NATURE 



{_Nov. 14, 1878 



of the fractions on each side of it. Thus if « = 5, the fractions 



1 + 2 

 are \, \, \, |, J, \, \, \ |, and, for example, 1 = ----; also 



4 + 5 

 the difference between any two consecutive fractions is equal to 

 unity divided by the product of their denominators. These 

 properties, discovered by Mr. Goodwyn, were afterwards proved 

 by Cauchy. Mr. Glaisher pointed out the gi-eat convenience of 

 the arrangement of the periods in Goodvvyn's tables, and ex- 

 hibited a table showing the number of periods corresponding to 

 every denominator up to 1000, and the number of figures in 

 each period. This table was obtained by vctual counting from 

 Goodwyn, and in every instance the product of the number of 

 figures in each period and the number of periods was found to 

 be equal to the number of numbers less than the denominator 

 and prime to it, as should be the case. After alluding to other 

 similar tables, und to tables by Gauss, Reuschle, Desmarest, 

 Shanks, &c., reference was made to the fact discovered by 

 Desmarest that the number of figures in the period of the 

 reciprocal of 487" is the same as the number of figures in the 

 period of the reciprocal of 487, or in other words, 10^^®= i 

 (mod 4872), In vol. iii. of Crelle Abel proposed the query, 

 "Can x>^-'^ — \ (mod /x"), if ju be a prime and x less than /u?" 

 Jacobi replied and showed that 3^"=! (mod I1-), 14"®=! 

 (mod 29^) and iS^^Si (mod 37^). The case found by Des- 

 marest is the only one known in which the conditions of Abel's 

 question are satisfied for ;tr=io; in fact we have 10- = 1 (mod 

 3*) and 10"*^= I (mod 487-), and there is no other known ca.-e 

 in which 10/ -1 = 1 (mod /^), p being a prime, although there 

 is no reason to suppose that such cases do not exist, and that 

 there is not some value of p for which 10/ -1 = 1 (mod p^\. 

 Desmarest has verified that for values of p less than 1000 the 

 congraence lO^-^Ei (mod p-) is only satisfied for p — 2, and 

 p = i^?i'j. Mr. Glaisher also exhibited the first fourteen printed 

 pages of the factor table for the fourth million, an account of 

 the construction of which was communicated to the Society on 

 February 11, 1878. 



Paris 



Academy of Sciences, November 4. — M. Fizeau in the 

 chair. — The following papers were read : — Researches on the 

 stability of the ground and of the vertical of Paris Observatory, 

 by M. Mouchez. M. Wolf is occupied with the former ques- 

 tion. M. Gaillot has been studying the latitude given at differ- 

 ent epochs. The variations of a few tenths of a second in this, 

 at different times of the year, are thought due to the influence of 

 temperature either on the instruments, or (rather) on the astro- 

 nomical refractions, whose coefiicient has not yet been ade- 

 quately determined ; or they may be due to a systematic error 

 of the declination of stars distributed regularly over the twenty- 

 four hours of right ascension, these hypotheses being more 

 admissible than that of a variation of the vertical. — On the re- 

 ciprocal displacements between oxygen, sulphur, and halogen 

 elements, combined with hydrogen, by M. Berthelot. — Recipro- 

 cal displacements between weak acids, by the same. Two weak 

 acids opposed to each other divide the base, the division being j 

 regulated by the state of partial decomposition of the two j 

 salts dissolved, which depends both on the proportion | 

 of water and on that of the corresponding acid. — On i 

 the reaction between mercuiy and hydrochloric gas, by JI. 

 Berthelot. 13*5 gr. of mercury and 48 cub. ctm. of pure hydro- 

 chloric gas put in a very resistant sealed glass tube and heated 

 to the highest possible temperature for an hour, yielded 

 a little over i cub. ctm. of hydrogen, indicating decom- 

 position of about one-twentieth of the hydrochloric gas. — Pre- 

 liminary note on the compound nature of the chemical elements, 

 by Mr. Lockyer. Be.-ides calcium, several substances considered 

 as elements are compounds. — On the native iron of Greenland 

 and the basalt containing it, by Prof. Lawrence Smith. He 

 gives an analysis of a memoir on the subject. He is convinced 

 the iron is of terrestrial origin, and in many cases so intimately 

 united with basalt that the felspathic and other crystals of the 

 latter penetrate the iron particles. The iron is probably a secon- 

 dary product formed by decomposing action of beds of lignite 

 and other organic matters which the immense basaltic dykes have 

 penetrated. — On a universal law relative to the dilatation of 

 bodies, by M. Levy, a reply to objections. — On the maturation of 

 the grain of ergot. The substance which plays the part of 

 sugar in this grain, the author finds identical with synanthrose, 

 the saccharine matter found vASynantherece, and more especially in 

 Jerusalem artichokes. It is the only saccharine matter present, and 

 It dimini hes rapidly in proportion as maturation advances (but 



does not wholly disappear), being replaced by starch, formed 

 doubtless at its expense. Wheat, oats, barley, and maize, do- 

 not contain synanthrose, but cane-sugar. Thus one may readily 

 detect in flour the fraudulent addition of ergot flour.— On the 

 dangers of the use of methylic alcohol m industry, by M. Poin- 

 care. Animals kept eight to sixteen months in air, ever re- 

 newed, but charged with vapours of methylic alcohol, undergo 

 hypertrophy and fatty degeneration of the liver, a like alteration 

 of the muscular fibres of the heart, epithelial cells, uriniferous 

 tubes, and the lung cells, also congestion of the nervous centres, 

 &c. — M. Gelis stated that, owing to lar^e demand, he proposed 

 manufacturing 200,000 kilogrammes of sulphocarbonate of potas- 

 sium (for phylloxera) for the coming year, and he de>ired the 

 Academy to obtain from the railway companies reduced prices 

 of transport.— Mr. Warton presented a marine compass with 

 nickel needles.— On the direction of the vertical of Paris 

 Observatory, by M. Gaillot. See first paper.— On a simple 

 property, characterising the mode of distribution of weight 

 of a solid, placed on an elastic horizontal ground, be- 

 tween different parts of its base, when the latter is a 

 horizontal elhpse, by M. Boussinesq.— On certain ordinate 

 series with reference to powers of a variable, by M. Appell. — 

 On the rectification of a class of curves of the fourth order, I 

 by M. Darboux. — On an iodised derivative of camphor, by M. 

 Aller. The formula is C10H15IO.— On the region of the solar 

 spectrum indispensable to vegetable life, by M. Bert. The part 

 thus necessary to life is that between the lines B and C ; but 

 it is not sufficient ; for behind red glass plants may live, indeed, 

 long, but they get elongated to excess and slender, with narrow 

 and little-coloured foliar limbs ; the blue and violet rays rectify 

 this. — On relations presented by phenomena of motion proper 

 to reproductive organs of some phanerogams with cross and 

 direct fertilisation, by M. Hffickel. Motion provoked in both 

 male and female organs seems to serve physiologically for cross 

 fertilisation, while spontaneous motion assumes direct fertilisa- 

 tion in plants which are not sensibly profited by crossing. The 

 former oftener characterises the more highly- organised plants, 

 the latter seems proper to the less highly-organised. — Repro- 

 duction of felspars by fusion and prolonged maintenance at a 

 temperature near that of fusion, by MM. Fouque and Levy, 

 The experiments here described were on oligcclase, labrador, 

 and albite. — On two specimens of natural crystals of sulphate] 

 of magnesia (epsomite) of remarkable dimensions, by M. D« 

 Rouville. 



CONTENTS p, 



Cleopatra's Needle AKD THE Wind PKESst;RE 



Draper's Scientific Memoirs 



A Catechism of Botany 



Omr Book Shelf: — 



Roberts' " Manual of Anthrcpcmelry" 



Muir's "Text-Bock c£ Ar.thmetic for Use in Higher Class 



Schools " 



B'aikie's " Elements of Dynamics (Mechanics), with Numercus 



Examples and Examination Questions 



Wilson's "Handbook to Map of the Geographical Distributicn of 



Animals" 



Letters to the Editor:— 



Gigantic Land Tortoises. — Alexis A. Julien; Dr. Jeffries 



WVMAN ...... 



The Figure of the Planet Mars. — H. Hennessy, F.R.S 3ij 



The Colour Sense. — Grant Allen 



Magnus's "Hydrostatics" and the "London Science Series." — 

 Philip Magnus ; The Reviewer 3| 



The Discovery of a Cranncg in Ayrshire. — Dr. F. Buchanan 

 White _ 3| 



The Power of Stupefying Spiders Possessed by Wasps. — Fkedk. 

 Smith 



The Expected Meteor Shower — W. F. Denning 



Geological Climate and Geological Time. — William Davies . . 



A " New Galvanometer. " — R. E. Bavnes 



Com.mercial Crises and Sun Spots. By Prof . W. Stanley Jevons, 



■ F.R.S 



The Werdermann Electric Light. By T. E. G.atehouse (With 



Illustrations) 31 



Duplexing the Atlantic Cable (With Illustrations) 38 



The Royal Society Medallists 



Afghanistan 4'3 



Our Astkoncmical Column : — 



The Solar Eclipse of i?79, July 19 4» 



Comets of Short Period 42 



The Saturnian Satellite Mimas' 4» 



The Minor Planet Isnene •;» 



Geoorai'kical Notes 13 



Notes -■'♦ 



University and Educational Intelligence 'P 



Societies and Academies 47 



