43° 



A' A TURE 



[March 5, 1908 



universities of Scotland, gives information concerning the 

 allocation of grants during that period. The publica.io)i 

 of this interim report, dealing only with nine months, was 

 necessitated by an alteration of the financial year of the 

 trust to bring it into line with the academic year of the 

 universities. Sums amounting to 22,oooi. have been 

 handed over to the four Scottish universities during the 

 nine months, bringing the total expenditure in this direc- 

 tion, since the inauguration of the first quinquennial 

 scheme of grants in January, 1903, to 156,489^. The con- 

 ditions which will regulate the second quinquennial dis- 

 tribution are under the consideration of a special sub- 

 committee, and will, it is hoped, be published shortly. 

 The total expenditure for 1906-7 under the scheme of 

 endowment of post-graduate study and research was 

 7004/., and the estimated expenditure for the current 

 academic year is 7615L The expenditure upon fees for 

 the summer session, 1907, amounted to 11,685?. The 

 proposed scheme of inclusive fees, that is, that in each 

 faculty a beneficiary of the trust should be granted all 

 such instruction as it is desirable for him to receive in 

 his course for a degree on the payment of one fee for 

 each academic year, is still under discussion. Numerous 

 appendices to the report provide detailed information as to 

 the dififerent items of e.xpenditure. 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, December 12, 1907.—" Further Considera- 

 tion of the Stability of the Pear-shaped Figure of a 

 Rotating Mass of Liquid." Bv Sir G. H. Darwin, 

 K.C.B., F.R.S. 



In vol. xvii.. No. 3 (1905), of the Memoirs of the 

 Imperial Academy, of St. Petersburg, M. Liapounoff has 

 published an abstract of his work on figures of equilibrium 

 of rotating liquid. In this paper he explains how he has 

 obtained a rigorous solution for the figure and stability of 

 the pear-shaped figure, and he pronounces it to be unstable. 

 In a paper in the Philosophical Transactions (vol. cc, 

 A, pp. 251-314) the present author arrived at an opposite 

 conclusion. 



The stability or instability depends on whether the sign 

 of a certain function is negative or positive. 



M. Liapounoff attributes the disagreement to the fact 

 that the author only computed a portion of an infinite 

 series, and only used approximate forms for the elliptic 

 integrals involved in the several terms. He believes that 

 the inclusion of the neglected residue of the infinite series 

 would lead to an opposite conclusion. 



In the author's comput,ation the critical function is 

 decisively negative, whilst .M. Liapounoff is equally clear 

 that it is positive. The inclusion of the neglected residue 

 of the series, which forms part of the function, undoubtedly 

 tends to make the whole function positive, but afte'r 

 making the revision it remained incredible, at least to the 

 author, that the neglected residue should amount to the 

 total needed to invert the sign. 



The analysis of his former investigation was re- 

 examined throughout, and the computations were repeated 

 by improved methods. The same method was also applied 

 to the investigation of Maclaurin's spheroid, where the 

 solution could be verified by the known e.xact result.' 



Dissent from so distinguished a mathematician as M. 

 Liapounoff is not to be undertaken lightlv, and therefore 

 especial pains were taken to ensure" correctness. The 

 author states his conviction that the source of the dis- 

 agreement is to be found in some matter of principle, and 

 not in the neglected residue of this series. 



Entomological Society, February 5 — \Tr. C. O. Water 

 house, president, in the chair.— £:A,;ii7iit.?.— Dr. T. A. 

 Chapman : A collection of butterflies made last summer 

 at Gavarnic, in the Pyrenees, including a number of 

 specimens of Ereh.ia Icfebvrei, with E. melas from south- 

 east Hungary, for comparison.— H. St. John Donis- 

 thoi-pe : Eleven species of ants taken in the hot-houses in 

 Kew Gardens in December, 1907, and January, 1908, eight 

 Tll,iil^'-"'' ¥^'h-Soc. Trans., 1903, vol. iv., p. ,.3, on "The Appro.vinw;e 

 Uetermm.T.on of the Form of Maclaurin's Spheroid, ■ and a further note on 

 the .sani: subject, recently s-nt to the same society. 



NO. 2001, VOL. 77] 



being new to the published Kew list, and six species not 

 before recorded as introduced in Britain. — J. E. Collin : 



Microscopically mounted specimens of the gnat EpidapUf 

 scabiei, Hopk., a potato pest in the United States recently 

 discovered in England attacking narcissus bulbs. — A. H. 

 Hamm : Very young larvse of Bitaris muralis, hatched in 

 captivity, the natural place of deposit of these eggs being 

 at the entrance to the burrow of the bee, Anthophora 

 pilipes^ in stone walls near Oxford. — Commander Walicer : 

 Two specimens of the rare Pyralis lienigialis, Zell, O , 

 taken at light in his house at Summertown, August, 1906, 

 and 1907. — R. E. Turner : A box of Thynnidae from 

 South America, mostly from Chile, with several new 

 species from Mendoza and the Peruvian Andes. — Prof. T. 

 Hudson Beare : .A specimen of Trachyphlaciis scabriculus 

 taken at St. Margaret's Bay in August, 1907, with the 

 two deciduous mandibles still in place. — Lieut. -Colonel 

 Manders : The $ of Papilio phorbanta from Bourbon, 

 an aberrant member of the Nireus group of Papilios, com- 

 pared with the other members of the same group from 

 the African mainland, Madagascar, and Mauritius. It 

 was pointed out that whereas in all the other species the 

 9 9s were some shade of green similar to the ^ S s, the 

 Bourbon insect was more or less uniformly brown. It 

 was suggested that this was due to mimicry, Euplaea 

 goiidoti, a species strictly confined to Bourbon, being 

 the model. — Hon. Walter Rothschild : Interesting 

 papilionids ; (i) Troides alexandrae, Rothsch., remarkable 

 lor the beauty of the c? and the gigantic size of the 9, 

 a new discovery by A. S. Meek, who found this fine 

 insect in the north-eastern portion of British New Guinea 

 at some distance inland from the coast ; (2) a gynandro- 

 morphic speciinen of Troides. the only one known of this 

 genus, obtained by Dr. L. Martin in South Celebes. It 

 belongs to T. Iiajipliron, the left side being 9 and the 

 right side jT . — R. Adkin : Bred specimens of Tortrix pro- 

 nubaiia, Hb., to demonstrate that the species is con- 

 tinuously brooded. — L. W. Newman : Long series of 

 Melitaea aurinia and Notodonta chaonia from various 

 localities in the United Kingdom to illustrate the wide 

 superficial variation of the respective species. — Dr. F. A. 

 Dixey : Specimens of Nychitona medusa. Cram., and 

 Psciidopontia paradoxa, Feld. — Papers. — (i) Two diplo- 

 pterous Hymenoptera from Queensland ; (2) notes on 

 Thynnidse, with remarks on some aberrant genera of the 

 Scotiidee : R. E. Turner. — Diaposematism, with reference 

 to some limitations of the Miillerian hypothesis of 

 mimicry : G. A. K. Marshall. 



ZoolOEical So'-ietv. Febmarv iS.— Dr. Henry Woodward, 

 F.R.S., vice-president, in the chair. — .A series of specimens 

 of internal parasites obtained from animals recently living 

 in the society's gardens : Dr. L. W. Sambon. Stress was 

 laid on the important additions to knowledge to be derived 

 from an adequate investigation of such material, and on 

 the practical results to the health of the animals in the 

 gardens that might be expected. — The inheritance of colour 

 ill domestic pigeons, with special reference to reversion : 

 R. Staples-Browne. A series of skins was exhibited 

 illustrating some experiments upon which the coinmunica- 

 lion was based. Crosses had been made between black 

 barbs and white fantails. The Fi generation was black 

 with some white feathers. In the F2 generation, among 

 other forms, blacks and whites were obtained, and also 

 some blues. Blues were found to be dominant to whites, 

 but blacks were dominant, or rather " epistatic," to the 

 blues, which accounts for the fact that the reversionary 

 form does not appear until the F2 generation. When two 

 blues of the F2 or later generations were mated together 

 blacks were never obtained again. A white in F2 mated! 

 to a fantail gave whites only. .\ second series of skins 

 illustrated a cross between a white tumbler and a white 

 fantail. Some while birds splashed with red had figured 

 ill the ancestry of the tumbler, although the bird itself 

 showed no trace of colour. In the Fi generation such' 

 splashed kinds occurred, which, when mated together, 

 gave in F2 birds which were red and white with some 

 distinct blue feathers. Possibly the white tuinbler was a 

 dominant white. — Mammals collected by Mr. M. P. Ander- 

 son during a trip to the Mongolian Plateau, N.W. of 

 Kalgan : O. Thomas. Nine species were mentioned, of 

 which two were described as new. The paper formed the 



