March i6, 1899] 



NA TURE 



479 



graphs of the latter. The President said he had examined the 

 slide, and could corroborate Mr. Keeley's description of the 

 structure of the diatoms. With regard to the coscinodiscus and 

 triceratium, he believed Mr, Morland was the first to work out 

 and correctly describe these structures, and Mr. Keeley's 

 observations confirmed those results ; but he believed the ac- 

 count of the structures of heliopelta and auliscus now given 

 was original. While he was on the subject of diatoms he 

 wished to mention a very interesting discovery made by Mr. 

 Morland, who found that the bracket which strengthened the 

 " plate" in arachnoidiscus was neither more nor less than what 

 an engineer would call a bead-headed girder, in the invention of 

 which the engineer had only copied what nature had already 

 accomplished in the strengthening girders of this diatom. — Dr. 

 llebb said the fourth part of Jlr. Millett's paper on the 

 Foraminifera of the Malay Archipelago had been received, but, 

 owing to its technical character, he proposed that it should be 

 taken as read. — The President read a paper descriptive of the 

 Powell iron microscope, constructed by Hugh Powell in 1S40 ; 

 the instrument, which was exhibited in the room, was still in 

 constant use by the President. Mr. Vezey suggested that an 

 exhibition should be held of historic microscopes, showing the 

 various stages of the development of the instrument ; and the 

 president said he hoped the Society would see its way to arrange 

 for an exhibition of the character proposed by Mr. Vezey. — ^!r. 

 Rheinberg read a paper in explanation of the chief features of 

 the exhibition of objects shown under multi-colour illumination, 

 arranged under twenty-seven microscopes. The President said 

 he believed one of the chief values of this method of illumin- 

 ation was that it might make it possible to use a larger axial 

 cone than heretofore, and that if they could only combine the 

 Gifford screen with this new method, he thought an advantage 

 would be secured, but caution would be necessary in the 

 selection of the colours. In photomicrography Mr. I\hein- 

 berg's method would prove useful. 



Cambridge. 

 Philosophical Society, February 20. — Prof. H. Lamb, 

 F. R. S. (Trin.), Victoria University, was elected a Fellow of the 

 Society, — The following papers were communicated to the 

 Society : — A semi-inverse method of solution of the equations 

 of elasticity, by Dr. C. Chree. The usual procedure in attack- 

 ing an elastic solid problem is first to determine expressions for 

 the displacements involving arbitrary constants, thence to deduce 

 expressions for the strains and stresses, and finally to determine 

 the values of the arbitrary constants by the aid of the surface 

 stress equations. In two papers published in 1895 the author 

 obtained a complete solution for an isotropic elastic solid ellip- 

 soid under certain important force systems, employing a semi- 

 inverse method in which expressions for the stresses formed the 

 basis of departure. Some little time ago the author noticed that 

 not only was this method applicable to the corresponding 

 problems in aeolotropy, but that the first stages of the work 

 were absolutely the same for all kinds of homogeneous elastic 

 material. The semi-inverse method thus leads at once to the 

 solution of such a problem as that of an ellipsoid of any shape 

 and any degree of aeolotropy rotating about a principal axis and 

 self gravitating. The procedure is perfectly straightforward, 

 the only practical difficulty being the complication of the ex- 

 pressions for the three fundamental arbitrary constants which 

 appear in the general formuLu for the stresses. In the present 

 paper the aim has been to illustrate the method by applying it 

 to a variety of the more interesting special cases, and not to 

 chronicle general results of forbidding length and complication. 

 For comparison with results found for rotating elongated or flat 

 ellipsoids, the corresponding problems have been solved by a 

 similar method for long cylinders and thin discs. Some of the 

 results may interest those who are concerned with speculations 

 about the structure of the earth, while others may prove of value 

 to engineers. — On change of independent variables and the 

 theory of cyclicants and reciprocants, by Mr. E. G. Gallop. The 

 problem considered is the change of a system of « independent 

 variables in a partial differential coeflicient. The solution was 

 given in a fully expanded form by Sylvester, and deduced by 

 Cayley from a theorem due to Jacobi on the reversion of series. 

 In this communication Jacobi's formula is developed in a manner 

 somewhat different from Cayley's method, and a result obtained 

 which leads on the one hand to Sylvester's expanded form, and 

 on the other to a symbolical formula which is also applicable to 

 any function of differential coefficients. This form involves n- 



NO. 1533, VOL. 59] 



quadro-linear partial differential operators analogous to the an- 

 nihilator of ordinary pure reciprocants, and ii{n - l) lineo-linear 

 operators of the type occurring in the theory of invariants. The 

 formula can also be applied to the differentiation of implicit 

 functions, and it is shown how a solution of the general equation 

 of infinite degree, or of a set of such equations, can be exhibited 

 in symbolical form. The method is then applied to the case of 

 the general linear transformation and to the theory of cyclicants 

 as developed by Prof. Elliott. Attention is also drawn to another 

 class of reciprocants in « variables which, perhaps more naturally 

 than cyclicants, may be regarded as generalisations of Sj'lvester's 

 reciprocants in one variable. Conditions are obtained which 

 ensure that a function of diff'erential coefficients may be a re- 

 ciprocant in this sense of the term. — On the combustion of car- 

 bon in electrolysis, by Mr. S. Skinner. A cell consisting of a 

 carbon electrode in potassium permanganate and a lead peroxide 

 electrode in dilute sulphuric acid produces a current flowing in 

 the external circuit from the lead peroxide to the carbon. The 

 permanganate ion is therefore brought against the carbon plate 

 and becomes reduced, forming mainly carbon dioxide gas and 

 permanganic acid. Such a cell has an electro-motive force of 

 0-33 volt. To find the relation between the carbon dioxide set 

 free and the current, a voltameter containing potassium perman- 

 ganate solution with a carbon anode and platinum kathode, was 

 connected in series with a water voltameter and a current passed 

 through them. With certain precautions it was found that one 

 volume of carbon dioxide was set free for two volumes of 

 hydrogen, and the author gives reasons for considering this 

 result as determining the electro-chemical equivalent of carbon. 

 The carbon dioxide produced in this way is not quite pure ; it 

 contains small percentages of oxygen and carbon monoxide. — 

 On the ionisation of a gas by " Entladungsstrahlen," by Prof. 

 J. J. Thomson. The paper contains an account of a series of 

 experiments which show that the "Entladungsstrahlen" dis- 

 covered by Prof. E. Wiedemann cause a gas through which they 

 pass to become a conductor of electricity. The experiments 

 show that with the discharge through a gas at a low pressure 

 the region near the kathode produces more " Entladungs- 

 strahlen " than the positive column, while none could be de- 

 tected from the dark space between the positive column and 

 the negative glow. 



P.^RIS. 

 Academy of Sciences, March 6, — M, v.an Tieghem in the 

 chair. — On some peculiarities of the theory of shooting-stars. 

 Possibility of repetition of activity of certain radiant points. 

 Existence of so-called stationary radiant points, by M. O. 

 Callandreau. The observations of Mr. Denning on the exist- 

 ence of families of shooting-stars which diverge from the same 

 point in the sky, with a maxiinum every three months, have been 

 called in question by M. Tisserand, but in the author's opinion 

 these observations cannot but be regarded as accurate, and their 

 theory is discussed by the formula; of Tisserand. The conditions 

 necessary for the formation of the so-called stationary foci are 

 also discussed mathematically, with application to the Orionids ; 

 shooting-stars from a fixed point near v-Orionis having been ob- 

 served by Denning over a period of twelve days. — M. Ilelmert 

 was elected a Correspondant for the Section of Geography and 

 Navigation in the place of the late Sir George Henry Richards. — 

 Measurement of the diameters of the satellites of Jupiter and of 

 Vesta by interference methods, carried out with the large equa- 

 torial of the Observatory of Paris, by M. Maurice Hamy. The 

 numbers obtained were in general agreement with those of 

 Michelson, the latter being slightly higher for satellites I., II,, 

 and III. The value for the minor planet Vesta (o"'54) agrees 

 exactly with the micrometric observations of M. Barnard. —Ab- 

 solute determination of directions making an angle of 45° with 

 the horizon. Application to the measurement of latitudes, by 

 MM. T- Perchot and W. Ebert. A mirror is floated upon an 

 annular ring of mercury, and making an angle of (45-|-.v)° with 

 the horizontal, x being the small error of setting. The method 

 described allows of an ex.act determination of r. For most 

 European observatories, not far removed from latitude 45°, the 

 method has important advantages, the error due to flexure, in 

 particular, being practically eliminated.— On the fundamental 

 problems of mathematical physics, by M. W. Steklofif.— On ana- 

 lytical prolongation, by M. E. Goursat.— Onan extension of the 

 calculus of linear substitutions, byM. Cyparissos Stephanos.— On 

 the arithmetical nature of the number e, by M. Emile Borel.— 

 On conjugate bundles, of which a system of curves are geodesies, 

 by M. C. Guichard.— On certain systems of equations of 



