230 



NA TURE 



[Jan. 3, 1884 



There are now something near 2000, and we are augmenting 

 them all the time. I have found many myself : if they were 

 distributed through the days of the year I think in some years I 

 should have had several every day. But the accessions to know- 

 edge which are constantly being made make it unsafe to indulge 

 in any prophecies that, because such and such things have not 

 been found, therefore such and such things cannot be ; for we find 

 such and such things really have been and really are dis- 

 covered. 



The successive changes that we have in the mammalia have 

 taken place in the feet, teeth, and brain, and the vertebral 

 column. The pans which present us the greatest numl)ers of 

 variations are those in which many parts are concerned, as in the 

 limbs and feet. In the Lo«er Eocene (Puerco) the toes were 

 5-5. In the Loup Fork fauna some possess toes but I-I. Prior 

 to this period no such reduction was know n, though in the Loup 

 Fork fauna a very few species were 5-5. Through this entire 

 series we have transitions steady and constant, from 5-5, to 4-5, 

 to 4-4, to 4-3, to 3-3, to 2-2, to l-i. In the Puerco period 

 there vxas not a single mammal of any kind which had a good 

 ankle-jfint, which had an ankle-joint constructed as ankle-joints 

 ought to be, with tongue and groove. The model ankle-joint is 

 a tongue-and-groove arrangement. In this period they were all 

 perfecily flat. As time passes on, we get them more and more 

 grooved, until in the Loup Fork fauna and the White River 

 fauna they are all grooved. In the sole of the foot, in the 

 Puerco fauna, they are all flat ; but in the Loup Fork fauna the 

 sole of the foot is in the air, and the toes only are applied to the 

 ground, with the exception of the line of monkeys, in which Ihe 

 feet have not become erect on the toes, and the elephant, in 

 which the feet are nearly fiat also, and the line of bears, where 

 they are also flat. As regards the ungulation between the small 

 liones of the palm and of the sole there is not a single instance in 

 which the bones of the toes are locked in the Lower Eocene, as 

 they are in the later and latest Tertiary. 



When we come to the limbs, the species of the Puerco fauna 

 have short legs. They have gradually lengthened out, and in 

 the late periods they are nearly all relatively long. 



( To he continued. ) 



SOCIETIES AND ACADEMIES 

 London 



Royal Society, Dec. 13, 1883. — " On the Figure of Equi- 

 librium of a Planet of Heterogeneous Density," by G. H. 

 Darwin, F.R.S., Plumian Professor of Astronomy in the Uni- 

 versity of Cambridge. 



If a rotating planet be formed of compressible fluid, the 

 strata of equal pressure are of equal density, and the ellip- 

 ticity of the strata increases from the centre outwards. Since 

 !t is supposed that the earth consolidated into its present 

 form from a fluid or semi-fluid condition, the determination of 

 the arrangement of internal density and of the law of ellipticity 

 in such a planet is often called the problem of the figure of the 

 e.arth. When the law of compressibility of the fluid is known, 

 the laws of density and ellipticity are determinate, but the differ- 

 ential equations involved are of such complexity that only one 

 solution of the problem is well known, viz. that associated with 

 the names of Legendre and Laplace.' 



In this solution the modulus of compressibility varies as the 

 square of the density, but the assumption of this law appears to 

 have been dictated more by the necessity of solving a certain 

 oifferenti.al equation than by physical considerations. 



The comparison of the solution of the problem with the ob- 

 served facts with regard to the earth may be made in several 

 ways. The constant which determines the rate of the earth's 

 precessional motion gives us information with regard to the 

 arrangement of density in the interior, and the ellipticity of the 

 surface is determined by geodesy and by the amount of a certain 

 i nequality in the moon's motion. Now, in order that the solu- 

 tion of the problem of the earth's figure may be satisfactory, the 

 same arrangement of internal density must give the observed 

 amounts both to the precessional constant and to the ellipticity 

 of the surface. 



Laplace's solution is highly satisfactory in this respect ; and at 

 the same time it makes the mean density of the whole earth about 



^ The late M. Roche seems to have also solved the prohlem in 1848, and 

 his paper isfublished in the Memoirs 0/ the Academy of ilonlfellier. 



twice as great as the density of the surface stratum. The density 

 of rock is about 2"8, and that of the whole earth is about 

 5-6. 



In this state of our knowledge another solution of this cele- 

 brated problem possesses some interest, even if its results are 

 not quite so satisfactory as those of Laplace's theory. 



In the present paper such a solution is ofl^ered. The law of 

 compressiljility of the fluid is such, that the modidus varies as a 

 power of the density, which power may range from negative 

 infinity to |. When the power is zero, we have constant com- 

 pressibility ; and when the power is unity, we have the same law 

 of c impressibility as in a gas. 



The solution is expressible in a far simpler algebraic form 

 than that of Laplace, and it differs froai his solution in 

 placing a far larger proportion of the mass of the planet in 

 the central regions. 



It is remarkable thit this solution affords for the case of the 

 earth a correspondence between the precessional constant and 

 the surface ellipticity equally good with that of Laplace. To 

 obtain this correspmdence we have to assume the compressibility 

 of the fluid to he nearly constant. 



The density of the surface layer appears however to be 3'7, 

 and this is considerably greater than that of ordinary rocks. 

 This result tells adversely to the acceptability of the proposed 

 solution, but the discrepancy is not so serious as might appear 

 at first sight. It appears from pendulum experiments on the 

 Himalayan plateau and on the Andes, that there is a consider- 

 able deficiency of density underneath those great ranges. This 

 woukl favour the view that our continents are a mere intu- 

 mescence of the surface layers. In this case there must be a 

 somewhat abrupt change in the law of density at only a few 

 miles below the surface. The theory of the earth's figure can 

 take no account of a sudden change of density on passing into 

 a swollen superficial layer, and the value of the surface density to 

 be used is that which is to be found immediately below the 

 swollen part. 



The author therefore points out that whilst the solution now 

 offered cannot be held to be quite as satisfactory as that of 

 Laplace, yet its inferiority is not of a kind to render altogether 

 unacceptable the contention that it may be somewhere near the 

 truth. 



Linnean Society, December 20, 1S83. — Alfred W. Bennett* 

 M.A., in the chair. — Messrs. N. Cantley, W. Dobson, F. (}• 

 Smart, and Rev. R. Thoni were elected Fellows of the Society 

 — Mr. S. O. Ridley exhibited and made remarks on a series of 

 177 verticil .sections of sponges collected in the neighbourhood 

 of Point de Galle, Ceylon, by Dr. W. C. Ondaatje, F.L.S., and 

 transmitted to England by him in letters. They are in most 

 instances sufficient for the identification of the genera and some 

 species. — Mr. F. Maule Campbell showed the web of a spider 

 { Tegenaria guyonii) which had been spun in the centre of a 

 pasteboard cylinder, the peculiarity being the manner in which 

 the solid part of the web was medially swung, whereas in this 

 species of spider it is more usually on the sides of objects. — A 

 paper was read by Mr. F. O. Bower on the structure of the 

 stem of Rhytichopetaluni montatmnt. The plant is a native of 

 Abyssinia, growing in districts 11,000 to 13,000 feet above the 

 level of the sea. It differs from its ally Lobelias in being perennial. 

 Internally it is succulent when young, but afterwards the surface 

 becomes scarred as the leaves drop off', and exteriorly is hardened 

 by a thick corky deposit. Rhyncltopetalutn, the author shows 

 in detail, has certain peculiarities in the arrangement of the 

 tissue of its leaf bundles, since the cortical system does not con- 

 sist of branches of bundles of the leaf trace, but are cauline 

 bundles, in this respect differing widely from such forms as 

 Lathyrus casuarina, many Begonias, &c. Rhyiicliopttalunt, 

 moreover, has the cortical bundles running obliquely, and 

 forming a regular four-sided meshed network related to the 

 leaf bases and bundles of leaf trace. In these respects it 

 approaches Cycas, in which latter the bundles of the acces- 

 sory cortical system are not so regular and are almost vertically 

 arranged. Some Cycads and Rhynchopetaltim also agree in the 

 exterior appearance of their stem, so that palreontologists might 

 be deceived in their judgment if two well-preserved specimens 

 were examined by them. — A communication was read on 

 the auditory ossicles of Rhytina stelleri by Alban Doran. 

 This was based on skeletons obtained by the Vega expedi- 

 tion, and shown at the late International Fisheries Exhibition 

 by the Swedish Government. The author arrives at the conclu- 



