April lo, 1890] 



NATURE 



549 



form of the ring, which, in coriibination with a slight eccentricity, 

 secured its stability. Maxwell found that the irregularities of a 

 ring possessing a permanent movement ought to be very sensible, 

 and that the appearance of the rings of Saturn was incompatible 

 with that required by his demonstration. He considered the 

 case of a planet occupying the centre of the ring, whereas 

 Laplace's hypothesis required a slight eccentricity. This ques- 

 tion was not, however, treated sej)arately, and M. Callandreau 

 has subjected it to mathematicil analysis. First, taking the case 

 of a symmetrical ring when the centre of gravity will be on a 

 symmetrical axis, and then the case required by I.aplace, viz. that 

 the centre of gravity is not exactly coincident with the geometrical 

 centre, the author shows that the conditions stated by Laplace 

 are not sufficient to ensure stability. 



Brooks's Comet {a 1890). — This comet was observed at 

 Paris on March 28. It was seen as a round nebulosity, 

 about 40" or 50" in diameter, with a very jironounced central 

 condensation, a.nd was about the tenth magnitude. 



Bright Lines in Stki.lak SrixTR.\.— The Rev. J. E. 

 Espin reports the discovery of bright lines in the spectrum of 

 0, as well as in that of Q.^. Orionis, and possibly in that of S 

 Coronx as well. 



ON THE DEFORMATION OF AN ELASTIC 

 SHELU 



Trills paper treats of the deformation of an elastic shell whose 

 ■^ radii of curvature are everywhere great in comparison with 

 the thickness, which is supposed uniform. The subject has been 

 dealt with in a very able manner by Mr, A. E, H. Love in a 

 recent paper (Phil. Trans., 1885), but it seemed desirable, on 

 various grounds, that it should be attacked from an independent 

 point of view. The method here followed is that explained in 

 a former communication, " On the Flexure of an Elastic Plate" 

 (December 1889). The results, as regards the general theory, 

 are closely analogous with those of Mr. Love, and a comparison 

 of the two investigations gives a physical interpretation to the 

 various groups of terms which enter into his equations. There 

 are some differences of detail, arising from a slight difference in 

 the quantities chosen to express the flexural strains, but they 

 are not practically important. 



The great difficulty of the present subject, as contrasted with 

 the theory for a plane plate, is, that we cannot draw an absolute 

 line of demarcation between the deformations in which the 

 cardinal feature is the extension of the middle surface, and those 

 which involve flexure with little or no extension. This appears 

 to arise mainly from the fact pointed out by Mr. Love, that it 

 is in general impossible to satisfy the boundary conditions by a 

 deformation in which the middle surface is absolutely unextended. 

 But, this being admitted, the question remains in any specific 

 problem, as to the amount and distribution of the extension, 

 and, in particular, whether there are any modes of deformation 

 (or of free vibration) in which, after all, it plays only a sub- 

 ordinate part. Mr. Love answers this question in the negative, 

 in opposition to the views advocated by Lord Rayleigh in two 

 well-known papers. In the present communication Mr. Love's 

 argument is examined, and it is pointed out that cases may occur 

 in which the extensions (though comparable with the flexural 

 strains) may be confined to so small a region of the shell (near 

 the edges) that their contribution to the total energy of deforma- 

 tion is insignificant. 



In order to bring the matter to an issue in a definite instance, 

 1 have chosen the case of a cylindrical plate (such as a boiler- 

 plate) bent by a proper application of force over its straight 

 edges, so that the strained form remains a surface of revolution, 

 the circular edges being free. The analytical work in this case 

 is very simple, and the physical meaning of the various terms 

 which occur is easily recognized. In the interpretation of the 

 result it appears that a good deal turns upon the ratio which the 

 breadth of the plate (in the direction of the generating lines) 

 bears to a mean proportional between the radius and the thick- 

 ness. If this ratio is large, the bending forces may be prac- 

 tically replaced by two equal and opposite, couples uniformly 

 distributed over the straight edges, and having these edges as 

 axes. The strained form is almost accurately cylindrical ; near 

 tlie circular edges we have extensions of the same order as the 

 flexural strains, but these rapidly die out (at the same time 



' Abstractor a Paper read by Prof. Horace Lamb, F. R.S., before the 

 Mathematical Society on January 9. 



fluctuating in sign) as we press inwards, and the anticipation 

 that their total energy would be small compared with that due 

 to flexure is confirmed. In such a case, then, the approximate 

 methods used by Lord Rayleigh, in which no account is taken 

 of the conditions at a free edge, are fully. justified. But if, 

 keeping the radius and the thickness constant, we diminish the 

 breadth of the plate until it is comparable with the mean pro- 

 portional aforesaid, we get a sort of transition case between a 

 plate and a bar, which cannot be satisfactorily treated except on 

 the basis of the general equations. Finally, when the breadth 

 becomes small in comparison with the mean proportional, the 

 plate behaves like a curved bar, and an approximate treatment 

 is again applicable. 



In an appendix I have worked out, from the general equations 

 of elasticity, the uniform flexure of an infinitely long cylindrical 

 plate ; this being, at present, the only case of flexure in which 

 it appears easy to carry out the solution (on these lines) to a fulf 

 interpretation. 



SCIENTIFIC SERIALS. 



Timehri, being the Journal of the Royal Agricultural and 

 Commercial Society of British Guiana (printed at the Argosy 

 Press, Demerara, vol. iii., part ii., new series). — This in- 

 teresting brochure contains matter of general interest, as well as^ 

 information which might be expected in an agricultural and 

 commercial journal. Specialization cannot be pushed to its 

 extreme limits in a colony, and a Society of this nature naturally 

 admits matter into its Journal which are not strictly either 

 agricultural or commercial. Thus the papers on primitive games 

 and on the wild flowers of Georgetown must be regarded, 

 respectively, as of ethnological and purely botanical interest, but, 

 nevertheless, occupy a great part of the number, especially if we 

 leave out of consideration the reports of meetings and other 

 official matter connected with the working of the Society. Fruit- 

 growing in the Gulf States of America, Caracas as a place of 

 resort, and a short paper on some scale insects inimical to vegeta- 

 tion are the principal topics of a distinctly economic value. 

 The paper entitled the " Letters of Aristodemus and Sincerus" 

 is a review of an old book published in 1785-88 in twelve volumes, 

 dealing with the colonies of Demerara and Essequibo, and are 

 therefore of great interest to the present population. In 1785 

 the colonies had just been given over by the French, who held 

 them on behalf of the Dutch for about three years. No town 

 existed up to that date in Demerara, but during the French 

 occupation a little village had grown up in the neighbourhood of 

 Brandwagt, which they called la twuvelk ville, or Longchamps. 

 The fort on the east bank of the Demerara River (now called 

 Fort William Frederick) was also built at the time, and named 

 Le Dauphin, while another on the opposite side was called La 

 Raine. From such historical, social, scientific, and economic 

 materials a most interesting although somewhat diffusive number 

 has been produced, showing evidence of mental activity and 

 high culture, pleasant to see far away from the main centres of 

 civilization. The style of the writing, the printing, and the 

 illustrations are all of a high class, llovv far the London 

 publisher, Mr. E. Stanford, of Cockspur Street, is responsible 

 for the excellent "get up" of the volume we are unable to even 

 conjecture ; but we trust we may be permitted to say, without 

 oiTence, that the number of Timehri before us is highly creditable 

 to the literary talent and tastes of British Guiana. 



Quarterly y onriial oj Microscopical Science, February. — On the 

 anatomy of the Madreporia ; V., by Dr. G. Herbert Fowler (plate 

 xxviii.). Gives an account of the anatomy oi Diiiicania barbadensis, 

 Galaxca esperi, Hctcropsainiiiia mttltilobata, and Bathyactis 

 symmetrica, and gives a figure of the typical stnicture of the 

 genus Madrepora. — Contributions to the anatomy of earthworms, 

 with descriptions of some new species, by Frank E. Beddard 

 (plates xxix. and xxx.). This paper gives an account of the 

 structure of three new species of Acanthodrilus, with remarks 

 on other species of the genus. The new species are A. atitarc- 

 ticiis, yi. rosce, and A. dalei. Further remarks on the reproductive 

 organs of Eudrilus, with special reference to the continuity of 

 ovary and oviduct. — On the certain points in the anatomy of 

 Perichaeta, with description of Perichcvta intermedia, n.sp. — On 

 the phagocytes of the alimentary canal, by Armand Ruffer 

 (plate xxxi. ). Concludes that the wandering cells of the lymphoid 

 tissues of the alimentary canal have the power of proceeding to 

 the free surfaces of such tissues, and of taking into their interior 



