WEBVTT 1 00:00:01.080 --> 00:00:04.040 Chapter nineteen, Part four of A short account of the 2 00:00:04.160 --> 00:00:09.439 History of mathematics. This is a LibriVox recording. All LibriVox 3 00:00:09.480 --> 00:00:13.000 recordings are in the public domain. For more information or 4 00:00:13.039 --> 00:00:16.960 to volunteer, please visit LibriVox dot org. This is a 5 00:00:17.039 --> 00:00:21.719 reading by Paul King PJK dot scripts dot mit dot edu. 6 00:00:21.960 --> 00:00:26.039 Forward slash p kJ. A short account of the history 7 00:00:26.039 --> 00:00:32.159 of mathematics by W. W. Rowse Ball, Chapter nineteen, Mathematics 8 00:00:32.159 --> 00:00:37.600 of Recent Times, Part four Clifford. I may, however add 9 00:00:37.640 --> 00:00:40.079 here a brief note on Clifford, who is one of 10 00:00:40.079 --> 00:00:43.479 the earliest English mathematicians of the latter half of this 11 00:00:43.640 --> 00:00:47.960 century to advocate the use of graphical and geometrical methods 12 00:00:48.000 --> 00:00:53.200 in preference to analysis. William king Don Clifford born at 13 00:00:53.240 --> 00:00:57.079 Exeter on May fourth, eighteen forty five and died at 14 00:00:57.119 --> 00:01:01.640 Madera on March third, eighteen seventy nine. Was educated at 15 00:01:01.640 --> 00:01:05.840 Trinity College, Cambridge, of which Society he was a fellow. 16 00:01:06.680 --> 00:01:10.000 In eighteen seventy one he was appointed Professor of Applied 17 00:01:10.040 --> 00:01:14.640 Mathematics at University College London, a post which he retained 18 00:01:14.680 --> 00:01:19.439 till his death. His remarkable felicity of illustration and power 19 00:01:19.560 --> 00:01:23.000 of seizing analogies made him one of the most brilliant 20 00:01:23.079 --> 00:01:28.519 expounders of mathematical principles. His health failed in eighteen seventy six, 21 00:01:29.159 --> 00:01:32.079 when the writer of this book undertook his work for 22 00:01:32.120 --> 00:01:36.439 a few months. Clifford then went to Algeria and returned 23 00:01:36.519 --> 00:01:38.840 at the end of the year, but only to break 24 00:01:38.879 --> 00:01:43.719 down again in eighteen seventy eight. His most important works 25 00:01:43.760 --> 00:01:48.280 are his Theory of bi Quaternions, on the Classification of 26 00:01:48.359 --> 00:01:54.040 Loki unfinished and the Theory of Graphs unfinished. His canonical 27 00:01:54.120 --> 00:01:59.120 dissection of a Riemann's surface and the Elements of dynamic 28 00:01:59.560 --> 00:02:03.799 also contain much interesting matter. I next turn to the 29 00:02:03.879 --> 00:02:09.159 question of mechanics treated analytically. The knowledge of mathematical mechanics 30 00:02:09.159 --> 00:02:12.759 of solids attained by the great mathematicians of the last 31 00:02:12.759 --> 00:02:15.599 century may be said to be summed up in the 32 00:02:15.759 --> 00:02:22.000 admirable Mechanique analytique by Lagrange and Treete de mechanique by Poisson, 33 00:02:22.719 --> 00:02:27.120 and the application of the results to astronomy is illustrated 34 00:02:27.120 --> 00:02:32.400 by Laplace's Mechanique Celeste. These works have been already described. 35 00:02:33.280 --> 00:02:36.360 The mechanics of fluids is more difficult than that of solids, 36 00:02:36.400 --> 00:02:41.319 and the theory is less advanced. Theoretical statics, especially the 37 00:02:41.319 --> 00:02:45.919 theory of potential and attractions, has received considerable attention from 38 00:02:45.960 --> 00:02:50.280 mathematicians of this century. I have already mentioned that the 39 00:02:50.319 --> 00:02:54.280 introduction of the idea of the potential is due to Lagrange, 40 00:02:54.840 --> 00:02:57.599 and it occurs in a memoir of a date as 41 00:02:57.680 --> 00:03:00.759 early as seventeen seventy three. The the idea was at 42 00:03:00.759 --> 00:03:04.520 once grasped by Laplace, who, in his memoir of seventeen 43 00:03:04.599 --> 00:03:07.639 eighty four used it freely and to whom the credit 44 00:03:07.680 --> 00:03:11.800 of the invention was formerly somewhat unjustly attributed. In the 45 00:03:11.879 --> 00:03:16.120 same memoir, Laplace also extended to space of three dimensions 46 00:03:16.120 --> 00:03:19.960 the idea of circular harmonic analysis, which had been introduced 47 00:03:20.000 --> 00:03:25.120 by Legentdre in seventeen eighty three. Green George Green was 48 00:03:25.159 --> 00:03:28.599 one of the earliest writers of this century who investigated 49 00:03:28.639 --> 00:03:32.240 further the properties of the potential. Green was born near 50 00:03:32.280 --> 00:03:36.560 Nottingham in seventeen ninety three in a humble condition in life, 51 00:03:36.879 --> 00:03:41.120 and died at Cambridge in eighteen forty one. Although self educated, 52 00:03:41.240 --> 00:03:45.080 he contrived to get access to various mathematical books, and 53 00:03:45.120 --> 00:03:47.840 in eighteen twenty seven wrote a paper on the potential 54 00:03:48.479 --> 00:03:52.240 in which the term was first introduced, proved its chief properties, 55 00:03:52.280 --> 00:03:56.599 and applied the results to electricity and magnetism. This contains 56 00:03:56.639 --> 00:04:00.039 the important theorem now known by his name. This t 57 00:04:00.120 --> 00:04:03.840 remarkable paper was seen by some neighbours who were able 58 00:04:03.919 --> 00:04:07.439 to appreciate the power shown in it. It was published 59 00:04:07.479 --> 00:04:10.759 by subscription in eighteen twenty eight, but does not seem 60 00:04:10.800 --> 00:04:15.000 to have attracted much attention at first. Similar results were 61 00:04:15.039 --> 00:04:19.319 independently established in eighteen thirty nine by Gauss, to whom 62 00:04:19.360 --> 00:04:23.639 their general dissemination was due. In eighteen thirty two and 63 00:04:23.720 --> 00:04:28.399 eighteen thirty three, Green presented papers to the Cambridge Philosophical 64 00:04:28.480 --> 00:04:32.959 Society on the equilibrium of fluids and on attractions in 65 00:04:33.040 --> 00:04:36.240 space of n dimensions, and in the latter year his 66 00:04:36.279 --> 00:04:39.240 memoir on the motion of a fluid agitated by the 67 00:04:39.319 --> 00:04:43.000 vibrations of a solid ellipsoid was read before the Royal 68 00:04:43.079 --> 00:04:47.000 Society of Edinburgh. In eighteen thirty three he entered at 69 00:04:47.079 --> 00:04:51.279 Caius College, Cambridge, and was subsequently elected to a fellowship. 70 00:04:51.839 --> 00:04:55.480 He then threw himself into original work, and produced in 71 00:04:55.519 --> 00:04:59.079 eighteen thirty seven his paper on the motion of waves 72 00:04:59.199 --> 00:05:02.560 in a canal and on the reflection and refraction of 73 00:05:02.720 --> 00:05:06.519 sound and light. In the latter, the geometrical laws of 74 00:05:06.600 --> 00:05:10.240 sound and light are deduced by the principle of energy 75 00:05:10.600 --> 00:05:14.800 from the undulatory theory. The phenomenon of total reflection is 76 00:05:14.839 --> 00:05:20.319 explained physically, and certain properties of the vibrating medium are deduced. 77 00:05:21.680 --> 00:05:26.639 He also discussed the propagation of light in any crystalline medium. 78 00:05:26.759 --> 00:05:30.399 Of Gauss's work on attractions, I have already spoken the 79 00:05:30.399 --> 00:05:33.319 theory of level surfaces and lines of force is largely 80 00:05:33.360 --> 00:05:37.240 due to Chasla's who also determine the attraction of an 81 00:05:37.279 --> 00:05:41.000 ellipsoid at any external point. I ought not to leave 82 00:05:41.040 --> 00:05:46.680 the subject of theoretical statics without mentioning Mobius. August ferden Anmobius, 83 00:05:46.720 --> 00:05:50.759 professor at Leipzig, who was born at Schlpforta on November seventeen, 84 00:05:50.879 --> 00:05:54.600 seventeen ninety and died on September twenty sixth, eighteen sixty eight, 85 00:05:54.879 --> 00:05:57.759 was one of the best known of Gauss's pupils. He 86 00:05:57.800 --> 00:06:02.160 published his verycentricius caut alcourd in eighteen twenty six. His 87 00:06:02.279 --> 00:06:05.839 collected works were published at Leipzig in four volumes eighteen 88 00:06:05.879 --> 00:06:09.439 eighty five to eighteen eighty seven. Among living writers, I 89 00:06:09.480 --> 00:06:14.079 may allude to Sir Robert Stallwell Ball, Loundian professor in 90 00:06:14.160 --> 00:06:18.199 the University of Cambridge, born in Dublin on July first, 91 00:06:18.240 --> 00:06:21.759 eighteen forty who issued his Theory of Screws in eighteen 92 00:06:21.879 --> 00:06:25.959 seventy six. Theoretical dynamics has been studied by most of 93 00:06:26.000 --> 00:06:29.160 the writers above mentioned. In addition to these, I may 94 00:06:29.199 --> 00:06:32.720 repeat that the principle of varying action was elaborated by 95 00:06:32.720 --> 00:06:36.800 Sir William Hamilton in eighteen twenty seven, and the Hamiltonian 96 00:06:36.879 --> 00:06:39.959 equations were given in eighteen thirty five. And I may 97 00:06:40.000 --> 00:06:43.399 call attention to Beartrand's work on dynamics. The use of 98 00:06:43.480 --> 00:06:48.160 generalized coordinates introduced by Lagrange has become the customary means 99 00:06:48.199 --> 00:06:52.199 of attacking dynamical as well as many physical problems. The 100 00:06:52.240 --> 00:06:55.720 standard English textbook on the dynamics of rigid bodies is 101 00:06:55.759 --> 00:06:59.319 that by Doctor Routh on the Mechanics of Fluids, liquids 102 00:06:59.360 --> 00:07:02.639 and gases. Apart from the physical theories on which they rest, 103 00:07:02.800 --> 00:07:05.319 I propose to say nothing except to refer to the 104 00:07:05.360 --> 00:07:09.920 memoirs of Green Sir George Stokes, Lord Kelvin, better known 105 00:07:10.000 --> 00:07:16.120 as Sir William Thompson and von Helmholtz. The fascinating but 106 00:07:16.199 --> 00:07:19.839 difficult theory of vortex rings is due to the two 107 00:07:19.879 --> 00:07:24.279 writers last mentioned. One problem in it has been also 108 00:07:24.360 --> 00:07:27.519 considered by J. J. Thompson, but it is a subject 109 00:07:28.000 --> 00:07:31.759 which is as yet rather beyond our powers of analysis. 110 00:07:32.759 --> 00:07:36.879 The subject of sound may be treated in connection with hydrodynamics, 111 00:07:37.120 --> 00:07:40.160 but on this I would refer to the reader who 112 00:07:40.199 --> 00:07:43.639 wishes for further information to the work published at Cambridge 113 00:07:43.680 --> 00:07:49.160 in eighteen seventy seven by Lord Raleigh, recently Cavenish Professor 114 00:07:49.279 --> 00:07:53.800 in the University of Cambridge. Theoretical astronomy is included in 115 00:07:54.560 --> 00:07:59.199 or at any rate closely connected with theoretical dynamics. Among 116 00:07:59.279 --> 00:08:02.000 those who in this century have devoted themselves to the 117 00:08:02.040 --> 00:08:06.040 study of theoretical astronomy, the name of Gauss is one 118 00:08:06.040 --> 00:08:08.720 of the most prominent to his work. I have already 119 00:08:08.720 --> 00:08:15.240 alluded Bessel. The best known of Gauss's contemporaries was Frederich 120 00:08:15.319 --> 00:08:19.600 Wilhelm Bassel, who was born in Minden on July twenty second, 121 00:08:19.759 --> 00:08:24.519 seventeen eighty four and died at Knigsburg on March seventeenth, 122 00:08:24.560 --> 00:08:28.000 eighteen forty six. Bessel commenced his life as a clerk 123 00:08:28.079 --> 00:08:30.639 on board ship, but in eighteen o six he became 124 00:08:30.680 --> 00:08:34.240 an assistant in the observatory at Lilenthal, and was thence 125 00:08:34.279 --> 00:08:36.600 in eighteen oh one promoted to be director of the 126 00:08:36.639 --> 00:08:40.440 new Prussian Observatory at Knigsburg, where he continued to live 127 00:08:40.519 --> 00:08:44.879 during the remainder of his life. Bessel introduced into pure 128 00:08:44.919 --> 00:08:48.159 mathematics those functions which are now called by his name. 129 00:08:49.200 --> 00:08:52.960 This was in eighteen twenty four, though their use is 130 00:08:52.519 --> 00:08:57.080 indicated in a memoir seven years earlier. But his most 131 00:08:57.120 --> 00:09:01.519 notable achievements where the reduction gave given in his fundamental 132 00:09:01.759 --> 00:09:07.320 astronomier Canigsburg eighteen eighteen of the Greenwich observations by Bradley 133 00:09:07.399 --> 00:09:10.639 of three thousand, two hundred twenty two stars and his 134 00:09:10.759 --> 00:09:15.879 determination of the annual parallax of sixty one Signai. Bradley's 135 00:09:15.879 --> 00:09:20.799 observations have been recently reduced again by doctor A. Auers 136 00:09:20.919 --> 00:09:27.120 of Berlin, the verier. Among the astronomical events of this century, 137 00:09:27.639 --> 00:09:31.519 the discovery of the planet Neptune by Leverrier and Adams 138 00:09:31.720 --> 00:09:36.080 is one of the most striking Urbane. Jean Joseph Leverrier, 139 00:09:36.639 --> 00:09:40.600 the son of a petty government employee in Normandy was 140 00:09:40.639 --> 00:09:43.919 born at Saint Loa on March eleventh, eighteen eleven, and 141 00:09:44.039 --> 00:09:47.759 died at Paris on September twenty third, eighteen seventy seven. 142 00:09:48.000 --> 00:09:51.200 He was educated at the Polytechnic School, and in eighteen 143 00:09:51.279 --> 00:09:56.080 thirty seven was appointed its lecturer on astronomy. There his 144 00:09:56.200 --> 00:10:00.159 earliest researches in astronomy were communicated to the Acaomy in 145 00:10:00.240 --> 00:10:04.320 eighteen thirty nine. In these he calculated, within much narrower 146 00:10:04.320 --> 00:10:08.039 limits than Laplace had done, the extent within which the 147 00:10:08.080 --> 00:10:13.879 inclinations and eccentricities of the planetary orbits vary. The independent 148 00:10:14.039 --> 00:10:18.480 discovery in eighteen forty six by Leverrier and Atoms of 149 00:10:18.519 --> 00:10:22.480 the planet Neptune, by means of the disturbance it produced 150 00:10:22.559 --> 00:10:26.600 on the orbit of Uranus, attracted general attention to physical 151 00:10:26.600 --> 00:10:31.559 astronomy and strengthened the opinion as to the universality of gravity. 152 00:10:31.960 --> 00:10:36.000 In eighteen fifty five, Leverrier succeeded Arago as director of 153 00:10:36.000 --> 00:10:40.320 the Paris Observatory and reorganized it in accordance with the 154 00:10:40.360 --> 00:10:44.480 requirements of modern astronomy. He now set himself the task 155 00:10:44.559 --> 00:10:49.440 of discussing the theoretical investigations of the planetary motions and 156 00:10:49.559 --> 00:10:53.440 of revising all tables which involve them. He lived just 157 00:10:53.559 --> 00:10:56.320 long enough to sign the last proof sheet of this 158 00:10:56.519 --> 00:11:01.600 work atoms. The co discover hover of Neptune was John 159 00:11:01.679 --> 00:11:05.320 Couch Adams, who was born in Cornwall on June fifth, 160 00:11:05.320 --> 00:11:10.720 eighteen nineteen, educated at Saint John's College, Cambridge, subsequently appointed 161 00:11:10.720 --> 00:11:15.399 to Loundian Professor in the University and director of the Observatory, 162 00:11:15.799 --> 00:11:19.039 and who died at Cambridge on January twenty first, eighteen 163 00:11:19.159 --> 00:11:24.120 ninety two. There are three important problems which are especially 164 00:11:24.279 --> 00:11:28.200 associated with the name of Adams. The first of these 165 00:11:28.320 --> 00:11:31.639 is his discovery of the planet Neptune from the perturbations 166 00:11:31.639 --> 00:11:35.399 it produced on the orbit of Uranus in point of time. 167 00:11:35.480 --> 00:11:40.519 This was slightly earlier than Laverier's investigation. The second memoir 168 00:11:40.600 --> 00:11:44.519 to which I referred was on the secular Acceleration of 169 00:11:44.559 --> 00:11:49.279 the Moon's mean Motion Philosophical Transactions, eighteen fifty five, Volume 170 00:11:49.320 --> 00:11:52.720 one hundred forty three, page three hundred seventy seven. Laplace 171 00:11:52.759 --> 00:11:55.639 had calculated this on the hypothesis that it was caused 172 00:11:55.639 --> 00:11:59.159 by the eccentricity of the Earth's orbit, and had obtained 173 00:11:59.159 --> 00:12:02.399 a result which agreed substantially with the value it deduced 174 00:12:02.399 --> 00:12:06.399 from a comparison of the records of ancient and modern eclipses. 175 00:12:06.960 --> 00:12:10.720 Adams shewed that certain terms in an expression had been neglected, 176 00:12:10.799 --> 00:12:13.360 and that if they were taken into account, the result 177 00:12:13.480 --> 00:12:16.879 was only about one half that found by Laplace. The 178 00:12:16.960 --> 00:12:22.240 correctness of the calculations of Adams was denied by Plaina, Ponte, Coulan, 179 00:12:22.879 --> 00:12:27.639 and other continental astronomers, but Delaunay in France and Cayley 180 00:12:27.720 --> 00:12:32.480 in England verified the work. The third investigation connected with 181 00:12:32.559 --> 00:12:36.240 the name of Adams is his determination of the orbit 182 00:12:36.360 --> 00:12:41.200 of the Leonids or shooting stars, which were especially conspicuous 183 00:12:41.200 --> 00:12:44.879 in November eighteen sixty six, and whose period is about 184 00:12:45.080 --> 00:12:50.159 thirty three years. Newton of Yale had shewn that there 185 00:12:50.200 --> 00:12:55.080 were only five possible orbits. Adams calculated the disturbance which 186 00:12:55.120 --> 00:12:58.320 would be produced by the planets on the motion of 187 00:12:58.440 --> 00:13:01.759 the node of the orbit of a swarm of meteors 188 00:13:01.799 --> 00:13:05.679 in each of these cases, and found that this disturbance 189 00:13:05.720 --> 00:13:09.039 agreed with the observations for one of the possible orbits, 190 00:13:09.440 --> 00:13:12.639 but for none of the others. Hence the orbit was known. 191 00:13:13.600 --> 00:13:17.279 Other well known astronomers of this century are Giovanni Antonio 192 00:13:17.320 --> 00:13:22.480 Amadeo Plina born at Volgera on November eighth, seventeen eighty 193 00:13:22.480 --> 00:13:26.960 one and died at Tehrann on January twentieth, eighteen sixty four, 194 00:13:27.320 --> 00:13:29.799 whose work on the motion of the Moon was published 195 00:13:29.799 --> 00:13:34.720 in eighteen thirty two. Philip Gustave Duchet, Count ponte Colan, 196 00:13:35.039 --> 00:13:39.519 born in seventeen ninety five and died at Portecolon on 197 00:13:39.879 --> 00:13:44.240 July twenty first, eighteen seventy one. Charles Eugene d' laune 198 00:13:44.360 --> 00:13:48.320 born at Losignier on April ninth, eighteen sixteen and drowned 199 00:13:48.320 --> 00:13:52.120 off Cherbourg on August third, eighteen seventy two, whose work 200 00:13:52.159 --> 00:13:55.480 on the lunar theory indicates the best method yet suggested 201 00:13:55.919 --> 00:14:00.200 for the analytical investigations of the whole problem, and whose 202 00:14:00.200 --> 00:14:05.759 incomplete Lunar Tables are among the astronomical achievements of this century. 203 00:14:06.279 --> 00:14:10.519 And Peter Andrew Henson born at Schleswig on December eighth, 204 00:14:10.759 --> 00:14:14.559 seventeen ninety five and died at Gotha, where he was 205 00:14:14.679 --> 00:14:18.279 head of the observatory, on March twenty eighth, eighteen seventy four, 206 00:14:18.799 --> 00:14:21.919 who compiled the Lunar Tables, published in London in eighteen 207 00:14:22.000 --> 00:14:25.879 fifty seven and celebrated the most delicate methods yet known 208 00:14:26.080 --> 00:14:30.480 for the determination of lunar and planetary perturbations. For an 209 00:14:30.519 --> 00:14:35.000 account of the numerous memoirs, see the Transactions of the 210 00:14:35.080 --> 00:14:38.919 Royal Society of London from eighteen seventy six to eighteen 211 00:14:39.080 --> 00:14:44.240 seventy seven. Among living mathematicians, I may mention the following names. 212 00:14:45.080 --> 00:14:49.759 Felix Tsarin of Paris, born in eighteen forty five, whose 213 00:14:49.840 --> 00:14:54.399 Mechadique Celeste forms a worthy pendant to Laplace's work of 214 00:14:54.440 --> 00:14:58.360 the same title. George William Hill born in New York 215 00:14:58.639 --> 00:15:02.039 in eighteen thirty eight, as until recently on the staff 216 00:15:02.039 --> 00:15:06.240 of American amphemorists, who in eighteen eighty four determine the 217 00:15:06.279 --> 00:15:09.440 inequalities of the Moon's motion due to the non spherical 218 00:15:09.519 --> 00:15:14.200 figure of the Earth, an investigation which completed Delaunay's lunar theory. 219 00:15:14.879 --> 00:15:17.919 Heil also dealt with the secular motion of the Moon's 220 00:15:17.919 --> 00:15:22.159 perigy and the motion of a planet's perigy under certain conditions, 221 00:15:22.600 --> 00:15:24.759 and he has written on the analytical theory of the 222 00:15:24.759 --> 00:15:27.679 moon of Jupiter and Saturn, with a view to the 223 00:15:27.720 --> 00:15:31.039 preparation of tables of their positions at any given time. 224 00:15:32.679 --> 00:15:37.600 Simon Newcombe born in Nova Scotia on March twelfth, eighteen 225 00:15:37.639 --> 00:15:42.600 thirty five, superintendent of the American Ephemerists, who re examined 226 00:15:42.600 --> 00:15:46.639 the Greenwich observations from the earliest times, applied the result 227 00:15:46.720 --> 00:15:51.720 of the lunar theory, and revised Hanson's tables. George Howard 228 00:15:51.799 --> 00:15:55.679 Doughran of Trinity College, Cambridge born in Kent in eighteen 229 00:15:55.759 --> 00:16:00.559 forty five, now Plumian Professor in the University of king Ambridge, 230 00:16:00.600 --> 00:16:03.919 who has written on the effect of tides on viscous spheroids, 231 00:16:04.120 --> 00:16:07.559 the development of planetary systems by means of tidal friction, 232 00:16:08.120 --> 00:16:13.399 the mechanics of meteoric swarms, et cetera. Perhaps also I 233 00:16:13.440 --> 00:16:18.519 may here mention Plant Career, who has discussed the difficult 234 00:16:18.559 --> 00:16:21.639 problem of three bodies and the form assumed by a 235 00:16:21.679 --> 00:16:25.519 mass of fluid under its own attraction. Within the last 236 00:16:25.559 --> 00:16:29.559 half century, the results of spectrum analysis have been applied 237 00:16:29.600 --> 00:16:33.919 to determine the constitution and directions of motions of the 238 00:16:33.960 --> 00:16:38.000 heavenly bodies to and from the Earth. The early history 239 00:16:38.000 --> 00:16:41.919 of spectrum analysis will be always associated with the names 240 00:16:41.919 --> 00:16:47.120 of Gustav Robert Kirschov and A. J. Engstrom of Uppsala 241 00:16:47.279 --> 00:16:50.879 and Sir George Stokes of Cambridge, but it pertains to 242 00:16:51.000 --> 00:16:55.679 optics rather than to astronomy. Within the last few years, 243 00:16:55.799 --> 00:16:59.480 the range of astronomy has been still further extended by 244 00:16:59.480 --> 00:17:02.399 the art of a photography. To what new developments this 245 00:17:02.559 --> 00:17:07.480 may lead, it is as yet impossible to say mathematical physics. 246 00:17:08.480 --> 00:17:11.440 An account of the history of mathematics in this century 247 00:17:11.920 --> 00:17:15.720 would not be other than misleading if there were no 248 00:17:15.839 --> 00:17:22.039 reference to the application of it to numerous problems in heat, elasticity, light, electricity, 249 00:17:22.160 --> 00:17:26.839 and other physical subjects. The history of mathematical physics is, however, 250 00:17:27.039 --> 00:17:29.440 so extensive that I could not pretend to do a 251 00:17:29.599 --> 00:17:33.319 justice even were its consideration properly included in a history 252 00:17:33.359 --> 00:17:37.240 of mathematics. Moreover, it is so closely connected with the 253 00:17:37.279 --> 00:17:41.519 works of living physicists, notably of von Helmholtz and of 254 00:17:41.599 --> 00:17:45.599 Lord Kelvin that are known as Sir William Thompson, that 255 00:17:45.680 --> 00:17:49.039 I may consider it outside the limits I have laid 256 00:17:49.079 --> 00:17:52.480 down for myself in this chapter. It is, however, interesting 257 00:17:52.559 --> 00:17:55.000 to note that the advance in our knowledge of physics 258 00:17:55.039 --> 00:17:58.480 is largely due to the application to it of mathematics, 259 00:17:58.839 --> 00:18:01.799 and every year, it becomes more difficult for an experimenter 260 00:18:01.880 --> 00:18:04.440 to make any mark on the subject unless he is 261 00:18:04.519 --> 00:18:10.960 also a mathematician. Amongst recent writers on mathematical physics, excluding 262 00:18:11.000 --> 00:18:16.039 all reference to experimental physics, as also to theories to 263 00:18:16.119 --> 00:18:20.119 which mathematical analysis has not yet been applied, I may 264 00:18:20.200 --> 00:18:24.759 specially mention the following, whose names are here arranged alphabetically, 265 00:18:25.119 --> 00:18:27.440 though the list is not in any way profess to 266 00:18:27.480 --> 00:18:33.519 be complete or exhaustive. J Buzenesque of Paris, who is 267 00:18:33.559 --> 00:18:39.000 written on optics. Ludwig Boltzmann of Vienna, whose writings greatly 268 00:18:39.039 --> 00:18:42.480 extended the kinetic theory of gases and have done something 269 00:18:42.519 --> 00:18:46.200 to bring the molecular physics within the domain of mathematics. 270 00:18:47.000 --> 00:18:53.319 Rudolph Julius Emmanuel Clausius born at Kozlen on January two, 271 00:18:53.559 --> 00:18:56.880 eighteen twenty two, had died at Bonn, where he was 272 00:18:56.960 --> 00:19:00.559 professor of physics, in August eighteen eighty eight, who was 273 00:19:00.640 --> 00:19:03.920 among the earliest to discuss the subject of heat from 274 00:19:03.920 --> 00:19:09.000 a mathematical point of view. Klebsch, who discussed the elasticity 275 00:19:09.039 --> 00:19:14.480 of solid bodies. Julius Wilhelm Richard Detikind, who is the 276 00:19:14.519 --> 00:19:17.559 author of a remarkable memoir on the vibrations of a 277 00:19:17.599 --> 00:19:22.519 liquid ellipsoid, which is treated as a problem in pure mathematics. 278 00:19:23.359 --> 00:19:29.039 Michael Faraday born at Newington on September twenty second, seventeen 279 00:19:29.119 --> 00:19:32.880 ninety one, and died at Hampton Court on August twenty fifth, 280 00:19:32.920 --> 00:19:36.480 eighteen sixty seven, who had a special gift in deducing 281 00:19:36.559 --> 00:19:42.000 results by general reasoning from fundamental principles, and in disentangling 282 00:19:42.039 --> 00:19:46.519 those principles from the symbols in which they are usually expressed. 283 00:19:46.799 --> 00:19:51.079 For further details see the biographies of Tyndal second edition 284 00:19:51.160 --> 00:19:56.240 eighteen seventy, Bence Jones eighteen seventy or Doctor Gladstone eighteen 285 00:19:56.319 --> 00:20:01.599 seventy two. George Francis Fitzgerald, Professor in Dublin, born there 286 00:20:01.680 --> 00:20:04.960 on August third, eighteen fifty one, who was written on 287 00:20:05.039 --> 00:20:10.759 electromagnetism and optics. John Bernard Leon Foucaut born at Paris 288 00:20:10.960 --> 00:20:15.880 on September eighteenth, eighteen nineteen, and died there of paralysis 289 00:20:16.240 --> 00:20:20.680 on February eleventh, eighteen sixty eight, whose chief memoirs were 290 00:20:20.720 --> 00:20:25.119 on the Predictability of photography eighteen forty on the Electric 291 00:20:25.240 --> 00:20:29.000 lamp eighteen forty nine, on the determination of the velocity 292 00:20:29.000 --> 00:20:32.119 of light in eighteen fifty, but repeated with improvements in 293 00:20:32.160 --> 00:20:36.240 eighteen sixty two. On his demonstration of the diurnal motion 294 00:20:36.400 --> 00:20:38.519 of the Earth by means of the rotation of the 295 00:20:38.519 --> 00:20:42.279 plane of oscillation of a simple pendulum eighteen fifty one, 296 00:20:43.119 --> 00:20:46.920 on the gyroscope eighteen fifty two, on the rotation of 297 00:20:46.960 --> 00:20:49.839 a copper disc between the poles of a magnet eighteen 298 00:20:49.920 --> 00:20:54.640 fifty five, and on a polarizer eighteen fifty seven. For 299 00:20:54.680 --> 00:20:58.839 further details see La ville se traveau de Leon Foucaut 300 00:20:58.960 --> 00:21:03.440 by JA la Lisijus, Paris, eighteen seventy five, and also 301 00:21:03.519 --> 00:21:07.039 a notice by J. Bertrand preface to the collected edition 302 00:21:07.279 --> 00:21:12.839 of Fucot's works, Paris, eighteen seventy eight. J. Willard Gibbs 303 00:21:13.039 --> 00:21:17.200 of Yale, America, who has written on the thermodynamics and 304 00:21:17.319 --> 00:21:23.680 Maxwell's electromagnetic theory. Richard Tetley Glazebrook of Trinity College, Cambridge, 305 00:21:24.039 --> 00:21:28.160 born at Liverpool on September eighteenth, eighteen fifty four, who 306 00:21:28.200 --> 00:21:32.039 has written on optics and electricity. His report in the 307 00:21:32.039 --> 00:21:36.519 Transactions of the British Association eighteen eighty five on theories 308 00:21:36.519 --> 00:21:39.759 of optics contains a valuable summary of most of the 309 00:21:39.839 --> 00:21:43.960 mathematical researches on that subject during this century and prior 310 00:21:44.079 --> 00:21:47.519 to the date of the report. After a brief allusion 311 00:21:47.559 --> 00:21:51.839 to the views of Green, Koshee, McCulloch and F. E. Neumann, 312 00:21:52.079 --> 00:21:54.960 he describes the more recent work according as it comes 313 00:21:55.039 --> 00:21:59.000 under the simple elastic solid theory or theories assuming an 314 00:21:59.039 --> 00:22:05.039 action between Matie and Ether, or Maxwell's electromagnetic theory. Green, 315 00:22:05.799 --> 00:22:09.079 whose physical memoirs were mostly on the theory of waves. 316 00:22:09.720 --> 00:22:12.839 Von Helmholtz, who is in the front rank of all 317 00:22:12.880 --> 00:22:16.960 departments of mathematics and physics. His collected papers were published 318 00:22:17.000 --> 00:22:21.279 in two volumes Leipzig, eighteen eighty two to eighteen eighty three. 319 00:22:21.599 --> 00:22:25.480 Oliver Heavyside, who has written on the mathematical theories of 320 00:22:25.480 --> 00:22:31.400 optics and electromagnetism. Lord Kelvin or Sir William Thompson, Professor 321 00:22:31.440 --> 00:22:35.960 at Glasgow born at Belfast, June eighteen twenty four, who 322 00:22:36.000 --> 00:22:39.880 has enriched every department of physics by his researches. His 323 00:22:39.960 --> 00:22:43.599 collected papers were published at Cambridge volume one in eighteen 324 00:22:43.640 --> 00:22:47.160 eighty two, at volume two in eighteen eighty four, and 325 00:22:47.240 --> 00:22:52.920 volume three in eighteen ninety Gustav Robert Kirschow, professor in physics, 326 00:22:52.920 --> 00:22:55.880 first at Heidelberg and then at Berlin. Born at Knigsburg 327 00:22:55.960 --> 00:22:59.279 on March twelfth, eighteen twenty four and died in Berlin 328 00:22:59.400 --> 00:23:03.480 October sie seventeenth, eighteen eighty seven, whose name will always 329 00:23:03.480 --> 00:23:07.400 be associated with the history of spectrum analysis and his 330 00:23:07.480 --> 00:23:11.880 researches on elasticity. His collected papers were published at Leipzig 331 00:23:12.440 --> 00:23:17.039 in eighteen eighty two. Gabriel Lamay born at Tours on 332 00:23:17.160 --> 00:23:20.839 July twenty seconds, seventeen ninety five and died at Paris 333 00:23:21.000 --> 00:23:25.079 in eighteen seventy, where he was professor at the Polytechnic School, 334 00:23:25.400 --> 00:23:28.400 whose best known works are his Course on Physics eighteen 335 00:23:28.480 --> 00:23:32.960 thirty six, his Treatise on Elasticity eighteen fifty two, his 336 00:23:33.000 --> 00:23:36.599 work on Functions eighteen fifty seven, an essay on the 337 00:23:36.640 --> 00:23:40.759 curve linear coordinates eighteen fifty nine, and lastly his Theory 338 00:23:40.759 --> 00:23:44.039 of Heat eighteen sixty one. He also wrote memoirs on 339 00:23:44.119 --> 00:23:48.000 different points in the theory of numbers. James Clerk Maxwell born 340 00:23:48.039 --> 00:23:51.599 at Edinburgh on June thirteenth, eighteen thirty one and died 341 00:23:51.640 --> 00:23:55.119 at Cambridge on November fifth, eighteen seventy nine, where he 342 00:23:55.200 --> 00:23:59.319 was Professor of Experimental Physics. His most important works were 343 00:23:59.359 --> 00:24:02.319 his memoir in eighteen fifty nine on the stability of 344 00:24:02.400 --> 00:24:06.759 Saturn's rings, various articles on color, his memoir on the 345 00:24:06.799 --> 00:24:11.920 electromagnetic field, his Electricity and Magnetism, issued in eighteen seventy three, 346 00:24:12.480 --> 00:24:15.799 his Theory of Heat published in eighteen seventy one, and 347 00:24:15.839 --> 00:24:19.119 his elementary textbook on Matter and Motion. To these, I 348 00:24:19.200 --> 00:24:23.119 may add his memoir on Reciprocal Figures, which are useful 349 00:24:23.119 --> 00:24:26.720 in graphics, and his papers on molecular theory of gases 350 00:24:27.200 --> 00:24:31.880 and cognate subjects. His Electricity and Magnetism has revolutionized the 351 00:24:31.880 --> 00:24:35.480 treatment of the subject. Poissin A. Gauss had explained the 352 00:24:35.480 --> 00:24:41.160 phenomenon of electrostatics by attraction and repulsions between imponderable particles, 353 00:24:41.559 --> 00:24:45.079 while Lord Kelvin Sir William Thompson in eighteen forty six 354 00:24:45.119 --> 00:24:48.759 has shewn that that the effects might be supposed analogous 355 00:24:48.799 --> 00:24:51.799 to a flow of heat from various sources of electricity 356 00:24:52.119 --> 00:24:57.319 properly distributed in electrodynamics. The theory then generally current was 357 00:24:57.359 --> 00:25:00.000 that proposed by W. E. Webber, in which the attraction 358 00:25:00.000 --> 00:25:04.759 action between electrified particles depends on their relative motion and position. 359 00:25:05.480 --> 00:25:09.960 Maxwell rejected all these hypotheses and explained the phenomenon by 360 00:25:10.000 --> 00:25:13.880 stresses and motions of a material medium. He concluded by 361 00:25:13.920 --> 00:25:16.640 shewing that if the medium were the same as the 362 00:25:16.640 --> 00:25:20.400 so called luminiferous ether, the velocity of light would be 363 00:25:20.440 --> 00:25:24.759 equal to the ratio of the electromagnetic and electrostatic units. 364 00:25:24.920 --> 00:25:30.240 Subsequent experiments have tended to confirm this conclusion. For fuller details, 365 00:25:30.400 --> 00:25:33.880 his collected works Cambridge two Volumes, eighteen ninety and His 366 00:25:34.039 --> 00:25:37.359 Life by L. Campbell and W. Garnett, London, eighteen eighty 367 00:25:37.359 --> 00:25:43.039 two may be consulted. McCulloch, who wrote on physical optics. 368 00:25:43.519 --> 00:25:48.720 Franz rus Numann of Knigsburg born at Uckermark on September eleventh, 369 00:25:48.759 --> 00:25:53.200 seventeen ninety eight, who wrote on elasticity and light. William 370 00:25:53.319 --> 00:25:57.559 John ran Keane of Glasgow born at Edinburgh on July fifth, 371 00:25:57.559 --> 00:26:01.480 eighteen twenty and died December twenty five, eighteen seventy two, 372 00:26:02.240 --> 00:26:06.119 whose discoveries in thermodynamics and hydromechanics will be found in 373 00:26:06.160 --> 00:26:09.359 the collected edition of his works issued in London in 374 00:26:09.400 --> 00:26:14.920 eighteen eighty one. Lord Rayleigh born on November twelfth, eighteen 375 00:26:15.039 --> 00:26:18.759 forty two, who, besides some classical papers on the mathematics 376 00:26:18.759 --> 00:26:23.039 of physical optics, has written the standard English work on sound, 377 00:26:23.279 --> 00:26:28.039 published at Cambridge in eighteen seventy seven. Paret de Saint Venon, 378 00:26:28.200 --> 00:26:32.559 whose researches on elasticity and torsion are well known. Sir 379 00:26:32.640 --> 00:26:36.839 George Gabriel Stokes, most of whose papers on hydromechanics or 380 00:26:36.880 --> 00:26:41.200 optics or allied subjects. These memoirs have been recently collected 381 00:26:41.200 --> 00:26:44.839 and published by the University of Cambridge. Peter Guthrie Tait, 382 00:26:45.079 --> 00:26:49.400 Professor in Edinburgh, born at Dalkeith on April twenty eighth, 383 00:26:49.480 --> 00:26:52.759 eighteen thirty one, who has written on the mathematics of 384 00:26:52.839 --> 00:26:57.440 various physical subjects, and especially on the molecular theory of gases. 385 00:26:58.559 --> 00:27:03.160 Joseph John Thompson of Trinity College and Cavendish Professor in 386 00:27:03.240 --> 00:27:07.480 the University of Cambridge, born at Manchester on December eighteenth, 387 00:27:07.559 --> 00:27:11.039 eighteen fifty six, who is written on vortex rings and 388 00:27:11.079 --> 00:27:15.759 the application of generalized coordinates to various physical problems. I 389 00:27:15.799 --> 00:27:19.000 may also allude to his report on the Transactions of 390 00:27:19.039 --> 00:27:23.160 the British Association eighteen eighty five on electric theories, which 391 00:27:23.200 --> 00:27:26.279 He classifies into those not founded on the principle of 392 00:27:26.359 --> 00:27:31.279 conservation of energy, such as those of Empire, Grassmann, Stefan 393 00:27:31.839 --> 00:27:36.519 and Courtweg. Those which rest on assumptions concerning the velocities 394 00:27:36.519 --> 00:27:41.599 and positions of electrified particles, such as those of Gauss, W. E. Webber, 395 00:27:41.799 --> 00:27:45.759 Riemann and Clausius. Those which require the existence of a 396 00:27:45.839 --> 00:27:48.599 kind of energy of which we have no other knowledge, 397 00:27:48.720 --> 00:27:52.079 such as the theory of C. Numonn, Those which rest 398 00:27:52.160 --> 00:27:55.599 on the dynamical considerations but in which no account is 399 00:27:55.640 --> 00:27:59.400 taken of the action of the dielectric, such as the 400 00:27:59.400 --> 00:28:02.720 theory of V. F. E. Neumann, And finally, those which 401 00:28:02.759 --> 00:28:06.480