WEBVTT 1 00:00:01.159 --> 00:00:04.320 Chapter eighteen, Part four of A Short Account of the 2 00:00:04.440 --> 00:00:09.400 History of Mathematics by W. W. Rowsball. This is a 3 00:00:09.439 --> 00:00:13.400 LibriVox recording. All LibriVox recordings are in the public domain. 4 00:00:14.080 --> 00:00:18.359 For more information or to volunteer, please visit LibriVox dot org. 5 00:00:19.440 --> 00:00:23.160 This is a reading by Paul King PJK dot scripts 6 00:00:23.160 --> 00:00:25.559 that I might t dot e d U forward slash 7 00:00:25.679 --> 00:00:29.199 p j K. A Short account of the History of 8 00:00:29.239 --> 00:00:35.520 mathematics by W. W. Rowsball, Chapter eighteen Leibniz and the 9 00:00:35.560 --> 00:00:42.359 Mathematicians of the first half of the eighteenth century, Part four. Cavendish, 10 00:00:43.640 --> 00:00:48.240 the Honorable Henry Cavendish was born at Nice on October tenth, 11 00:00:48.280 --> 00:00:52.960 seventeen thirty one, and died in London on February twenty fourth, 12 00:00:53.039 --> 00:00:58.000 eighteen ten. His tastes for scientific research and mathematics were 13 00:00:58.039 --> 00:01:02.439 formed at Cambridge, where he resided from seventeen forty nine 14 00:01:02.920 --> 00:01:08.359 to seventeen fifty three. He created experimental electricity and was 15 00:01:08.400 --> 00:01:11.239 one of the earliest writers to treat chemistry as an 16 00:01:11.280 --> 00:01:14.879 exact science. I mention him here on account of his 17 00:01:15.000 --> 00:01:18.920 experiment in seventeen ninety eight to determine the density of 18 00:01:18.920 --> 00:01:22.280 the Earth by estimating its attraction as compared with that 19 00:01:22.359 --> 00:01:25.439 of two given lead balls. The result is that the 20 00:01:25.480 --> 00:01:27.680 mean density of the Earth is about five and a 21 00:01:27.719 --> 00:01:31.599 half times that of water. This experiment was carried out 22 00:01:31.640 --> 00:01:34.879 in accordance with a suggestion which had been first made 23 00:01:34.920 --> 00:01:39.000 by John Mitchell, a fellow of Queen's College, Cambridge, who 24 00:01:39.000 --> 00:01:44.200 had died before he was able to carry it into effect. Rumford, 25 00:01:44.840 --> 00:01:49.439 Sir Benjamin Thompson, Count Rumford, born at Concord on March 26 00:01:49.640 --> 00:01:54.000 twenty sixth, seventeen fifty three and died at Auteil on 27 00:01:54.280 --> 00:01:58.640 August twenty first, eighteen fifteen. Was of English descent and 28 00:01:58.719 --> 00:02:01.079 fought on the side of the lawyer Illis in the 29 00:02:01.120 --> 00:02:04.920 American War of Secession. On the conclusion of peace, he 30 00:02:05.000 --> 00:02:09.199 settled in England, but subsequently entered the service of Bavaria, 31 00:02:09.680 --> 00:02:13.240 where his military and civil powers of organization proved of 32 00:02:13.240 --> 00:02:17.599 great value. At a later period he again resided in England, 33 00:02:18.199 --> 00:02:22.639 and when there he founded the Royal Institution. The majority 34 00:02:22.680 --> 00:02:26.199 of his papers were communicated to the Royal Society of London. 35 00:02:26.919 --> 00:02:29.639 Of these, the most important is his memoir, in which 36 00:02:29.639 --> 00:02:34.080 he shewed that heat and work are mutually convertible. Young. 37 00:02:35.240 --> 00:02:38.879 Among the most eminent physicists of his time was Thomas Young, 38 00:02:39.400 --> 00:02:43.120 who was born in Milverton on June thirteenth, seventeen seventy 39 00:02:43.120 --> 00:02:47.080 three and died in London on May tenth, eighteen twenty nine. 40 00:02:48.000 --> 00:02:50.479 He seems as a boy to have been somewhat of 41 00:02:50.520 --> 00:02:53.919 a prodigy, being well read in modern languages and literature 42 00:02:54.400 --> 00:02:57.319 as well as in science. He always kept up his 43 00:02:57.439 --> 00:03:01.120 literary tastes, and it was he who first furnished the 44 00:03:01.240 --> 00:03:06.879 key to decipher the Egyptian hieroglyphics. He was destined to 45 00:03:06.879 --> 00:03:11.439 be a doctor, and after attending lectures at Edinburgh and Gottingen, 46 00:03:11.719 --> 00:03:15.120 entered im Manual College, Cambridge, from which he took his 47 00:03:15.240 --> 00:03:19.759 degree in seventeen ninety nine, and to his stay at 48 00:03:19.800 --> 00:03:24.960 the university he attributed much of his future distinction. His 49 00:03:25.039 --> 00:03:29.639 medical career was not particularly successful, and his favorable maxim 50 00:03:30.199 --> 00:03:33.759 that a medical diagnosis is only a balance of probabilities 51 00:03:34.439 --> 00:03:38.000 was not appreciated by his patients, who looked for certainty 52 00:03:38.039 --> 00:03:42.879 and returned for their fee. Fortunately, his private means were ample. 53 00:03:43.599 --> 00:03:48.039 Several papers contributed to various learned societies from seventeen ninety 54 00:03:48.080 --> 00:03:51.759 eight onwards prove him to have been a mathematician of 55 00:03:51.879 --> 00:03:57.080 considerable power. But the researches which have immortalized his name 56 00:03:57.560 --> 00:03:59.439 are those by which he laid down the laws of 57 00:03:59.479 --> 00:04:02.840 interference of waves and light, and was thus able to 58 00:04:02.879 --> 00:04:06.039 suggest the means by which the chief difficulties in the 59 00:04:06.080 --> 00:04:09.159 way of acceptance of the undulatory theory of light could 60 00:04:09.159 --> 00:04:16.439 be overcome. Wallaston. Another experimental physicist of the same time 61 00:04:16.519 --> 00:04:21.360 in school was William Hyde Wallaston, who was born at 62 00:04:21.439 --> 00:04:25.560 Dereham on August sixth, seventeen sixty six and died in 63 00:04:25.600 --> 00:04:30.000 London on December twenty second, eighteen twenty eight. He was 64 00:04:30.160 --> 00:04:34.240 educated at Caius College, Cambridge, of which society he was 65 00:04:34.279 --> 00:04:38.399 a fellow. Besides his well known chemical experiments, he has 66 00:04:38.439 --> 00:04:43.160 celebrated for his researches on experimental optics and for the 67 00:04:43.199 --> 00:04:51.879 improvements which he affected in astronomical instruments. Dalton. Another distinguished 68 00:04:51.920 --> 00:04:55.120 writer of the same period was John Dalton, who was 69 00:04:55.160 --> 00:05:00.160 born in Cumberland on September fifth, seventeen sixty six and 70 00:05:00.199 --> 00:05:04.240 died at Manchester on July twenty seventh, eighteen forty four. 71 00:05:04.759 --> 00:05:08.160 Dalton investigated the tension of vapors and the law of 72 00:05:08.199 --> 00:05:12.240 the expansion of a gas under changes of temperature. He 73 00:05:12.319 --> 00:05:16.319 also found the atomic theory in chemistry. It will be 74 00:05:16.399 --> 00:05:19.759 gathered from these notes that the English school of physicists 75 00:05:19.759 --> 00:05:22.879 at the beginning of this century were mostly concerned with 76 00:05:22.920 --> 00:05:26.360 the experimental side of the subject, but in fact no 77 00:05:26.519 --> 00:05:30.759 satisfactory theory could be formed without some similar careful determination 78 00:05:30.879 --> 00:05:34.800 of the facts. The most eminent French physicists of the 79 00:05:34.879 --> 00:05:41.560 same time were Fourier, Poissin Ampere, and Fresnol. Their method 80 00:05:41.680 --> 00:05:44.920 of treating the subject is more mathematical than that of 81 00:05:44.959 --> 00:05:49.319 their English contemporaries, and the two first named were distinguished 82 00:05:49.319 --> 00:05:55.800 for general mathematical ability. Fourier. The first of these French 83 00:05:55.839 --> 00:06:00.560 physicists was Jean Baptiste Joseph Fourier, who was born at 84 00:06:00.639 --> 00:06:04.759 Auterre on March twenty first, seventeen sixty eight and died 85 00:06:04.759 --> 00:06:08.879 at Paris on May sixteenth, eighteen thirty. He was the 86 00:06:08.920 --> 00:06:12.040 son of a tailor and was educated by the Benedictines. 87 00:06:13.120 --> 00:06:16.040 The commissions in the scientific corps of the army was, 88 00:06:16.160 --> 00:06:19.000 as still the case in Russia, reserved for those of 89 00:06:19.040 --> 00:06:23.240 good birth, and being thus ineligible, he accepted a military 90 00:06:23.319 --> 00:06:27.439 lectureship on mathematics. He took a prominent part in his 91 00:06:27.480 --> 00:06:31.319 own district in promoting the revolution, and was rewarded by 92 00:06:31.319 --> 00:06:34.639 an appointment in seventeen ninety five in the normal school, 93 00:06:34.759 --> 00:06:39.439 and subsequently by a chair at the Polytechnic School. He 94 00:06:39.519 --> 00:06:43.600 went with Napoleon on his Eastern expedition in seventeen ninety 95 00:06:43.639 --> 00:06:47.680 eight and was made governor of Lower Egypt, cut off 96 00:06:47.680 --> 00:06:51.560 from France by the English fleet, he organized the workshops 97 00:06:51.879 --> 00:06:54.680 on which the French army had to rely for their 98 00:06:54.800 --> 00:06:59.600 munitions of war. He also contributed several mathematical papers to 99 00:06:59.600 --> 00:07:03.959 the Agiat Institute, which Napoleon founded at Cairo with a 100 00:07:04.040 --> 00:07:08.240 view of weakening English influence in the East. After the 101 00:07:08.240 --> 00:07:11.959 British victories and the capitulation of the French under General 102 00:07:12.000 --> 00:07:15.959 Manon in eighteen oh one, he returned to France and 103 00:07:16.120 --> 00:07:19.759 was made prefect of Grenoble, and it was while there 104 00:07:20.040 --> 00:07:23.759 that he made his experiments on the propagation of heat. 105 00:07:24.680 --> 00:07:27.959 He moved to Paris in eighteen sixteen. In eighteen twenty 106 00:07:28.040 --> 00:07:32.680 two he publishes Theory and a Letigue les chere, in 107 00:07:32.759 --> 00:07:36.519 which he bases his reasoning on Newton's law of cooling, 108 00:07:36.680 --> 00:07:40.199 namely that the flow of heat between two adjacent molecules 109 00:07:40.560 --> 00:07:44.319 is proportional to the infinitely small difference of their temperatures. 110 00:07:45.439 --> 00:07:48.800 He states that the theory demands that the temperatures of 111 00:07:48.879 --> 00:07:52.759 stellar space should be between minus fifty degrees celsius and 112 00:07:52.879 --> 00:07:57.240 minus sixty degrees celsius, a conclusion which it has been 113 00:07:57.519 --> 00:08:01.680 as yet impossible to prove or disproof. In this work 114 00:08:01.720 --> 00:08:06.480 issues that any function of a variable, whether continuous or discontinuous, 115 00:08:06.879 --> 00:08:09.879 can be expanded in a series of signs of multiples 116 00:08:09.879 --> 00:08:13.319 of the variable, a result which is constantly used in 117 00:08:13.399 --> 00:08:19.279 modern analysis. Lagrange had given particular cases of the theorem 118 00:08:19.560 --> 00:08:23.360 and had implied that the method was general, but he 119 00:08:23.399 --> 00:08:28.000 had not pursued the subject. Fourier left an unfinished work 120 00:08:28.120 --> 00:08:33.159 on determinate equations, which was edited by Navier and published 121 00:08:33.200 --> 00:08:37.759 in eighteen thirty one. This contains much original matter. In particular, 122 00:08:37.840 --> 00:08:40.799 there is a demonstration of Fourier's theorem on the position 123 00:08:41.000 --> 00:08:45.679 of the roots of an algebraic equation. Lagrange had shown 124 00:08:45.840 --> 00:08:49.480 how the roots of an algebraical equation might be separated 125 00:08:49.519 --> 00:08:53.120 by means of another equation whose roots were the squares 126 00:08:53.279 --> 00:08:55.919 of the differences of the roots of the original equation. 127 00:08:57.399 --> 00:09:01.720 Budan in eighteen o seven and X eighteen eleven had 128 00:09:02.279 --> 00:09:06.159 enunciated the theorem generally known by the name of Fourier, 129 00:09:06.960 --> 00:09:11.919 but the demonstration was clumsy and not altogether satisfactory. Fourier's 130 00:09:11.960 --> 00:09:15.320 proof is the same as that usually given in textbooks 131 00:09:15.320 --> 00:09:18.679 on the theory of equations. The final solution of the 132 00:09:18.759 --> 00:09:22.080 problem was given in eighteen twenty nine by Jacques Chain, 133 00:09:22.200 --> 00:09:29.159 Francois Sturm Saudiq Calnou. Among Fourier's contemporaries who were interested 134 00:09:29.200 --> 00:09:33.159 in the theory of heat, the most eminent was Saldi Calno, 135 00:09:33.960 --> 00:09:39.360 son of the eminent geometrician mentioned previously. Saudi Calno was 136 00:09:39.360 --> 00:09:42.440 born at Paris in seventeen ninety six and died there 137 00:09:42.480 --> 00:09:46.639 of cholera in August eighteen thirty two. He was an 138 00:09:46.679 --> 00:09:50.519 officer in the French army. In eighteen twenty four he 139 00:09:50.600 --> 00:09:55.679 issued a short work entitled Reflection selepresence montris deu feu, 140 00:09:56.480 --> 00:10:00.279 in which he attempted to determine in what way heat 141 00:10:00.320 --> 00:10:04.639 produced its mechanical effect. He made the mistake of assuming 142 00:10:04.759 --> 00:10:08.399 that heat was material, but his essay was the commencement 143 00:10:08.519 --> 00:10:16.799 of the modern theory of thermodynamics. Poissant Semeon. Denis Poisson 144 00:10:17.039 --> 00:10:21.279 born at Pithiviers on June twenty first, seventeen eighty one 145 00:10:21.440 --> 00:10:24.720 and died at Paris on April twenty fifth, eighteen forty 146 00:10:25.360 --> 00:10:29.240 is almost equally distinguished for his application of mathematics to 147 00:10:29.320 --> 00:10:33.840 mechanics and to physics. His father had been a common soldier, 148 00:10:34.399 --> 00:10:38.799 and on his retirement was given some small administrative post 149 00:10:39.320 --> 00:10:42.840 in his native village. When the revolution broke out, he 150 00:10:42.879 --> 00:10:45.919 appears to have assumed the government of the place, and, 151 00:10:46.240 --> 00:10:50.320 being left undisturbed, became a person of some local importance. 152 00:10:51.879 --> 00:10:55.039 The boy was put out to nurse, and he used 153 00:10:55.080 --> 00:10:58.480 to tell how one day his father, coming to see him, 154 00:10:58.600 --> 00:11:01.720 found that the nurse had gone out on pleasure bent 155 00:11:02.159 --> 00:11:05.320 while she had left him suspended by a small cord 156 00:11:05.600 --> 00:11:09.759 to a nail fixed in the wall. This, she explained, 157 00:11:10.120 --> 00:11:13.879 was a necessary precaution to prevent him from perishing under 158 00:11:13.919 --> 00:11:19.200 the teeth of the various animals and animicula that roamed 159 00:11:19.240 --> 00:11:23.559 on the floor. Poissin used to add that his gymnastic 160 00:11:23.639 --> 00:11:26.879 efforts carried him incessantly from one side to the other, 161 00:11:27.480 --> 00:11:30.840 and it was thus in his tenderest infancy that he 162 00:11:30.960 --> 00:11:34.200 commenced those studies on the pendulum that were there to 163 00:11:34.279 --> 00:11:38.840 occupy so large a part of his mature age. He 164 00:11:38.960 --> 00:11:43.039 was educated by his father and destined, much against his will, 165 00:11:43.080 --> 00:11:46.679 to be a doctor. His uncle offered to teach him 166 00:11:46.720 --> 00:11:49.000 the art, and began by making him prick the veins 167 00:11:49.000 --> 00:11:52.480 of cabbage leaves with a lancet. When perfect in this 168 00:11:52.759 --> 00:11:55.919 he was allowed to put on blisters, but in almost 169 00:11:55.919 --> 00:11:59.360 the first case he did this by himself. The patient 170 00:11:59.399 --> 00:12:01.720 died in a few hours, and though all the medical 171 00:12:01.759 --> 00:12:04.240 practitioners of the place assured him that the event was 172 00:12:04.279 --> 00:12:07.399 a very common one, he vowed he would have nothing 173 00:12:07.440 --> 00:12:11.039 more to do with the profession. Returning home, he found 174 00:12:11.080 --> 00:12:14.559 amongst the official papers sent to his father a copy 175 00:12:14.600 --> 00:12:18.080 of the Questions set at the Polytechnic School, and at 176 00:12:18.120 --> 00:12:21.960 once found his career. At the age of seventeen, he 177 00:12:22.120 --> 00:12:25.639 entered the Polytechnic, and his abilities excited the interests of 178 00:12:25.759 --> 00:12:29.320 Lagrange and Laplace, whose friendship he retained to the end 179 00:12:29.360 --> 00:12:33.240 of their lives. A memoir on Finite Differences, which he 180 00:12:33.279 --> 00:12:37.080 wrote when only eighteen, was reported on so favorably by 181 00:12:37.200 --> 00:12:40.639 Legendre that it was ordered to be published in the 182 00:12:40.679 --> 00:12:45.120 Recuere des Sevante et cage. Directly he had finished the course, 183 00:12:45.159 --> 00:12:48.039 he was made a lecturer at the school, and he 184 00:12:48.120 --> 00:12:51.840 continued through his life to hold various government, scientific posts 185 00:12:51.919 --> 00:12:56.159 and professorships. He was somewhat of a socialist, and remained 186 00:12:56.200 --> 00:12:59.840 a rigid Republican till eighteen fifteen. With a view to 187 00:12:59.840 --> 00:13:05.600 me making another empire impossible, he joined the Legitimists. He took, however, 188 00:13:05.720 --> 00:13:08.759 no active part in politics, and made the study of 189 00:13:08.799 --> 00:13:13.840 mathematics his amusement as well as his business. His works 190 00:13:13.840 --> 00:13:16.960 and memoirs are between three and four hundred in number. 191 00:13:17.799 --> 00:13:21.120 The chief treatises which he wrote were as Treates de 192 00:13:21.240 --> 00:13:26.360 Mechanique two volumes, eighteen eleven and eighteen thirty three, which 193 00:13:26.440 --> 00:13:30.480 was long a standard work, His Theory nouver de laxion 194 00:13:30.559 --> 00:13:35.200 Capelli in eighteen thirty one, his Theory mathematic de lecheur 195 00:13:35.720 --> 00:13:38.960 in eighteen thirty five, to which a supplement was added 196 00:13:39.000 --> 00:13:43.720 in eighteen thirty seven, and is recherche les probability de 197 00:13:43.919 --> 00:13:48.559 jugement in eighteen thirty seven. He had intended, if he 198 00:13:48.600 --> 00:13:51.360 had lived, to write a work which should cover all 199 00:13:51.399 --> 00:13:55.120 mathematical physics, and in which these would have been incorporated 200 00:13:56.759 --> 00:13:59.799 of his memoirs on the subject of pure mathematics, the 201 00:14:00.120 --> 00:14:05.360 most important are those on definite integrals and the Fourier's series. 202 00:14:06.320 --> 00:14:09.679 These are to be found on the Jenel Polytechnique from 203 00:14:09.679 --> 00:14:13.120 eighteen thirteen to eighteen twenty three and in the Memoir 204 00:14:13.240 --> 00:14:18.240 de Lacademie for eighteen twenty three. Their application to physical 205 00:14:18.279 --> 00:14:22.120 problems constituting one of his chief claims to distinction his 206 00:14:22.320 --> 00:14:27.399 essay on the Calculus of variations Mamou de Lacademie eighteen 207 00:14:27.440 --> 00:14:31.240 thirty three and his papers on the Probability of the 208 00:14:31.279 --> 00:14:36.519 mean results of observations Connaissance de Tempe eighteen twenty seven 209 00:14:36.960 --> 00:14:40.360 and following years. Most of his memoirs were published in 210 00:14:40.440 --> 00:14:45.360 the three periodicals here mentioned. Perhaps the most remarkable of 211 00:14:45.399 --> 00:14:48.720 his memoirs and applied mathematics are those on the theory 212 00:14:48.759 --> 00:14:53.080 of electrostatics and magnetism, which originated a new branch of 213 00:14:53.120 --> 00:14:56.879 mathematical physics. He supposed that the results were due to 214 00:14:56.919 --> 00:15:01.720 the attractions and repulsions of imponderable part of the most 215 00:15:01.720 --> 00:15:06.399 important of those on physical astronomy are the two re 216 00:15:06.399 --> 00:15:09.159 read in eighteen oh six printed in eighteen oh nine 217 00:15:09.559 --> 00:15:14.120 on the secular inequalities of the mean motions of the planets, 218 00:15:14.159 --> 00:15:18.080 and on the variations of arbitrary constants introduced into the 219 00:15:18.120 --> 00:15:24.480 solutions of questions on mechanics. In those Poissan discusses the 220 00:15:24.559 --> 00:15:28.799 question of the stability of the planetary orbits, which Legendre 221 00:15:28.960 --> 00:15:32.840 had already proved to the first degree of approximation for 222 00:15:32.919 --> 00:15:37.159 the distributing forces. Enchows that the result can be extended 223 00:15:37.240 --> 00:15:40.799 to the third order of small quantities. These were the 224 00:15:40.840 --> 00:15:44.600 memoirs which led to Lagrange's famous memoir of eighteen oh eight. 225 00:15:45.399 --> 00:15:49.120 Poissan also published a paper in eighteen twenty one on 226 00:15:49.200 --> 00:15:52.399 the libration of the Moon, and another in eighteen twenty 227 00:15:52.440 --> 00:15:55.360 seven on the motion of the Earth about its center 228 00:15:55.399 --> 00:15:59.080 of gravity. His most important memoirs and the theory of 229 00:15:59.120 --> 00:16:02.039 attraction are one in eighteen twenty nine on the attraction 230 00:16:02.120 --> 00:16:05.440 of spheroids, and another in eighteen thirty five on the 231 00:16:05.480 --> 00:16:10.679 attraction of a homogeneous ellipsoid. The substitution of the correct 232 00:16:10.720 --> 00:16:16.159 equation involving the potential, namely grad squared v equals negative 233 00:16:16.200 --> 00:16:20.559 four pi row for Laplace's form of it, Pi squared 234 00:16:20.639 --> 00:16:24.039 v equals zero was first published in eighteen thirteen in 235 00:16:24.120 --> 00:16:29.720 De Bouditaine des science of the society Phiromatique. Lastly, I 236 00:16:29.759 --> 00:16:32.799 may mention his memoir in eighteen twenty five on the 237 00:16:32.799 --> 00:16:39.240 theory of waves. Empeire Andre Marie Ampere was born at 238 00:16:39.320 --> 00:16:44.159 Leon in January twenty second, seventeen seventy five, and died 239 00:16:44.200 --> 00:16:48.679 at Marseilles on June tenth, eighteen thirty six. He was 240 00:16:48.720 --> 00:16:51.559 widely read in all branches of learning, and lectured and 241 00:16:51.600 --> 00:16:54.960 wrote on many of them. But after the year eighteen 242 00:16:54.960 --> 00:16:58.039 o nine, when he was made professor of analysis at 243 00:16:58.080 --> 00:17:02.519 the Polytechnic School in Paris, he confined himself almost entirely 244 00:17:02.600 --> 00:17:07.480 to mathematics and science. His papers on the connection between 245 00:17:07.480 --> 00:17:12.480 electricity and magnetism were written in eighteen twenty. According to 246 00:17:12.519 --> 00:17:17.000 his theory propounded in eighteen twenty six, a molecule of 247 00:17:17.079 --> 00:17:20.799 matter which can be magnetized is traversed by a cloud 248 00:17:20.839 --> 00:17:25.319 of electric current, and a magnetization is produced by any 249 00:17:25.400 --> 00:17:29.079 cause which makes the direction of these currents in the 250 00:17:29.079 --> 00:17:35.319 different molecules of the body approach parallelism. Fresnel Augustin Jean 251 00:17:35.440 --> 00:17:39.680 Fresnel born at Broglie on May tenth, seventeen eighty eight 252 00:17:39.799 --> 00:17:44.279 and died at Verderey on July fourteenth, eighteen twenty seven. 253 00:17:44.519 --> 00:17:47.759 Was a civil engineer by profession, but he devoted his 254 00:17:47.920 --> 00:17:52.319 leisure to the study of physical optics. The undulatory theory 255 00:17:52.359 --> 00:17:55.440 of light, which huck Reugens and Euler had supported on 256 00:17:55.559 --> 00:17:59.240 a priori grounds, had been based on experiment by the 257 00:17:59.319 --> 00:18:05.920 researches of Fresnel deduced the mathematical consequences of these experiments 258 00:18:05.960 --> 00:18:10.160 and explained the phenomenon of the interference of both ordinary 259 00:18:10.200 --> 00:18:16.759 and polarized light. Billout Fresnel's friend and contemporary, Jean Baptiste Biot, 260 00:18:17.200 --> 00:18:20.440 who was born at Paris on April twenty first, seventeen 261 00:18:20.519 --> 00:18:24.359 seventy four and died there in eighteen sixty two, requires 262 00:18:24.359 --> 00:18:27.880 a word or two in passing. Most of his mathematical 263 00:18:27.920 --> 00:18:31.319 work was in connection with the subject of optics, and 264 00:18:31.440 --> 00:18:35.759 especially with the polarization of light. His systematic works were 265 00:18:35.839 --> 00:18:39.279 produced within the years eighteen o five. In eighteen seventeen, 266 00:18:40.079 --> 00:18:43.519 a selection of his more valuable memoirs was published in 267 00:18:43.640 --> 00:18:50.160 Paris in eighteen fifty eight. Arago Francois Jean Dominique Arago 268 00:18:50.519 --> 00:18:55.039 was born at Estangel in the Pyrenees on February twenty 269 00:18:55.079 --> 00:18:59.480 sixth seventeen eighty six and died in Paris on October second, 270 00:18:59.519 --> 00:19:04.319 eighteen fifty three. He was educated at the Polytechnic School, Paris, 271 00:19:04.839 --> 00:19:08.400 and we gather from his autobiography that, however distinguished were 272 00:19:08.400 --> 00:19:12.839 the professors of that institution, they were remarkably incapable of 273 00:19:12.880 --> 00:19:18.000 imparting their knowledge or maintaining discipline. In eighteen o four 274 00:19:18.039 --> 00:19:21.839 he was made secretary to the Observatory, and then from 275 00:19:21.880 --> 00:19:24.279 eighteen o six to eighteen o nine he was engaged 276 00:19:24.279 --> 00:19:27.680 in measuring a meridian arc in order to determine the 277 00:19:27.720 --> 00:19:30.480 exact length of a meter. He was then made one 278 00:19:30.519 --> 00:19:33.759 of the astronomers at Paris, given a residence there, and 279 00:19:33.839 --> 00:19:36.880 made a professor at the Polytechnic School, where he enjoyed 280 00:19:36.880 --> 00:19:41.400 a marked success as a lecturer. He subsequently gave popular 281 00:19:41.480 --> 00:19:45.519 lectures on astronomy, which were both lucid and accurate, a 282 00:19:45.519 --> 00:19:50.640 combination of qualities which was rarer than now. He reorganized 283 00:19:50.680 --> 00:19:54.759 the National Observatory, the management of which had long been inefficient. 284 00:19:55.200 --> 00:19:58.680 But in doing this he shewed himself dictatorial and passionate, 285 00:19:59.160 --> 00:20:01.960 and the same defaul efects of character revealed themselves in 286 00:20:02.039 --> 00:20:05.519 many of the events of his life. He remained to 287 00:20:05.559 --> 00:20:09.440 the end a consistent Republican, and after the Coup d'ettas 288 00:20:09.920 --> 00:20:13.839 of eighteen fifty two, though half blind and dying, he 289 00:20:13.960 --> 00:20:17.359 resigned his post as an astronomer rather than take the 290 00:20:17.400 --> 00:20:21.119 oath of allegiance. It is to the credit of Napoleon 291 00:20:21.119 --> 00:20:24.759 the Third that he gave directions that the old man 292 00:20:24.799 --> 00:20:27.559 should be in no way disturbed, and that he should 293 00:20:27.559 --> 00:20:29.400 be left free to say and do what he liked. 294 00:20:30.480 --> 00:20:34.799 His earliest physical researches were on the pressure of steam 295 00:20:35.079 --> 00:20:39.400 at different temperatures and the velocity of sound eighteen eighteen 296 00:20:39.680 --> 00:20:44.440 to eighteen twenty two. His magnetic observations mostly took place 297 00:20:44.799 --> 00:20:49.200 from eighteen twenty three to eighteen twenty six. He discovered 298 00:20:49.319 --> 00:20:53.559 what had been called rotary magnetism and the fact that 299 00:20:53.640 --> 00:20:58.039 most bodies could be magnetized. These discoveries were completed and 300 00:20:58.160 --> 00:21:03.519 explained by Faraday. He warmly supported Fresnel's optical theories, and 301 00:21:03.640 --> 00:21:08.319 the two philosophers conducted together those experiments on the polarization 302 00:21:08.400 --> 00:21:11.920 of light, which led to the interference that the vibrations 303 00:21:11.960 --> 00:21:15.960 of the luminiferous ether were transverse to the direction of motion, 304 00:21:16.799 --> 00:21:21.240 and that the polarization consisted in a resolution of rectilinear 305 00:21:21.319 --> 00:21:25.920 motion into components at right angles to each other. The 306 00:21:25.960 --> 00:21:30.799 subsequent invention of the polariscope and the discovery of rotatory 307 00:21:30.839 --> 00:21:35.920 polarization are due to Arago. The general idea of the 308 00:21:35.960 --> 00:21:39.400 experimental determination of the velocity of light in the manner 309 00:21:39.519 --> 00:21:44.119 subsequently affected by Faisot and Foucot, was suggested by him 310 00:21:44.480 --> 00:21:48.519 in eighteen thirty eight, but his failing eyesight prevented his 311 00:21:48.720 --> 00:21:53.119 arranging the details or making the experiments. It will be 312 00:21:53.240 --> 00:21:56.640 noticed that some of the last members of the French 313 00:21:56.680 --> 00:22:01.559 school were alive at a comparatively recent date, but nearly 314 00:22:01.640 --> 00:22:05.079 all mathematical work was done before the year eighteen thirty. 315 00:22:06.240 --> 00:22:09.160 They are the direct successors of the French writers who 316 00:22:09.240 --> 00:22:13.319 flourished at the commencement of this century, and seem to 317 00:22:13.400 --> 00:22:16.240 have been out of touch with the great German mathematicians 318 00:22:16.279 --> 00:22:19.599 of the early part of it, on whose researches much 319 00:22:19.640 --> 00:22:22.759 of the best work of this century is based. They 320 00:22:22.799 --> 00:22:25.240 are thus placed here, though their writings are in some 321 00:22:25.440 --> 00:22:28.160 cases of a later date than those of gauss Abel, 322 00:22:28.400 --> 00:22:34.799 Jacobi and other mathematicians of recent times. The introduction of 323 00:22:34.880 --> 00:22:40.519 analysis into England, the complete isolation of the English school 324 00:22:40.559 --> 00:22:44.079 and its devotion to geometrical methods are the most marked 325 00:22:44.119 --> 00:22:46.599 features in its history during the latter half of the 326 00:22:46.640 --> 00:22:51.000 eighteenth century, and the absence of any considerable and valuable 327 00:22:51.039 --> 00:22:56.160 contributions to the advancement of mathematical science was a natural consequence. 328 00:22:57.160 --> 00:23:00.240 One result of this was that the energy of the 329 00:23:00.279 --> 00:23:04.400 englishmen of science was largely devoted to practical physics and 330 00:23:04.519 --> 00:23:08.920 practical astronomy, which were in consequence studied in Britain, perhaps 331 00:23:08.920 --> 00:23:13.920 more than elsewhere. Almost the only English mathematician at the 332 00:23:13.960 --> 00:23:17.359 beginning of this century who used analytical methods and whose 333 00:23:17.400 --> 00:23:21.559 work requires mentioned here is Ivory, to whom the celebrated 334 00:23:21.599 --> 00:23:25.920 theorem of attractions is due. James Ivory was born in 335 00:23:26.039 --> 00:23:29.720 Dundee in seventeen sixty five and died at Douglastown on 336 00:23:29.799 --> 00:23:35.119 September twenty first, eighteen forty five. After graduating at Saint Andrews, 337 00:23:35.440 --> 00:23:38.559 he became the managing partner in a flax spinning company 338 00:23:38.640 --> 00:23:42.319 in Forfardshire, but continued to devote most of his leisure 339 00:23:42.400 --> 00:23:46.319 to mathematics. In eighteen o four he was made professor 340 00:23:46.359 --> 00:23:49.640 at the Royal Military College at Marlow, which has now 341 00:23:49.680 --> 00:23:55.680 moved to Sandhurst. He contributed numerous papers to the Philosophical Transactions, 342 00:23:55.759 --> 00:23:59.480 the most remarkable being those on attractions. In one of these, 343 00:23:59.519 --> 00:24:03.079 in eighteen he shewed how the attraction of a homogeneous 344 00:24:03.079 --> 00:24:06.720 ellipsoid on an external point is a multiple of that 345 00:24:06.839 --> 00:24:10.559 of another ellipsoid on an internal point, the latter can 346 00:24:10.640 --> 00:24:15.319 be easily obtained. He criticized Laplace's solution of the method 347 00:24:15.359 --> 00:24:19.519 of Lee squares with unnecessary bitterness and in terms which 348 00:24:19.559 --> 00:24:24.319 proved his incompetence to understand it. The Cambridge Analytical school. 349 00:24:25.119 --> 00:24:27.599 Toward the close of the last century, the more thoughtful 350 00:24:27.599 --> 00:24:31.039 members of the Cambridge School of Mathematics began to recognize 351 00:24:31.079 --> 00:24:35.319 that their isolation from the continental contemporaries was a serious evil. 352 00:24:36.279 --> 00:24:40.200 The earliest attempt in England to explain the notation and 353 00:24:40.279 --> 00:24:43.519 methods of the calculus as used on the continent was 354 00:24:43.640 --> 00:24:46.960 due to Woodhouse, who stands out as the apostle of 355 00:24:47.039 --> 00:24:50.240 the new movement. It is doubtful if he could have 356 00:24:50.279 --> 00:24:53.799 brought the analytical methods into vogue by himself, but his 357 00:24:53.960 --> 00:24:59.279 views were enthusiastically adopted by three undergraduates, Babbage, Peacock and Herschel, 358 00:24:59.799 --> 00:25:02.839 who he succeeded in carrying out reforms that he had 359 00:25:02.880 --> 00:25:06.720 suggested in a book which will fall into the hands 360 00:25:06.720 --> 00:25:09.720 of few but English readers. I may be pardoned for 361 00:25:09.799 --> 00:25:13.119 making space for a few remarks on these four mathematicians. 362 00:25:13.839 --> 00:25:17.160 The original stimulus came from French sources, and I therefore 363 00:25:17.200 --> 00:25:20.079 placed these remarks at the close of my account of 364 00:25:20.160 --> 00:25:23.519 the French school. But I should add that the English 365 00:25:23.559 --> 00:25:27.119 mathematicians of this century at once struck out a line 366 00:25:27.319 --> 00:25:33.559 independent of their French contemporaries. Woodhouse Robert Woodhouse was born 367 00:25:33.640 --> 00:25:37.680 at Norwich on April twenty eighth, seventeen seventy three. Was 368 00:25:37.839 --> 00:25:41.640 educated at Caius College, Cambridge, of which society he was 369 00:25:41.680 --> 00:25:46.799 subsequently a fellow, was Plumian Professor in the university, and 370 00:25:46.960 --> 00:25:50.799 continued to live at Cambridge till his death on December 371 00:25:50.839 --> 00:25:55.519 twenty third, eighteen twenty seven. His earliest work, entitled The 372 00:25:55.559 --> 00:25:59.880 Principles of Analytical Calculation, was published at Cambridge in An 373 00:26:00.000 --> 00:26:04.319 eighteen o three. In this he explained the differential notation 374 00:26:05.039 --> 00:26:09.079 and strongly pressed the employment of it, but he severely 375 00:26:09.119 --> 00:26:13.960 criticized the methods used by Continental writers and their constant 376 00:26:14.000 --> 00:26:18.759 assumption of non evident principles. This was followed in eighteen 377 00:26:18.799 --> 00:26:23.000 o nine by a trigonometry Plain and Spherical, and in 378 00:26:23.039 --> 00:26:27.440 eighteen ten by historical treatise on the Calculus of variations 379 00:26:27.920 --> 00:26:33.880 and isoparametrical problems. He next produced an Astronomy, the first 380 00:26:33.960 --> 00:26:37.880 volume usually bound in two on practical and Descriptive Astronomy, 381 00:26:38.359 --> 00:26:41.920 being issued in eighteen twelve, the second volume, containing an 382 00:26:41.960 --> 00:26:45.759 account of the treatment of physical astronomy by Laplace and 383 00:26:45.920 --> 00:26:50.880 other Continental writers, being issued in eighteen eighteen. All these 384 00:26:50.920 --> 00:26:55.519 works deal critically with the scientific foundation of the subjects considered, 385 00:26:55.839 --> 00:27:00.319 a point which is not unfrequently neglected in modern textbook boks. 386 00:27:02.839 --> 00:27:07.640 A man like Woodhouse, of scrupulous honor, universally respected, a 387 00:27:07.680 --> 00:27:11.480 trained logician, and with a caustic wit, was well fitted 388 00:27:11.759 --> 00:27:14.599 to introduce a new system. And the fact that when 389 00:27:14.640 --> 00:27:18.680 he first called attention to the Continental analysis, he exposed 390 00:27:18.720 --> 00:27:22.319 the unsoundness of some of the usual methods of establishing it. 391 00:27:22.480 --> 00:27:26.680 More like an opponent than a partisan, and was politic 392 00:27:26.839 --> 00:27:30.799 as it was honest. Woodhouse did not exercise much influence 393 00:27:30.799 --> 00:27:34.759 on the majority of his contemporaries, and the movement might 394 00:27:34.759 --> 00:27:37.319 have died away for the time being had it not 395 00:27:37.400 --> 00:27:42.359 been for the advocacy of Peacock, Herschel and Babbage, who 396 00:27:42.400 --> 00:27:46.759 formed an analytical Society with the object of advocating the 397 00:27:46.880 --> 00:27:50.759 general use in the University of analytical methods and of 398 00:27:50.799 --> 00:27:57.240 the differential notation. Peacock George Peacock, who was the most 399 00:27:57.240 --> 00:27:59.839 influential of the early members of the New School, was 400 00:28:00.000 --> 00:28:04.960 born at Denton on April ninth, seventeen ninety one. He 401 00:28:05.079 --> 00:28:09.440