue in eighteen twenty of two volumes of
Speaker 1: examples illustrative of the new method, one by Peacock on
Speaker 1: the differential and integral calculus and the other by Herschel
Speaker 1: on the calculus of finite differences. Since then, English works
Speaker 1: on the infinitesimal calculus have a bet have abandoned the
Speaker 1: exclusive use of the fluctional notation. It should be noticed
Speaker 1: in passing that Lagrange and Laplace, like the majority of
Speaker 1: other modern writers, employ both the fluctional and the differential notation.
Speaker 1: It was the exclusive adoption of the former that was
Speaker 1: so hampering. Amongst those who materially assisted in extending the
Speaker 1: use of the new analysis were William Wherwell seventeen ninety
Speaker 1: four to eighteen sixty six and George Beidell Airy eighteen
Speaker 1: o one to eighteen ninety two, both fellows at Trinity College, Cambridge.
Speaker 1: The former issued in eighteen nineteen a work on Mechanics,
Speaker 1: and the latter, who was a pupil of Peacock, published
Speaker 1: in eighteen twenty six in his Tracts, in which the
Speaker 1: new method was applied with great success to various physical problems.
Speaker 1: The efforts of the society were supplemented by the rapid
Speaker 1: publication of good texts books in which analysis was freely used.
Speaker 1: The employment of analytical methods spread from Cambridge over the
Speaker 1: rest of Britain, and by eighteen thirty those methods have
Speaker 1: come into general use there end of section thirty two.
Speaker 1: Recording by Paul King, Mississauga, Ontario, h d T, P
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