August 27, 1903] 



NATURE 



393 



handling of the diverse topics which he passes under 

 review." And though Lord Salisbury himself said 

 in that address, " In presence of the high priests of 

 science I am only a layman, and all the skill of all 

 the chemists the Association contains will not trans- 

 mute a layman into any more precious kind of metal," 

 yet on that occasion he proceeded to give in a masterly 

 fashion " a survey not of our science but of our 

 ignorance." The references to the want of know- 

 ledge of the nature of the capricious differences which 

 separate the atoms from each other; the description 

 of the ether as "a half-discovered entity"; the ex- 

 planation of the deep obscurity which at the time of 

 the address still enveloped the origin of the infinite 

 variety of life, and the impossibility of demonstrating 

 the process of natural selection in detail, combined to 

 make the Oxford British Association address com- 

 parable in importance with the great controversy at 

 the same city when the Association met there thirty- 

 four years previously. 



The study of science was for many years the solace 

 which Lord Salisbury sought from the cares of State, 

 and it is ,far from fanciful to suppose that these 

 investiga,trt9ns influenced his political outlook and con- 

 tributed to his success in meeting the difficulties of 

 government. But whether this is so or not, there 

 can be no doubt that Lord Salisbury's acquaintance 

 with physical and chemical science was of an intimate 

 nature, and added greatly to the joy and comfort of 

 the short years of his retirement. 



Lord Salisbury held many other appointments and 

 received numerous academic distinctions. Among 

 these may be mentioned that from 1869 to the time 

 of his death he was Chancellor of the University of 

 Oxford, and his interest in higher education was also 

 shown by the fact of his being a member of the 

 Council of King's College, London. He was a 

 Doctor of Civil Law of Oxford, and a Doctor of 

 Laws of Cambridge University, as well as a Fellow 

 of the Royal Society. 



., This brief notice of a great career may be fittingly 

 closed with a paragraph from Dr. Traill's mono- 

 graph. " Lord Salisbury's record is that of an 

 English statesman who, while directing the affairs 

 of his country abroad with singular skill and judg- 

 ment, has also guided its domestic policy in the paths 

 of wisdom and equity, and, though loyally submitting 

 to the ' will of the majority ' in all things lawful, 

 has held it his first duty to maintain the just rights 

 of every class, however small a minority it may con- 

 stitute, in the State." 



PROF. LUIGI CREMONA. 



AN interesting account of the life and work of the 

 late Prof. Cremona, by Prof. Blaserna, appears 

 in the Proceedings of the Royal Society of Edinburgh 

 (vol. xxiv.), an advance copy of which has been re- 

 ceived. By permission of the general secretary of the 

 Society, we print a free translation of Prof. Blaserna 's 

 contributioq,and extracts from a note appended to it. 



Prof. Luigi Cremona was born at Pavia on 

 December 7, 1830, and studied there until the year 

 1848, when he suspended his academic work to join 

 the ranks of the Italian volunteers, and to take part in 

 the heroic defence of Venice until the capitulation of 

 that famous town. He then graduated in mathe- 

 matics at Pavia, where he had among his teachers 

 Francesco Brioschi, and among his fellow-students 

 Eugenio Beltrami and Felice Casarati. Thereafter he 

 taught in the Gymnasium at Cremona and in the 

 Beccarian Lyceum at Milan. 



NO. 1765, VOL. 68] 



In i860 he was appointed to the new chair of higher 

 geometry in the University of Bologna, then re- • 

 organised by the Italian Government, and thence he 

 passed, in 1866, to the Polytechnic at Milan. When, 

 after the year 1870, the Italian Government undertook 

 the organisation of the great University of Rome, with 

 its annexed engineering school, Cremona was called, 

 in 1873, to be professor of higher geometry in the 

 university and director of the engineering school, 

 which he reconstructed and established in the old Con- 

 vent of St. Pietro in Vincoli. The duties of this 

 double post he discharged with fidelity and distinction 

 to the last years of his life. _ . 



Although Cremona had been a pupil of Brioschi, an 

 eminent analyst, his predilection was always for geo- 

 metry, in which he may be said to have created a 

 classical school. His numerous publications refer 

 chiefiy to the theory of algebraic curves and surfaces. 

 All the problems that arose in this department of 

 mathematics between i860 and 1880 attracted his 

 attention, and everywhere he left an indelible trace of 

 the depth and the clearness which characterised his 

 genius. 



To general theory are dedicated the " Introduction 

 to a Geometrical Theory of Plane Curves " (1862) and 

 " Preliminaries to a Theory of Surfaces " (1866), two 

 monographs in which he expounds, with originality 

 of view and wonderful unity of method, results partly 

 known and partly new. He demonstrated the fruit- 

 fulness of the theorems contained in the second of these 

 memoirs by applying them to the study of surfaces of 

 the third order, in the " M^moire de G^ometrie pure 

 sur les Surfaces du troisieme Ordre," which gained in 

 1886 the Steiner prize of the Academy of Berlin, and 

 which will remain for all time a classic model of 

 geometric research. 



But the originality of Cremona appears still more 

 distinctly in his study of the transformations to which 

 his name is now attached. Already in the first half 

 of the nineteenth century a theory had arisen of the 

 projective transformations which change the points 

 and straight lines of one plane into the points and 

 straight lines of another plane, and side by side with 

 these had also been examined the correspondences 

 which transform straight lines into circles or conies. 

 But the idea of treating from a more general point of 

 view the transformations which change straight lines 

 into algebraic curves of any order n whatever belongs 

 to Cremona, who established the basis of this theory 

 in two memoirs (1863-65), and afterwards extended it 

 to space of three dimensions (1871-72), thus opening 

 to geometers a vast field of research, which has not 

 been exhausted at the present day. 



While, by these works, of which I have mentioned 

 only the most extensive, and by his splendid lectures, 

 Cremona was firing the rising generation with the 

 love of pure science, and thus exercising a great in- 

 fluence on original geometric research in Italy during 

 the last thirty years, on the other hand he was never 

 weary of showing his interest in the technical appli- 

 cations of mathematics. His little work on " Reci- 

 procal Figures in Graphical Statics " is a beautiful 

 example of this interpenetration of pure and applied 

 science, an interpenetration which characterises 

 another side of his broad genius. Always pursuing 

 this order of ideas, he took assiduous care with his 

 engineering students in Rome to keep science and 

 practice side by side, inciting them to attain that just 

 balance of different faculties of which he gave himself 

 so fine an example. 



Besides all this, Luigi Cremona was a statesman. 

 Nominated a Senator of the kingdom in 1879, he took 

 an active part in all the work of the Senate. He was, 

 indeed, one of the most respected and influential of the 



