350 



NATURE 



[February 7, 1901 



whether, if they are not so amended, the use of both is 

 admissible for different groups. Some even go so far as to 

 say that an obvious error in the spellingof a name,as,forex- 

 ample, Rhinchosaurus in place of Bhynchosaurus, should 

 not be amended, and that the previous use of the in- 

 correctly spelt name should be no bar to its subsequent 

 employment for another group in the correct form. To 

 many, at least, of those who have even the slightest 

 knowledge of the classics such a practice must be re- 

 pugnant. And to a certain extent, at any rate, the same 

 remark will apply to hybrid names, although the general 

 consensus of opinion is now against the amendrnent of 

 these. Less objection can be taken to meaningless 

 names, or anagrams (such as Xotodon, the anagram of 

 Toxodon), which, if euphoniously formed, serve their 

 purpose fairly well. And the old objection against so- 

 called barbarous names has of late years been waived by 

 many workers. Although it is by no means a general 

 view, such names are more euphonious when Latinised, 

 as Linsanga in place of Linsang, and Coendua for 

 Coendou. Then again there are names like Camelo- 

 pardalis (giraffe), Hippotigris (zebra), and Hippocamelus 

 (a deer), given on the supposition that the animals to 

 which they refer are intermediate between the two 

 indicated by the compound title. The two former have 

 late classical authority, and may further be justified on 

 account of the coloration of the animals to which they 

 refer, but to some persons, at least, the acceptation of the 

 third is objectionable. It must be confessed, however, 

 that when once individual fancy is allowed play in matters 

 of this sort, it is difficult to know where to draw the line. 



Another class of names are those which have been 

 given to species on the evidence of manned specimens, or 

 examples whose place of locality was incorrectly recorded. 

 The great bird-of-paradise was thus named apoda, while 

 the name ecaudatus has similarly been applied to at least 

 one mammal. Again, a bear inhabiting the Himalaya 

 has been named tibetanus^ while there are even more 

 flagrant instances of misapplied geographical titles. Many 

 workers of the modern school assert that no errors of this 

 kind should be amended ; while some would even say that 

 although Tibet is the accepted modern way of spelling 

 the country of the lamas, yet that if the specific title was 

 originally spelt thibetaniis, so it must remain for all time. 

 A common-sense, rather than a pedantic, view can, we 

 think, be the only safe guide in such cases. When a 

 name inculcates an error in geographical distribution, its 

 retention, from this point of view, is clearly indefensible. 

 So, again, in the case of names due to misconception or 

 maimed specimens. Where, for instance, the name 

 ecaudatus denotes a long-tailed animal, its retention is 

 against common sense. On the other hand, where the 

 feet of a bird are inconspicuous, as in the swift, no 

 great exception can be taken to the use of the name apus. 



The last point in dispute to which we have space to 

 refer is the right of an author to withdraw a name pro- 

 posed by himself in favour of some later title. A well- 

 known instance of this is afforded by the name Dauben- 

 tonia, proposed by Geoffroy in 1795 fo"^ the aye-aye, but, 

 on account of preoccupation in botany, subsequently 

 withdrawn by him in favour of Cuvier's name Chiromys (or 

 Cheiroviys^ as it was originally spelt). Whereas the right 

 of withdrawal was denied by Gray (and the older name 

 revived), by Sir Wilham Flower it was admitted. The 

 modern tendency is to follow Gray. If the preoccupa- 

 tion of a zoological name by a botanical were now ad- 

 mitted, of course Geoffroy's change would be followed. 

 The question is whether, being right according to the 

 views of his own time, there is sufficient justification for 

 saying that he acted ultra vires. Moreover, the possi- 

 bility is to be borne in mind that the next generation of 

 zoologists will revert to the view that the use of a generic 

 term in botany bars its subsequent employment m the 

 sister science. 



NO. 163 2, VOL. 63] 



To arrive at a settlement in regard to these and many 

 other points in dispute will require forbearance and the 

 subordination of individual inclinations to the voice of 

 the majority ; compromise and common sense being, we 

 venture to think, at least as necessary as adherence to 

 inelastic rules. 



In the foregoing we have purposely refrained from 

 making any reference to Mr. H. M. Bernard's proposal 

 to abolish specific names in those forms of life " which 

 cannot be at once arranged in a natural system," for the 

 reason that, if we understand him aright, it is his inten- 

 tion that the abolition in question should apply only (for 

 the present, at any rate) to corals, sponges, and perhaps 

 other low types of invertebrates. Whatever, therefore, 

 may be its merits or demerits, the proposal is not yet 

 intended to apply to such forms of life as are capable of 

 being arranged in some approximation to a " natural 

 system " ; and the discussion of the disputable points 

 in connection with specific names alluded to above 

 is accordingly not yet rendered superfluous. 



R. L. 



CHARLES HERMITE. 



AMONG those mathematicians who assisted in making 

 the nineteenth: century, and more especially the 

 Victorian era, a period of unparalleled activity in the 

 scientific world, the name of Charles Hermite will be 

 indelibly imprinted in our annals as that of one who 

 did much to develop the study of higher algebra, 

 geometry, analysis and theory of functions. 



Charles Hermite was born at Paris in 1822, and at the 

 age of twenty he entered the Ecole Polytechnique. His 

 mathematical genius was not long in showing itself, for 

 shortly afterwards we find him corresponding, at the 

 instigation of Liouville, with Jacobi on the subject of 

 Abelian functions, and the predictions of the latter 

 mathematician that Hermite would soon extend the 

 fields of study which he himself had done so much to 

 open out was soon verified. From the theory of con- 

 tinuous functions Hermite soon passed on to the theory 

 of forms, and gave a general solution of the problem of 

 arithmetical equivalence of quadratic forms. He also 

 discovered a new arithmetical demonstration of Sturm's 

 and Cauchy's theorems on the separation of roots of 

 algebraic equations. 



The study of higher algebra, which sprang into exist- 

 ence with the discovery of invariants, was opened up 

 simultaneously by Cayley, Sylvester and Hermite, and it 

 would appear that to the latter mathematician we are 

 indebted for the law of reciprocity, the discovery of 

 associated covariants and gauche invariants, and the 

 formation of the complete system of covariants of cubic 

 and biquadratic forms and invariants of the quintic. 

 Concurrently with these researches in arithmetic and 

 algebra, Hermite was engaged on the study of the trans- 

 formation of hyperelliptic functions and expansions of 

 elliptic functions, and he was also the first to show that 

 the number of non-equivalent classes of quadratic fornis 

 having integral coefficients and a given discriminant is 

 finite. In 1856 Hermite was elected to the Institut, 

 being then thirty-four years of age. In 1858 he took an 

 important step in connection with the study of elliptic 

 and theta functions by introducing a new variable con- 

 nected with the -q of Jacobi by the relation q = e<--^<^, so 

 that a) = t/^7/6. He was then led to consider the three 

 modular functions denoted by ^(w), x('^) ^^^ "^i^)- 



A transcendental solution of the quintic in^olvrng 

 elliptic integrals was given by Hermite, the first paper 

 appearing in the Coinptes rendusiox 1858 and subsequent 

 papers in 1865 and 1866. After Hermite's first publication, 

 Kronecker, in a letter to Hermite, gave a second solution, 

 in which was obtained a simple resolvent of the sixth 

 degree. 



