March 9, 1899] 



NA rURE 



445 



portant contribution. In the first place he not only 

 confirms, by clear and independent evidence, the decision 

 accepted by the officers of the Great Trigonometrical 

 Survey of India, that the names such as Gaurisankar, 

 Deodhunga, &c., applied by B. H. Hodgson and H. 

 .Schlagintweit to the highest peak of the Himalayas, do 

 not belong to it at all, although the first of them has 

 been extensively used on German maps, but he also 

 shows that there is a Tibetan name Jomo-kang-kar, 

 meaning "The Lady White Glacier," which apparently 

 does apply to the culminating peak of the Everest group. 

 Secondly he points out that, according to the Tibetans, 

 there is another mountain, due north of Mount Everest, 

 that exceeds even that peak in height, and must therefore 

 be the highest mountain in the world, unless some other 

 Tibetan peak, as yet unmeasured, exceeds it. Ap- 

 parently no European has yet set eyes upon this 

 mysterious summit of the upper Lap-chi-kang ; its dis- 

 covery and measurement afford a grand opportunity for 

 a future geographer and explorer. Before quitting this 

 subject, a hope may be expressed that no one will be found 

 so utterly lost to all sense of humour as to adopt the 

 barbarous hybrid term of Koti^^-kar-Everest for the 

 monarch of the Himalayas : it is astounding to find 

 Major Waddell writing calmly of the matter, and ap- 

 parently without any appreciation of the fact that the 

 name is absurd. This is the more surprising, for Major 

 Waddell is justly severe on the ignorance which insists 

 on adding superfluous aspirates and other letters to 

 native names, and he reproves the people who write 

 "Thibetian" for Tibetan and " Gnathong '' for Na-tang. 

 Major Waddell has paid great attention to Sikhimese 

 birds, but he appears to have a rather imperfect ac- 

 quaintance with the mammals. He writes of the " marsh- 

 deer or sambhar " (p. 260) apparently under the idea that 

 both are names applied to the same animal, he calls the 

 Gpotnchcr or Gumcheii of Tibetans a tailless rat or 

 marmot, whereas it is a Lagonys or pika, and he even 

 writes of the Serow, a goat-antelope, as the Serow deer. 

 He must have been misled by some of his followers into 

 supposing (p. 113) that tracks he saw on Tendong, a feu- 

 miles north of Darjeeling, in oak and magnolia forests, 

 about 8500 feet above the sea, were those of Bharal, Ovis 

 Jialiura, an animal that does not inhabit this part of 

 Sikhim. and that never enters forests at all. It may be 

 added that, especially with regard to Latin names, the 

 book appears not to have been read quite as carefully as is 

 necessary, for 07'is mt/u/ra becomes Oi'i's /it'/n//- on p. 113, 

 and Otis natura on pp. 216 and 225 ; whilst A^ecirogale 

 for Neciogale (p. 219), caerulus for caeruleus (pp. 77, 240', 

 Grandula for Grandala (p. 216), and Calliophis for 

 Callophis (p. 77), are other instances of misprints. To 

 some extent names of places suffer from the same want 

 of revision ; thus the Sibu Pass of the map and Seeboo 

 Pass of p. 215, is apparently the Sherboo Pass at p. 161. 

 Another curious case of oversight is the statement, on p. 

 330, that the peaks of the Everest group are shut out 

 from view at Senchal by a dark ridge, although a figure of 

 the peaks in question, as seen from Senchal, is given on 

 p. l^ ; the fact being that it is the lower portions of the 

 Everest group, not the peaks, that are shut out. 



These, however, are minor drawbacks, and do not 

 prevent the work from being a valuable addition to 

 Himalayan literature. W. T. B. 



PROFESSOR SOPH US LIE. 

 T T is with much regret that we have to announce the 

 ••■ death of this distinguished Norwegian mathematician, 

 which took place on February iS of the present year. 



Born at Christiania on December 12, 1842, he gradu- 

 ated as Doctor in the University of that city in 1868. 

 Four years later he was appointed professor extraordin- 



NO. 1532, VOL. 59] 



arius of mathematics; and in 1886 he succeeded Klein 

 as professor at Leipzig, when the latter was nominated to 

 Gottingen. During the last few years a strong desire 

 has been felt by his fellow-countrymen that he should 

 occupy a professorship in his native country, and that a 

 post should be specially created for him in Christiania. 

 It was only quite recently that this desire had been 

 gratified ; unhappily too late to be effective. His 

 strength had been undermined by the intense ardour 

 with which he pursued his investigations ; and his 

 health, thus broken, has forbidden any long tenure of a 

 chair in which, as had been hoped, he would be able to. 

 continue his mathematical researches. 



When once the merit of his work began to be recog- 

 nised, scientific honours were bestowed upon him freely. 

 He had received the honorary or foreign membership of 

 societies and academies in great numbers ; in particular, 

 in England alone, he was enrolled among the foreign 

 members of the Royal Society, and among the honorary 

 members of the Cambridge Philosophical Society and 

 the London Mathematical Society. 



The list of his scientific productions includes over 100 

 papers, many of them of considerable length, and six 

 volumes. Probably he will be best known by the 

 treatise "Theorie der Transformationsgruppen," in the 

 preparation of which he was assisted by the loj'al devo- 

 tion of Dr. F. Engel. It is a work of great originality, 

 containing many methods and a wide range of develop- 

 ment ; it exhibits in masterly manner the suggestive 

 application of new methods to fundamental subjects ; 

 and it may be described briefly as a systematic exposi- 

 tion of Lie's investigations on groups of transformations 

 that are continuous and finite. Among the subjects 

 to which application is made, may be mentioned the 

 theory of ordinary differential equations ; the theory 

 of partial differential equations, both single and in 

 systems ; differential invariants and their types ; the 

 solution of Pfaff's problem ; tangential transformations, 

 specially in spaces of two and three dimensions, and 

 more generally in 11 dimensions ; groups of functions 

 transformable into one another, and a substantial simpli- 

 fication (by the use of their properties) in the integration 

 of systems of partial differential equations ; a complete 

 determination of types of the groups of transformation in 

 one, two, and three variables, and a partial determination 

 of those in it variables. It concludes with a profound study 

 of the foundations of geometry from the point of view of 

 Riemann and Helmholtz ; and after a critical disqussion 

 of the significance of the hypotheses which they made, 

 he propounds a solution of his own, based upon more 

 elementary hypotheses. 



In a couple of instances, his lectures in amplification 

 and elucidation of portions of his theory were edited and 

 published in volume form by Dr. G. Scheffisrs, whose 

 help is gratefully acknowledged : one of these relates to 

 differential equations that admit of known infinitesimal 

 transformations ; the other to continuous groups. 



Two other works were promised by him. One of these, 

 to be written in co-operation with Dr. Engel, was to deal 

 with the theory of infinite continuous groups and the 

 application of the general group-theory to the integration 

 of differential equations : this work has not appeared. 

 The other, to be written in co-operation with Dr. Scheft'ers, 

 was to be devoted to a systematic exposition of his geo- 

 metrical investigations ; the first volume has appeared 

 under the title, " Geoirietrie der Beriihrungstransform- 

 ationen." 



As already indicated, his name at the present time 

 would probably be associated most closely with the 

 theory of continuous groups. .\n inspection of his 

 memoirs, however slight, is sufficient to indicate his 

 keen and essential interest in the domain of geometry. 

 But while his method was that of the group-theory, and 

 while his investigations so frequently referred to geo- 



