January io, 1S95] 



NA TURE 



263 



The relation 7„ - o is treated a? the equation of a curve wiih 

 coordinate^ .V and y; and wtien f and y can be ex;>ressed as 

 functions of a puiaeter c, ths qaantities 7, and i, can also 

 be expressed as functions of this parameter. For instance, 

 7i3 = o reduces to the quadratic in p 



/- - (I - c- - c')/ - <r(l + f)= = o 



by means of the substitutions 



.v = j{i ^ :), y = z{i - j), z = c\p- \); 



and now in K'ein's Modular Equation of the Thirteenth Order, 



given in the Proc. L. M.S. ix. p 

 \ - c - 4<r-' 



1 26, it is found that 



= - + 



I 



c- 3- 



When one root t „ of this modular equation is given by 

 _ I3f(i + c\ _ 13 



C \ -T C 



the remaining 13 roots, typified by t,., are given by 



(. + t-^'^ ) 



where o 



4. S. 



O, I, : 



12, 



(Klein, Math. Ann. xvii. p. 567). 



It has been shown in the Proc. L.M.S. xxv. p. 252, 



that 



and now, putting 



9 = 





x'y*i 



(<r=«r = - 



J.1.J,-. 



,16,10 



(ff=,)"=*-^, (0-;,)" = 



I all functions off and ^C, where 



C = I + 4ir + dc" + 2f^ + i-i + 2c'' + t:". 



The solution in the same minner of the Modular Equation of 

 the Seventh Order has alieady been given in the Proc. L.M.S. 

 xxv. p. 224 ; while the Kilth Order introduces Klein's icosa- 

 hedron function. A similar procedure will serve for the 

 Eleventh Order. — On certain definite iheia-function integrals, 

 by Prof. L. J. Rogers. — On a class of groups defined liy con- 

 gruences (second paper), by Prof. W. liurnside, F. R.S. — 

 Electrical vibrations in condensing systems, by Dr. J. Larmor, 

 F. U.S. It is only by the introduction of considerable c.ipacity 

 that the vibrations ol electrical systems of simple geometrical 

 form can assume a character at all simple and steady ; for this 

 reason it is of practical importance to be able to estimate the 

 periods of vibrations in the dielectric plates of condensers. It 

 lis shown that the modes and periuds for such a plate are pre- 

 Icisely the same as those of the acoustical vibrations of a plate 

 of air of the same form and the same law of thickness, enclosed 

 on both faces, and also round its edge, by rigid walls, the only 

 dilTerence being that the velocity of electric propagali n replaces 

 the velocity of sound. For example, if the condenser is a 

 spherical one, the period-, of the free vibrations are equal to the 

 lime required for an electric pulse to travel round its 

 ciicumference, divuled by (/«'- + «;'-, where m is any integer ; 

 and this result will also practically hold good for a con 

 denser of this form which is not a complete sphere, but has 

 a hole through it at the point oppoiie to the place where 

 the inner coating is connected with the exciter. The 

 leriods for a flat condenser of uniform thickness correspond to 

 the well-known ones of standing water-waves in a cylindrical 

 vessel o( the same form of contour. If a condenser is divided 

 iby cutting across its conducting coats, as is done in the ordinary 

 guard-rini;, the separate parts will vi' rate without interfering 

 'with each others periols. Various other cases are treated ; for 

 example, the propagation of electric waves in a compound 



NO. 1315, VOL. 51] 



plate composed, say, of air above and a liquid below. — On the 

 integration of Allegrei's integral, by .Mr. A. E. Daniels.— On 

 the complex number formed by two quaternary matrices, by 

 Dr. G. G. Morrice. 



Linnean Society, December 20, 1894. — Mr. C. B. Clarke, 

 F.R. S., President, in the chair.— Mr. W. B. Hemsley ex- 

 hibited a series of specimens and figures illustrating parasitism 

 of Loranlhus aphyllus and other plar.ts, from the Herbarium, 



Kew. Mr. J. E. Harting exhibited a specimen of a small 



Siberian warbler, Phylloscopiis superciliosus. which had been 

 obtained near Beverley, Yorkshire, in October last, and made 

 some remarks on its haunts, habits, and migration, and upon 

 the previous instances which had been noted of its accidental 

 occurrence in the Britih Islands.— Mr. H. M. Bernard gave 

 the substance of a paper on the spinning glands in Phrynus, 

 not previously known, and described their position and their 

 morpholoi;ical importance in .\rachnidan phylogen. The penis 

 was described as a pair of rudimentary filamentous appendages 

 of the genital segment, and consequently of importance as 

 bearing further testimony to the view that the limbs on the 

 abdomen of the ancestral form were not plates as in Limulus, 

 but appendages like Ih se on the thorax. The presence of 

 these limbs explains the curious genital operculum of the 

 Pedipalfi, which is not a primitive feature derived from 

 Eurypterine ancestors, as some would maintain, but a purely 

 secondary specialisation acquired within the Arachnid phylism. 

 — .\ paper was then read by Mr. Percy Groon), enliil.d " Con- 

 tribunons to the knowledge of .Monocotyledonous saprophytes," 

 or plants which are dependent for their existence on the pre- 

 sence in the substratum of decaying organic matter. He 

 obseived that, like parasites, they may be divided into those 

 which possess chlorophyll (Jicmis iprophyta) and those which 

 have none (holosapropliyles). Hitherto very few experiments, 

 he said, had been made on kemiiapri'phylts, and hence our 

 acquaintance with them was largely speculative. The remarks 

 which he had now to offer referred almost entirely to /;o/«ay»r£>- 

 phyles, or at least to plants with very little trace of chlorophyll. 

 Alter an interesting discussion, in which Sir D. Brandis, Mr. 

 H. N. Ridley, and others took part, the Society adjourned 

 to January 17. 



Paris. 

 Academy of Sciences, December 31, 1894— M. Loewy in 

 thechair. — -^ study of<,;raphitcs liom iron, by M. Henri Moissan. 

 Al the ordinary pressure, the graphite is purer when formed at 

 a higher temperature. The graphite produced at the highest 

 temperature is the most stab.e in pre-ence of nitric acid and 

 potassium ch'orate. Under ])tessure, the crystals and masses of 

 graphite appear to have suffered incipient fusion. During the 

 solution of the cast-iron by acids, hydroxy compounds are 

 formed, which resist a dull red heat, but burn like the graphite 

 it-elf. — Report was made favourably on a memoir by M. 

 Riquier, to be printed in the Recueil Jts Memoircs da Savants: 

 itran^crs, under the tile " On the existence of inegrals in any 

 ditiereniial system, and on the reduction of such a system to a 

 completely integrable linear form of the first order." — On the 

 radial velocity of f Hercules, by .M. H. Deslandres. A 

 specirophotographic determination in which the line displace- 

 ments are measured on photographs taken with comparison 

 spectra on each side of the star spectrum. The mean value of 

 the radial velocity of this star is - 70 km., as deteruiined by M. 

 Belopolsky ; the author confirms this exceptional value, finding 

 -60 41, a second observer finds the velocity -62 97. — On the de- 

 termination of 1 he number of loots common to a sjsiein of simul- 

 taneous equations, and on the calculation of the sum of the values 

 of a function in these points, by M. Walther Dyck.— On the solu- 

 tion of numerical equations by means of recurring series, by M. R. 

 Ferrin. — On dehniie integrals of divisors, by M. N. Bougaief. — 

 On certain cundiiions to be realised for the measurement of elec- 

 trical resistances by means of alternating currents and the tele- 

 phone, by M. R. Colson. — On the sulphides of nickel and 

 cobalt, by M. .\. Villiers. This is a study of the c-jcdiiions of 

 precipitation ol nickel and cobalt sulphides, and ol the means 

 whcicby lie precipitation may be whidly or paitly prevented. — 

 On calcium ethoxide, by M. de Forcrand. Calcium carbide, 

 C,Ca, gives with ethjl alcohol compounds of the type 

 «CaO -f- M'CsHgO, and not an-elhoxide. The compounds 

 obtained are (I) 3CaO.4C.jH6O and (2) CaO.CJ IjO. At the 

 same time gas is disengaged, consisting chiefly ol acetylene (So 

 per cent ), and an easily liquefied elhylenic hydrocarbon (10 per 



