April 12, 1900J 



NATURE 



569 



He was thus led to examine the properties of the surface 

 of constant negative curvature, to which he gave the 

 name oi fsetidospherc, and the geometry of such a surface 

 was found to be identical with the geometry of Gauss 

 and Lobatschewsky. As his old pupil and successor at 

 Pavia, Prof. Carlo Somigliana, remarks, " It can thus be 

 said that although the germs of his results can be traced 

 back to some of his predecessors, and, in particular, can 

 be found in the profound considerations of Riemann, and 

 other advances have come subsequently, yet his work 

 represents and synthesises the most decisive step that has 

 been made in modern times by the geometric conception 

 of real space." 



Nor was the " Saggio d'interpretazione " by any means 

 Beltrami's only contribution to mathematical literature 

 at the period under consideration. We find him extend- 

 ing the properties of surfaces of constant curvature to 

 n dimensional space ; and his papers on differential 

 parameters, on the flexure of ruled surfaces, and on the 

 g^eneral theory of surfaces, published a few years pre- 

 viously to the " Saggio," are well known to mathe- 

 maticians. 



In 1873, Beltrami migrated to Rome as professor of 

 rational dynamics and higher analysis, and was elected 

 a Fellow of the Italian equivalent of our Royal Society, 

 the Reale Accademia dei Lincei. His sojourn in Rome 

 was of brief duration ; for, much to the regret of his 

 friends there, he went to Pavia in 1876, where he lectured 

 on mathematical physics and higher mechanics, and it 

 was not until i8gi that an opportunity offered itself for 

 him to return to Rome. It was only two years ago that 

 Beltrami was prevailed on to accept the office of Presi- 

 dent of the " Lincei," and last year he was unanimously 

 elected to the senatorial rank. As a general rule, how- 

 ever, he avoided all public appointments, and the only 

 other post he held was on the Italian Council of Educa- 

 tion. He preferred to devote his entire energies to the 

 studies in which he was interested, and sought no 

 scientific distinctions ; still, the laurels which he had 

 well earned were freely showered on him by the acade- 

 mies of Bologna, Lombardy, Turin, Naples, Paris, 

 Gottingen, Brussels, Munich and Berlin ; and the London 

 Mathematical Society was also proud to place his name 

 on its list of foreign mathematicians. 



We have hitherto spoken chiefly of Beltrami's work as 

 a pure mathematician, but his later investigations tended 

 more especially in the direction of applied mathematics. 

 Hydrodynamics, theory of potential, elasticity, physical 

 optics, electricity and magnetism, conduction of heat and 

 thermodynamics were all made the subject of papers, 

 each of which "shed a bright light on some difficult or 

 controversial point." In the theory of the potential con- 

 siderable simplifications of method were made, and the 

 papers on potentials of symmetric distributions and on 

 the attractions of ellipsoids are described by Somigliana 

 as "true models of classical elegance." In the theory of 

 elasticity. Lame's equations were shown to be intimately 

 related to the euclideity of space, and the generalisations 

 for spaces of constant curvature opened up a new field 

 for research, of which Beltrami endeavoured to make use 

 in accounting for the uncertainties in Maxwell's theory, 

 which substitutes action in a continuous medium for 

 action at a distance. 



The last period of his researches was devoted to 

 developing Maxwell's theories of electro-magnetic 

 phenomena, a difficult task, for which Beltrami's mathe- 

 matical knowledge well fitted him. All who have read Max- 

 well's treatise realise that it contains many obscure points 

 and demonstrations of hardly a rigorous nature, and most 

 of those who have failed to follow his arguments have 

 preferred to regard the results as statements of Maxwell's 

 ^yiews, rather than inquire into the validity of the reason- 

 ing on which they were based. Beltrami, on the other 

 hand, being well versed in the art of e.xact expression 



NO. 1589, VOL. 61] 



and the elegances of neatness of analytical form, was not 

 contented with Maxwell's rough-and-ready methods, but 

 devoted long hours of deep thought to co-ordinating and 

 perfecting the ideas which he regarded as incomplete. 

 Among his latest contributions to the Atti dei Lincei we 

 notice a paper on thermodynamic potentials published in 

 1895. 



As a professor, Beltrami's lectures are said to have 

 been characterised by the same perfection of style and 

 exactness of form which are so conspicuous in his 

 writings. His genial manner and high culture made him 

 a centre no less in general society than in the scientific 

 world. Shakespeare's epithet, "Cunning in music and in 

 mathematics " well applies to Beltrami, and we learn from 

 Signor Pietro Cassani's obituary address to the Venetian 

 Academy, that having been taught music in his early 

 days by his mother, and afterwards under Ponchielli, he 

 would often delight his friends by his renderings on the 

 piano of the masterpieces of Bach, Mendelssohn and 

 Schumann. 



The life that has been brought to such a sad close 

 must have been in many respects an ideal life. Beltrami 

 had every opportunity for devoting himself to the studies 

 which he chose as his life's work ; he knew nothing of 

 rivalries and petty jealousies, as he made no enemies ; 

 but, on the other hand, we cannot but suppose that his 

 experience of the necessities of making the best of some- 

 what uncongenial surroundings during his years of rail- 

 way work had a beneficial influence on his after life, in 

 preventing Beltrami from attempting to live up to a false 

 ideal. His loss adds another to the many gaps in the 

 mathematical world, but his published works form a 

 fitting memorial of their author, and several of them bid 

 fair to be handed down to posterity among the mathe- 

 matical classics. 



We are indebted to Prof. Blaserna, of Rome, for much 

 valuable information on which this account is based. 



G. H. Bryan. 



PROF. ST. GEORGE MIVART. 



BY the sudden death, at the age of seventy-two, of 

 Prof. St. George Mivart, the world in general 

 and science in particular are distinctly the poorer. For 

 he was essentially a many-sided man ; and although an 

 energetic and accurate investigator in several branches 

 of biology, was in no sense a specialist whose efforts 

 were restricted to the elucidation of abstruse facts or the 

 elaboration of theories in which the general public could 

 take little or no interest. On the contrary, ever since 

 1870, when he first began to contribute to the higher 

 grade of popular reviews, he has kept himself constantly 

 in evidence, and has thus become known to a very wide 

 circle of readers, especially as the apostle of the evolu- 

 tion of organic nature under divine guidance. 



St. George Mivart was born at his father's house in 

 Brook Street, Grosvenor Square, on November 20, 1827. 

 He was educated successively at Clapham Grammar 

 School, Harrow, King's College, London, and St. Mary's 

 College, Oscott ; his adoption, in 1844, of the principles 

 of the Romish faith being at that time a bar to his matri- 

 culating at Oxford, where it was his father's intention 

 that his education should have been completed. In 1851 

 he was called to the Bar at Lincoln's Inn, but his legal 

 career, if he ever practised at all, was a brief one ; and 

 in a short time his attention was concentrated first 

 on medical and later on biological studies. By 1862 

 Mivart had made such a reputation in medico-biological 

 studies that he was appointed a lecturer at the Medical 

 School of St.' Mary's Hospital. Previously to this, in 

 1885, he became a Fellow of the Zoological Society, of 

 which body he was elected a Vice-President in 1869, and 

 again in 1896 ; indeed, he continued in the latter office 



