Speaker 1: Chapter nineteen, Part four of A short account of the
Speaker 1: History of mathematics. This is a LibriVox recording. All LibriVox
Speaker 1: recordings are in the public domain. For more information or
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Speaker 1: reading by Paul King PJK dot scripts dot mit dot edu.
Speaker 1: Forward slash p kJ. A short account of the history
Speaker 1: of mathematics by W. W. Rowse Ball, Chapter nineteen, Mathematics
Speaker 1: of Recent Times, Part four Clifford. I may, however add
Speaker 1: here a brief note on Clifford, who is one of
Speaker 1: the earliest English mathematicians of the latter half of this
Speaker 1: century to advocate the use of graphical and geometrical methods
Speaker 1: in preference to analysis. William king Don Clifford born at
Speaker 1: Exeter on May fourth, eighteen forty five and died at
Speaker 1: Madera on March third, eighteen seventy nine. Was educated at
Speaker 1: Trinity College, Cambridge, of which Society he was a fellow.
Speaker 1: In eighteen seventy one he was appointed Professor of Applied
Speaker 1: Mathematics at University College London, a post which he retained
Speaker 1: till his death. His remarkable felicity of illustration and power
Speaker 1: of seizing analogies made him one of the most brilliant
Speaker 1: expounders of mathematical principles. His health failed in eighteen seventy six,
Speaker 1: when the writer of this book undertook his work for
Speaker 1: a few months. Clifford then went to Algeria and returned
Speaker 1: at the end of the year, but only to break
Speaker 1: down again in eighteen seventy eight. His most important works
Speaker 1: are his Theory of bi Quaternions, on the Classification of
Speaker 1: Loki unfinished and the Theory of Graphs unfinished. His canonical
Speaker 1: dissection of a Riemann's surface and the Elements of dynamic
Speaker 1: also contain much interesting matter. I next turn to the
Speaker 1: question of mechanics treated analytically. The knowledge of mathematical mechanics
Speaker 1: of solids attained by the great mathematicians of the last
Speaker 1: century may be said to be summed up in the
Speaker 1: admirable Mechanique analytique by Lagrange and Treete de mechanique by Poisson,
Speaker 1: and the application of the results to astronomy is illustrated
Speaker 1: by Laplace's Mechanique Celeste. These works have been already described.
Speaker 1: The mechanics of fluids is more difficult than that of solids,
Speaker 1: and the theory is less advanced. Theoretical statics, especially the
Speaker 1: theory of potential and attractions, has received considerable attention from
Speaker 1: mathematicians of this century. I have already mentioned that the
Speaker 1: introduction of the idea of the potential is due to Lagrange,
Speaker 1: and it occurs in a memoir of a date as
Speaker 1: early as seventeen seventy three. The the idea was at
Speaker 1: once grasped by Laplace, who, in his memoir of seventeen
Speaker 1: eighty four used it freely and to whom the credit
Speaker 1: of the invention was formerly somewhat unjustly attributed. In the
Speaker 1: same memoir, Laplace also extended to space of three dimensions
Speaker 1: the idea of circular harmonic analysis, which had been introduced
Speaker 1: by Legentdre in seventeen eighty three. Green George Green was
Speaker 1: one of the earliest writers of this century who investigated
Speaker 1: further the properties of the potential. Green was born near
Speaker 1: Nottingham in seventeen ninety three in a humble condition in life,
Speaker 1: and died at Cambridge in eighteen forty one. Although self educated,
Speaker 1: he contrived to get access to various mathematical books, and
Speaker 1: in eighteen twenty seven wrote a paper on the potential
Speaker 1: in which the term was first introduced, proved its chief properties,
Speaker 1: and applied the results to electricity and magnetism. This contains
Speaker 1: the important theorem now known by his name. This t
Speaker 1: remarkable paper was seen by some neighbours who were able
Speaker 1: to appreciate the power shown in it. It was published
Speaker 1: by subscription in eighteen twenty eight, but does not seem
Speaker 1: to have attracted much attention at first. Similar results were
Speaker 1: independently established in eighteen thirty nine by Gauss, to whom
Speaker 1: their general dissemination was due. In eighteen thirty two and
Speaker 1: eighteen thirty three, Green presented papers to the Cambridge Philosophical
Speaker 1: Society on the equilibrium of fluids and on attractions in
Speaker 1: space of n dimensions, and in the latter year his
Speaker 1: memoir on the motion of a fluid agitated by the
Speaker 1: vibrations of a solid ellipsoid was read before the Royal
Speaker 1: Society of Edinburgh. In eighteen thirty three he entered at
Speaker 1: Caius College, Cambridge, and was subsequently elected to a fellowship.
Speaker 1: He then threw himself into original work, and produced in
Speaker 1: eighteen thirty seven his paper on the motion of waves
Speaker 1: in a canal and on the reflection and refraction of
Speaker 1: sound and light. In the latter, the geometrical laws of
Speaker 1: sound and light are deduced by the principle of energy
Speaker 1: from the undulatory theory. The phenomenon of total reflection is
Speaker 1: explained physically, and certain properties of the vibrating medium are deduced.
Speaker 1: He also discussed the propagation of light in any crystalline medium.
Speaker 1: Of Gauss's work on attractions, I have already spoken the
Speaker 1: theory of level surfaces and lines of force is largely
Speaker 1: due to Chasla's who also determine the attraction of an
Speaker 1: ellipsoid at any external point. I ought not to leave
Speaker 1: the subject of theoretical statics without mentioning Mobius. August ferden Anmobius,
Speaker 1: professor at Leipzig, who was born at Schlpforta on November seventeen,
Speaker 1: seventeen ninety and died on September twenty sixth, eighteen sixty eight,
Speaker 1: was one of the best known of Gauss's pupils. He
Speaker 1: published his verycentricius caut alcourd in eighteen twenty six. His
Speaker 1: collected works were published at Leipzig in four volumes eighteen
Speaker 1: eighty five to eighteen eighty seven. Among living writers, I
Speaker 1: may allude to Sir Robert Stallwell Ball, Loundian professor in
Speaker 1: the University of Cambridge, born in Dublin on July first,
Speaker 1: eighteen forty who issued his Theory of Screws in eighteen
Speaker 1: seventy six. Theoretical dynamics has been studied by most of
Speaker 1: the writers above mentioned. In addition to these, I may
Speaker 1: repeat that the principle of varying action was elaborated by
Speaker 1: Sir William Hamilton in eighteen twenty seven, and the Hamiltonian
Speaker 1: equations were given in eighteen thirty five. And I may
Speaker 1: call attention to Beartrand's work on dynamics. The use of
Speaker 1: generalized coordinates introduced by Lagrange has become the customary means
Speaker 1: of attacking dynamical as well as many physical problems. The
Speaker 1: standard English textbook on the dynamics of rigid bodies is
Speaker 1: that by Doctor Routh on the Mechanics of Fluids, liquids
Speaker 1: and gases. Apart from the physical theories on which they rest,
Speaker 1: I propose to say nothing except to refer to the
Speaker 1: memoirs of Green Sir George Stokes, Lord Kelvin, better known
Speaker 1: as Sir William Thompson and von Helmholtz. The fascinating but
Speaker 1: difficult theory of vortex rings is due to the two
Speaker 1: writers last mentioned. One problem in it has been also
Speaker 1: considered by J. J. Thompson, but it is a subject
Speaker 1: which is as yet rather beyond our powers of analysis.
Speaker 1: The subject of sound may be treated in connection with hydrodynamics,
Speaker 1: but on this I would refer to the reader who
Speaker 1: wishes for further information to the work published at Cambridge
Speaker 1: in eighteen seventy seven by Lord Raleigh, recently Cavenish Professor
Speaker 1: in the University of Cambridge. Theoretical astronomy is included in
Speaker 1: or at any rate closely connected with theoretical dynamics. Among
Speaker 1: those who in this century have devoted themselves to the
Speaker 1: study of theoretical astronomy, the name of Gauss is one
Speaker 1: of the most prominent to his work. I have already
Speaker 1: alluded Bessel. The best known of Gauss's contemporaries was Frederich
Speaker 1: Wilhelm Bassel, who was born in Minden on July twenty second,
Speaker 1: seventeen eighty four and died at Knigsburg on March seventeenth,
Speaker 1: eighteen forty six. Bessel commenced his life as a clerk
Speaker 1: on board ship, but in eighteen o six he became
Speaker 1: an assistant in the observatory at Lilenthal, and was thence
Speaker 1: in eighteen oh one promoted to be director of the
Speaker 1: new Prussian Observatory at Knigsburg, where he continued to live
Speaker 1: during the remainder of his life. Bessel introduced into pure
Speaker 1: mathematics those functions which are now called by his name.
Speaker 1: This was in eighteen twenty four, though their use is
Speaker 1: indicated in a memoir seven years earlier. But his most
Speaker 1: notable achievements where the reduction gave given in his fundamental
Speaker 1: astronomier Canigsburg eighteen eighteen of the Greenwich observations by Bradley
Speaker 1: of three thousand, two hundred twenty two stars and his
Speaker 1: determination of the annual parallax of sixty one Signai. Bradley's
Speaker 1: observations have been recently reduced again by doctor A. Auers
Speaker 1: of Berlin, the verier. Among the astronomical events of this century,
Speaker 1: the discovery of the planet Neptune by Leverrier and Adams
Speaker 1: is one of the most striking Urbane. Jean Joseph Leverrier,
Speaker 1: the son of a petty government employee in Normandy was
Speaker 1: born at Saint Loa on March eleventh, eighteen eleven, and
Speaker 1: died at Paris on September twenty third, eighteen seventy seven.
Speaker 1: He was educated at the Polytechnic School, and in eighteen
Speaker 1: thirty seven was appointed its lecturer on astronomy. There his
Speaker 1: earliest researches in astronomy were communicated to the Acaomy in
Speaker 1: eighteen thirty nine. In these he calculated, within much narrower
Speaker 1: limits than Laplace had done, the extent within which the
Speaker 1: inclinations and eccentricities of the planetary orbits vary. The independent
Speaker 1: discovery in eighteen forty six by Leverrier and Atoms of
Speaker 1: the planet Neptune, by means of the disturbance it produced
Speaker 1: on the orbit of Uranus, attracted general attention to physical
Speaker 1: astronomy and strengthened the opinion as to the universality of gravity.
Speaker 1: In eighteen fifty five, Leverrier succeeded Arago as director of
Speaker 1: the Paris Observatory and reorganized it in accordance with the
Speaker 1: requirements of modern astronomy. He now set himself the task
Speaker 1: of discussing the theoretical investigations of the planetary motions and
Speaker 1: of revising all tables which involve them. He lived just
Speaker 1: long enough to sign the last proof sheet of this
Speaker 1: work atoms. The co discover hover of Neptune was John
Speaker 1: Couch Adams, who was born in Cornwall on June fifth,
Speaker 1: eighteen nineteen, educated at Saint John's College, Cambridge, subsequently appointed
Speaker 1: to Loundian Professor in the University and director of the Observatory,
Speaker 1: and who died at Cambridge on January twenty first, eighteen
Speaker 1: ninety two. There are three important problems which are especially
Speaker 1: associated with the name of Adams. The first of these
Speaker 1: is his discovery of the planet Neptune from the perturbations
Speaker 1: it produced on the orbit of Uranus in point of time.
Speaker 1: This was slightly earlier than Laverier's investigation. The second memoir
Speaker 1: to which I referred was on the secular Acceleration of
Speaker 1: the Moon's mean Motion Philosophical Transactions, eighteen fifty five, Volume
Speaker 1: one hundred forty three, page three hundred seventy seven. Laplace
Speaker 1: had calculated this on the hypothesis that it was caused
Speaker 1: by the eccentricity of the Earth's orbit, and had obtained
Speaker 1: a result which agreed substantially with the value it deduced
Speaker 1: from a comparison of the records of ancient and modern eclipses.
Speaker 1: Adams shewed that certain terms in an expression had been neglected,
Speaker 1: and that if they were taken into account, the result
Speaker 1: was only about one half that found by Laplace. The
Speaker 1: correctness of the calculations of Adams was denied by Plaina, Ponte, Coulan,
Speaker 1: and other continental astronomers, but Delaunay in France and Cayley
Speaker 1: in England verified the work. The third investigation connected with
Speaker 1: the name of Adams is his determination of the orbit
Speaker 1: of the Leonids or shooting stars, which were especially conspicuous
Speaker 1: in November eighteen sixty six, and whose period is about
Speaker 1: thirty three years. Newton of Yale had shewn that there
Speaker 1: were only five possible orbits. Adams calculated the disturbance which
Speaker 1: would be produced by the planets on the motion of
Speaker 1: the node of the orbit of a swarm of meteors
Speaker 1: in each of these cases, and found that this disturbance
Speaker 1: agreed with the observations for one of the possible orbits,
Speaker 1: but for none of the others. Hence the orbit was known.
Speaker 1: Other well known astronomers of this century are Giovanni Antonio
Speaker 1: Amadeo Plina born at Volgera on November eighth, seventeen eighty
Speaker 1: one and died at Tehrann on January twentieth, eighteen sixty four,
Speaker 1: whose work on the motion of the Moon was published
Speaker 1: in eighteen thirty two. Philip Gustave Duchet, Count ponte Colan,
Speaker 1: born in seventeen ninety five and died at Portecolon on
Speaker 1: July twenty first, eighteen seventy one. Charles Eugene d' laune
Speaker 1: born at Losignier on April ninth, eighteen sixteen and drowned
Speaker 1: off Cherbourg on August third, eighteen seventy two, whose work
Speaker 1: on the lunar theory indicates the best method yet suggested
Speaker 1: for the analytical investigations of the whole problem, and whose
Speaker 1: incomplete Lunar Tables are among the astronomical achievements of this century.
Speaker 1: And Peter Andrew Henson born at Schleswig on December eighth,
Speaker 1: seventeen ninety five and died at Gotha, where he was
Speaker 1: head of the observatory, on March twenty eighth, eighteen seventy four,
Speaker 1: who compiled the Lunar Tables, published in London in eighteen
Speaker 1: fifty seven and celebrated the most delicate methods yet known
Speaker 1: for the determination of lunar and planetary perturbations. For an
Speaker 1: account of the numerous memoirs, see the Transactions of the
Speaker 1: Royal Society of London from eighteen seventy six to eighteen
Speaker 1: seventy seven. Among living mathematicians, I may mention the following names.
Speaker 1: Felix Tsarin of Paris, born in eighteen forty five, whose
Speaker 1: Mechadique Celeste forms a worthy pendant to Laplace's work of
Speaker 1: the same title. George William Hill born in New York
Speaker 1: in eighteen thirty eight, as until recently on the staff
Speaker 1: of American amphemorists, who in eighteen eighty four determine the
Speaker 1: inequalities of the Moon's motion due to the non spherical
Speaker 1: figure of the Earth, an investigation which completed Delaunay's lunar theory.
Speaker 1: Heil also dealt with the secular motion of the Moon's
Speaker 1: perigy and the motion of a planet's perigy under certain conditions,
Speaker 1: and he has written on the analytical theory of the
Speaker 1: moon of Jupiter and Saturn, with a view to the
Speaker 1: preparation of tables of their positions at any given time.
Speaker 1: Simon Newcombe born in Nova Scotia on March twelfth, eighteen
Speaker 1: thirty five, superintendent of the American Ephemerists, who re examined
Speaker 1: the Greenwich observations from the earliest times, applied the result
Speaker 1: of the lunar theory, and revised Hanson's tables. George Howard
Speaker 1: Doughran of Trinity College, Cambridge born in Kent in eighteen
Speaker 1: forty five, now Plumian Professor in the University of king Ambridge,
Speaker 1: who has written on the effect of tides on viscous spheroids,
Speaker 1: the development of planetary systems by means of tidal friction,
Speaker 1: the mechanics of meteoric swarms, et cetera. Perhaps also I
Speaker 1: may here mention Plant Career, who has discussed the difficult
Speaker 1: problem of three bodies and the form assumed by a
Speaker 1: mass of fluid under its own attraction. Within the last
Speaker 1: half century, the results of spectrum analysis have been applied
Speaker 1: to determine the constitution and directions of motions of the
Speaker 1: heavenly bodies to and from the Earth. The early history
Speaker 1: of spectrum analysis will be always associated with the names
Speaker 1: of Gustav Robert Kirschov and A. J. Engstrom of Uppsala
Speaker 1: and Sir George Stokes of Cambridge, but it pertains to
Speaker 1: optics rather than to astronomy. Within the last few years,
Speaker 1: the range of astronomy has been still further extended by
Speaker 1: the art of a photography. To what new developments this
Speaker 1: may lead, it is as yet impossible to say mathematical physics.
Speaker 1: An account of the history of mathematics in this century
Speaker 1: would not be other than misleading if there were no
Speaker 1: reference to the application of it to numerous problems in heat, elasticity, light, electricity,
Speaker 1: and other physical subjects. The history of mathematical physics is, however,
Speaker 1: so extensive that I could not pretend to do a
Speaker 1: justice even were its consideration properly included in a history
Speaker 1: of mathematics. Moreover, it is so closely connected with the
Speaker 1: works of living physicists, notably of von Helmholtz and of
Speaker 1: Lord Kelvin that are known as Sir William Thompson, that
Speaker 1: I may consider it outside the limits I have laid
Speaker 1: down for myself in this chapter. It is, however, interesting
Speaker 1: to note that the advance in our knowledge of physics
Speaker 1: is largely due to the application to it of mathematics,
Speaker 1: and every year, it becomes more difficult for an experimenter
Speaker 1: to make any mark on the subject unless he is
Speaker 1: also a mathematician. Amongst recent writers on mathematical physics, excluding
Speaker 1: all reference to experimental physics, as also to theories to
Speaker 1: which mathematical analysis has not yet been applied, I may
Speaker 1: specially mention the following, whose names are here arranged alphabetically,
Speaker 1: though the list is not in any way profess to
Speaker 1: be complete or exhaustive. J Buzenesque of Paris, who is
Speaker 1: written on optics. Ludwig Boltzmann of Vienna, whose writings greatly
Speaker 1: extended the kinetic theory of gases and have done something
Speaker 1: to bring the molecular physics within the domain of mathematics.
Speaker 1: Rudolph Julius Emmanuel Clausius born at Kozlen on January two,
Speaker 1: eighteen twenty two, had died at Bonn, where he was
Speaker 1: professor of physics, in August eighteen eighty eight, who was
Speaker 1: among the earliest to discuss the subject of heat from
Speaker 1: a mathematical point of view. Klebsch, who discussed the elasticity
Speaker 1: of solid bodies. Julius Wilhelm Richard Detikind, who is the
Speaker 1: author of a remarkable memoir on the vibrations of a
Speaker 1: liquid ellipsoid, which is treated as a problem in pure mathematics.
Speaker 1: Michael Faraday born at Newington on September twenty second, seventeen
Speaker 1: ninety one, and died at Hampton Court on August twenty fifth,
Speaker 1: eighteen sixty seven, who had a special gift in deducing
Speaker 1: results by general reasoning from fundamental principles, and in disentangling
Speaker 1: those principles from the symbols in which they are usually expressed.
Speaker 1: For further details see the biographies of Tyndal second edition
Speaker 1: eighteen seventy, Bence Jones eighteen seventy or Doctor Gladstone eighteen
Speaker 1: seventy two. George Francis Fitzgerald, Professor in Dublin, born there
Speaker 1: on August third, eighteen fifty one, who was written on
Speaker 1: electromagnetism and optics. John Bernard Leon Foucaut born at Paris
Speaker 1: on September eighteenth, eighteen nineteen, and died there of paralysis
Speaker 1: on February eleventh, eighteen sixty eight, whose chief memoirs were
Speaker 1: on the Predictability of photography eighteen forty on the Electric
Speaker 1: lamp eighteen forty nine, on the determination of the velocity
Speaker 1: of light in eighteen fifty, but repeated with improvements in
Speaker 1: eighteen sixty two. On his demonstration of the diurnal motion
Speaker 1: of the Earth by means of the rotation of the
Speaker 1: plane of oscillation of a simple pendulum eighteen fifty one,
Speaker 1: on the gyroscope eighteen fifty two, on the rotation of
Speaker 1: a copper disc between the poles of a magnet eighteen
Speaker 1: fifty five, and on a polarizer eighteen fifty seven. For
Speaker 1: further details see La ville se traveau de Leon Foucaut
Speaker 1: by JA la Lisijus, Paris, eighteen seventy five, and also
Speaker 1: a notice by J. Bertrand preface to the collected edition
Speaker 1: of Fucot's works, Paris, eighteen seventy eight. J. Willard Gibbs
Speaker 1: of Yale, America, who has written on the thermodynamics and
Speaker 1: Maxwell's electromagnetic theory. Richard Tetley Glazebrook of Trinity College, Cambridge,
Speaker 1: born at Liverpool on September eighteenth, eighteen fifty four, who
Speaker 1: has written on optics and electricity. His report in the
Speaker 1: Transactions of the British Association eighteen eighty five on theories
Speaker 1: of optics contains a valuable summary of most of the
Speaker 1: mathematical researches on that subject during this century and prior
Speaker 1: to the date of the report. After a brief allusion
Speaker 1: to the views of Green, Koshee, McCulloch and F. E. Neumann,
Speaker 1: he describes the more recent work according as it comes
Speaker 1: under the simple elastic solid theory or theories assuming an
Speaker 1: action between Matie and Ether, or Maxwell's electromagnetic theory. Green,
Speaker 1: whose physical memoirs were mostly on the theory of waves.
Speaker 1: Von Helmholtz, who is in the front rank of all
Speaker 1: departments of mathematics and physics. His collected papers were published
Speaker 1: in two volumes Leipzig, eighteen eighty two to eighteen eighty three.
Speaker 1: Oliver Heavyside, who has written on the mathematical theories of
Speaker 1: optics and electromagnetism. Lord Kelvin or Sir William Thompson, Professor
Speaker 1: at Glasgow born at Belfast, June eighteen twenty four, who
Speaker 1: has enriched every department of physics by his researches. His
Speaker 1: collected papers were published at Cambridge volume one in eighteen
Speaker 1: eighty two, at volume two in eighteen eighty four, and
Speaker 1: volume three in eighteen ninety Gustav Robert Kirschow, professor in physics,
Speaker 1: first at Heidelberg and then at Berlin. Born at Knigsburg
Speaker 1: on March twelfth, eighteen twenty four and died in Berlin
Speaker 1: October sie seventeenth, eighteen eighty seven, whose name will always
Speaker 1: be associated with the history of spectrum analysis and his
Speaker 1: researches on elasticity. His collected papers were published at Leipzig
Speaker 1: in eighteen eighty two. Gabriel Lamay born at Tours on
Speaker 1: July twenty seconds, seventeen ninety five and died at Paris
Speaker 1: in eighteen seventy, where he was professor at the Polytechnic School,
Speaker 1: whose best known works are his Course on Physics eighteen
Speaker 1: thirty six, his Treatise on Elasticity eighteen fifty two, his
Speaker 1: work on Functions eighteen fifty seven, an essay on the
Speaker 1: curve linear coordinates eighteen fifty nine, and lastly his Theory
Speaker 1: of Heat eighteen sixty one. He also wrote memoirs on
Speaker 1: different points in the theory of numbers. James Clerk Maxwell born
Speaker 1: at Edinburgh on June thirteenth, eighteen thirty one and died
Speaker 1: at Cambridge on November fifth, eighteen seventy nine, where he
Speaker 1: was Professor of Experimental Physics. His most important works were
Speaker 1: his memoir in eighteen fifty nine on the stability of
Speaker 1: Saturn's rings, various articles on color, his memoir on the
Speaker 1: electromagnetic field, his Electricity and Magnetism, issued in eighteen seventy three,
Speaker 1: his Theory of Heat published in eighteen seventy one, and
Speaker 1: his elementary textbook on Matter and Motion. To these, I
Speaker 1: may add his memoir on Reciprocal Figures, which are useful
Speaker 1: in graphics, and his papers on molecular theory of gases
Speaker 1: and cognate subjects. His Electricity and Magnetism has revolutionized the
Speaker 1: treatment of the subject. Poissin A. Gauss had explained the
Speaker 1: phenomenon of electrostatics by attraction and repulsions between imponderable particles,
Speaker 1: while Lord Kelvin Sir William Thompson in eighteen forty six
Speaker 1: has shewn that that the effects might be supposed analogous
Speaker 1: to a flow of heat from various sources of electricity
Speaker 1: properly distributed in electrodynamics. The theory then generally current was
Speaker 1: that proposed by W. E. Webber, in which the attraction
Speaker 1: action between electrified particles depends on their relative motion and position.
Speaker 1: Maxwell rejected all these hypotheses and explained the phenomenon by
Speaker 1: stresses and motions of a material medium. He concluded by
Speaker 1: shewing that if the medium were the same as the
Speaker 1: so called luminiferous ether, the velocity of light would be
Speaker 1: equal to the ratio of the electromagnetic and electrostatic units.
Speaker 1: Subsequent experiments have tended to confirm this conclusion. For fuller details,
Speaker 1: his collected works Cambridge two Volumes, eighteen ninety and His
Speaker 1: Life by L. Campbell and W. Garnett, London, eighteen eighty
Speaker 1: two may be consulted. McCulloch, who wrote on physical optics.
Speaker 1: Franz rus Numann of Knigsburg born at Uckermark on September eleventh,
Speaker 1: seventeen ninety eight, who wrote on elasticity and light. William
Speaker 1: John ran Keane of Glasgow born at Edinburgh on July fifth,
Speaker 1: eighteen twenty and died December twenty five, eighteen seventy two,
Speaker 1: whose discoveries in thermodynamics and hydromechanics will be found in
Speaker 1: the collected edition of his works issued in London in
Speaker 1: eighteen eighty one. Lord Rayleigh born on November twelfth, eighteen
Speaker 1: forty two, who, besides some classical papers on the mathematics
Speaker 1: of physical optics, has written the standard English work on sound,
Speaker 1: published at Cambridge in eighteen seventy seven. Paret de Saint Venon,
Speaker 1: whose researches on elasticity and torsion are well known. Sir
Speaker 1: George Gabriel Stokes, most of whose papers on hydromechanics or
Speaker 1: optics or allied subjects. These memoirs have been recently collected
Speaker 1: and published by the University of Cambridge. Peter Guthrie Tait,
Speaker 1: Professor in Edinburgh, born at Dalkeith on April twenty eighth,
Speaker 1: eighteen thirty one, who has written on the mathematics of
Speaker 1: various physical subjects, and especially on the molecular theory of gases.
Speaker 1: Joseph John Thompson of Trinity College and Cavendish Professor in
Speaker 1: the University of Cambridge, born at Manchester on December eighteenth,
Speaker 1: eighteen fifty six, who is written on vortex rings and
Speaker 1: the application of generalized coordinates to various physical problems. I
Speaker 1: may also allude to his report on the Transactions of
Speaker 1: the British Association eighteen eighty five on electric theories, which
Speaker 1: He classifies into those not founded on the principle of
Speaker 1: conservation of energy, such as those of Empire, Grassmann, Stefan
Speaker 1: and Courtweg. Those which rest on assumptions concerning the velocities
Speaker 1: and positions of electrified particles, such as those of Gauss, W. E. Webber,
Speaker 1: Riemann and Clausius. Those which require the existence of a
Speaker 1: kind of energy of which we have no other knowledge,
Speaker 1: such as the theory of C. Numonn, Those which rest
Speaker 1: on the dynamical considerations but in which no account is
Speaker 1: taken of the action of the dielectric, such as the
Speaker 1: theory of V. F. E. Neumann, And finally, those which
Speaker 1: rest on the dynamical considerations and in which the action
Speaker 1: of the dielectric is considered, such as Maxwell's theory. In
Speaker 1: the report, these theories are described, criticized, and compared with
Speaker 1: the results of experiments. Wilhelm Eduard Weber died in eighteen
Speaker 1: ninety one, whose most important investigations were in connection with
Speaker 1: electro dynamics. His works are being produced by the Royal
Speaker 1: Society of Gottingen. Volume one edited by W. Voight Berlin
Speaker 1: eighteen ninety two and Gustav Heinrich Wiedemann of Bail born
Speaker 1: October sec In eighteen twenty six, who is the author
Speaker 1: of an admirable textbook on electricity and allied subjects, four volumes,
Speaker 1: eighteen eighty two to eighteen eighty five. I am well
Speaker 1: aware that the above list excludes many who have studied
Speaker 1: physics from a strictly mathematical point of view, and I
Speaker 1: give it not as an ac out of a contemporary work,
Speaker 1: but as a pendent to this chapter, which may serve
Speaker 1: as an indication of the subjects discussed by many mathematicians
Speaker 1: in recent times, illustrated by the names of a few
Speaker 1: of them. To make it more than this would involve
Speaker 1: the knowledge to which I can make no pretense. End
Speaker 1: of Part thirty seven reading by Paul King, Mississauga, Ontario,
Speaker 1: p J K dot scripts dot M, I, T dot E,
Speaker 1: d U forward slash p K J. This is the
Speaker 1: end of a short account of the history of mathematics
Speaker 1: by W. W. Rouse Ball