NA TURE 



[May 1 1, 1905 



The Transposition of Zoological Names. 



I WISH to say how thoroughly I agree with Mr. 

 fLydekker in his remarks on the unwisdom of transposing 

 .zoological names, and on the confusion caused by this 

 objectionable practice. To the instances which he has 

 mentioned I may add the following cases relating to two 

 well known and familiar species of animals. Linnaus 

 called the only European hare known to him Leptis 

 tiinidiis, and for many years that name was applied to the 

 common brown hare of Central Europe, while the northern 

 hare, which changes to white in winter, was known by 

 Pallas 's appropriate name, Lcpiis variabilis. This was 

 the nomenclature used by Blasius, by Bell in his " British 

 •Quadrupeds," and in all the ordinary text-books of zoology. 

 It was, however, pointed out some years ago, first, I 

 believe, by Lilljeborg, that the Lcpus timidus of Linnseus 

 had been based mainly upon the northern or variable hare, 

 or that at all events Linna?us had confounded the two 

 species together. In these circumstances obviously the 

 best plan was to call the middle-European brown hare by 

 its next given name, Lepus europeus, and this course has 

 been adopted by most writers. But the advocates of un- 

 restricted priority are not content with this, and insist 

 upon calling the variable hare Lepits timidt4s, the con- 

 sequence being that when that name is used it is impossible 

 to know which of two perfectly distinct animals is in- 

 tended by it. 



Another still more objectionable transposition of two 

 well known names has been lately suggested. Linnaeus, in 

 the twelfth edition of the " Systema Naturae," gave the 

 name Ttirdus musicus to the song-thrush and that of 

 Tmdus iliacus to the redwing, and these familiar terms 

 have been used by all writers for these well known birds 

 respectively ever since. But about a year ago it was dis- 

 covered by an ardent member of the new school of priority \ 

 that in his tenth edition of the " Systema " Linn^us had 

 unfortunately {by some error in his MS. or of his printer) 

 attached the diagnosis of Tardus musicus to T. iliacus, and 

 that of T. iliacus to T. musicus. It was admitted that 

 Linna;us had corrected the mistake in his later edition of 

 1760, but even Linnaeus could not be allowed to correct 

 his own errors in the face of the inviolable law of 

 " priority." In future, therefore, it was maintained, the 

 song-thrush must be called T. iliacus and the redwing 

 T. musicus ! This course has been actually adopted by a 

 subsequent writer, but w-e may trust that it will not meet 

 with general approval, and that the song-thrush and red- 

 wing will remain under the old names given to them by 

 the father of scientific nomenclature in 1760, and used by 

 every subsequent writer until 1904. P. L. Sclater. 



Modern Algebra. 



The publication of Messrs. Grace and Young's treatise 

 on algebra will direct attention to the importance and 

 ■difficulty of the theory of the concomitants of ternary and 

 quaternary quantics in connection with plane and solid 

 geometry. There are one or two points on which I propose 

 to make some remarks. 



In the first place, canonical forms are sometimes de- 

 ficient in generality, and this will be the case whenever 

 the form is the analytical expression for some special 

 property of an anautotomic curve. Of this defect the 

 canonical form of a ternary cubic furnishes a striking 

 example, for it is the analytical expression for the theorem 

 that through each of the three real points of inflexion one 

 real straight line can be drawn which passes through one 

 pair of conjugate imaginary points of inflexion on an 

 anautotomic cubic curve ; and since autotomic cubics do 

 not possess this property such curves cannot be represented 

 by the canonical form. 



In the next place, anautotomic curves are not by any 

 means the most interesting species of curves, and to go 

 through the process of calculating their concomitants, and 

 then specialising them for some particular species of auto- 

 tornic curves, is often very laborious. In the case of 

 unicursal quartics, many interesting results might be 

 obtained by calculating directlv the concomitants of the 

 •quantic («iJ/37. 7a, a$y-, and this would give results applic- 

 able to all unicursal quartics, except those which possess 

 NO. 1854, VOL. 72] 



the five compound singularities called the tacnode, the 

 rhamphoid cusp, the oscnode, the tacnode cusp, and the 

 triple point. Also, since an evectant is the tangential 

 equation of a curve which is related in a special manner 

 to the original one, an examination of the evectants of 

 the above quantic would lead to interesting results con- 

 cerning conies and other curves connected with trinodal 

 quartics. 



In this subject geometrical methods are a powerful 

 assistance to pure analysis. For example, let U be a 

 ternarv cubic in (a, 0, 7) ; eliminate 7 by means of the 

 equation P = ky, and equate to zero the discriminant of the 

 resulting cubic equation in a/0. This will give a sextic 

 equation A (fe) = o, which determines the six tangents drawn 

 from A to the curve. The condition that the curve U=o 

 should have a node is that the equation A(fe) = o should 

 have a double root; hence the discriminant of this binary 

 sextic is the discriminant of the original ternary cubic U. 



Manv other examples of a similar kind could be men- 

 tioned, and we may observe that from the discriminant 

 of a binary duodecimic, all the conditions that a quartic 

 curve should possess point singularities may be obtained. 



.'\pril 28. A. B. Basset. 



Current Theories of the Consolidation of the Earth. 



In Lord Kelvin's philosophical and justly celebrated 

 paper on the secular cooling of the earth (Thomson and 

 Tail's ■' Nat. Phil.," vol. i., part ii.. Appendix D), the 

 assumption is made that the earth was once a fiery molten 

 mass, liquid throughout, or melted to a great depth all 

 round. He cites Bischof's experiments showing that 

 " melted granite, slate, and trachyte all contract by some- 

 thing about 20 per cent, in freezing," and continues : — 



" Hence, if, according to any relations whatever among 

 the complicated physical circumstances concerned, freezing 

 did really commence at the surface, either all .round or 

 in any part, before the whole globe had become solid, the 

 solidified superficial layer must have broken up and sunk 

 to the bottom, or to' the centre, before it could have 

 attained a sufficient thickness to rest stably on the lighter 

 liquid below. It is quite clear, indeed, that if at any time 

 the earth were in the condition of a thin shell of, let us 

 suppose, 50 feet or 100 feet thick of granite, enclosing a 

 continuous melted mass of 20 per cent, less specific gravity 

 in its upper parts, where the pressure is small, this con- 

 dition cannot have lasted many minutes. The rigidity of 

 a solid shell of superficial extent so vast in comparison 

 with its thickness, must be as nothing, and the slightest 

 disturbance would cause some part to bend down, crack, 

 and allow the liquid to run over the whole solid. The 

 crust itself would in consequence become shattered into 

 fragments, which would all sink to the bottom, or meet 

 in the centre and form a nucleus there if there is none to 

 begin with." 



In adhering to these views. Lord Kelvin has been 

 followed by Prof. G. H. Darwin (cf. "Tides and Kindred 

 Phenomena of the Solar System," p. 257) and other 

 eminent mathematicians ; so that the theory that the earth 

 consolidated bv the building up of a solid nucleus through 

 the sinking of portions of the crust of greater specific 

 gravity is no doubt generally accepted by geologists and 

 others interested in the physics of the earth. 



Recent researches on the pressures within the planets 

 (cf. Aslronomische Nachrichten, No. 3092) have thrown 

 great doubt on this mode of consolidation of the globe. 

 The line of argument by which we reach this conclusion 

 is a double one : — 



(i) It is shown that the effect of pressure in the highly 

 heated fluid assumed to have constituted the molten earth 

 would have been to dissolve the portions of the sinking 

 crust before they attained any considerable deoth. 



(2) The increasing density of the fluid itself would have 

 prevented sinking of the crust below one-tenth of the 

 radius, so that a solid central nucleus could not have been 

 built up in this way. 



To see this clearlv. let us supoose that the earth were 

 a molten mass, and that a crust of rock several kilometres 

 in area, and a considerable fraction of a kilometre in thick- 

 ness, had formed, and begun to sink in the molten fluid 



