68 



NATURE 



[May 19, 1892 



arabic as determined by their osmotic pressures, by C. E. Line- 

 barger. The molecular mass of gum arabic is found to be about 

 2500, of dextrine 1134, and of colloid tungstic acid 1750. In 

 each of these three cases the colloid molecule is seven times the 

 simple molecule. 



American Jotirnal of Mathematics, ^q\. xiv., No. 2. (Balti- 

 more, Johns Hopkins Press, April 1892.) — The number before 

 us opens with a paper entitled " Some Theorems relating to 

 Groups of Circles and Spheres," by Prof. W. Woolsey Johnson 

 (PP- 97-114). The title at once calls to mind Mr. Lachlan's 

 memoir "On Systems of Circles and Spheres" (Phil. Trans., 

 vol. 177). The author thus puts the connection between the 

 papers: "(i) If there be 5 circles or 6 spheres in each group, 

 the product or determinant of powers is equal to zero ; and (2) 

 if there be 4 circles or spheres in each group, the power determi- 

 nant is the product of two determinants each of which depends 

 upon one of the groups." Mr. Lachlan's results are derived 

 principally from the first of the above theorems, whereas it is 

 Prof. Johnson's object "to point out some other results deriv- 

 able from the second theorem, and particularly to evaluate the 

 power determinants for groups of smaller numbers of circles and 

 spheres." The two memoirs are an interesting application of 

 a " Theorem in the Geometry of Position " (the multiplication 

 of two determinants) due to Cay ley {Camb. Math. Journ., 

 vol. ii., 1841).— The next paper, by C. H. Chapman, is an 

 '"Application of Quaternions to Projective Geometry " (pp. 115- 

 4°)- — Then follows an adaptation of G. W. Hill's method 

 [American Journal of Mathematics, \o\.'\.) "so as to include 

 that class of mequalities which depends also on the ratio of the 

 solar and lunar distances, and, in particular, the principal part 

 of the parallactic inequality," by E. W. Brown. The title of 

 the paper is " On the part of the Parallactic Inequalities in the 

 Moon's Motion, which is a Function of the Mean Motions of the 

 Sun and Moon" (pp. 141-60). — The two remaining papers 

 were read before the New York Mathematical Society, viz. 

 " On the Curves which are self- reciprocal in a Linear Nul- 

 system, and their Configurations in Space," by C. P. Stein- 

 metz (pp. 161-86); and "A Classification of Logarithmic 

 Systems," by Irving Stringham (pp. 187-94).— This last is an 

 attempt to use the logarithmic spiral, defined as a geometrical 

 locus, as the means for defining the logarithm and demonstrating 

 its properties. 



Bulletin of the Neiv York Mathematical Society, vol. i. 

 Nos. 6, 7 (New York : March, April, 1892).— The first of 

 these numbers opens with a discussion of the mechanical 

 axioms, or laws of motion, as presented by Newton. The 

 author. Prof. W. Woolsey Johnson, examines at some length 

 (pp. 129-39) the views put forward in Thomson and Tait, 

 " Natural Philosophy " ; Tait, " Mechanics " (" Encyc. Brit.") ; 

 and Williamson and Tarleton, "Dynamics." The article is a 

 careful piece of reasoning, founded upon the principle that "it is 

 desirable to include among the axioms of mechanics the smallest 

 basis of postulated principles upon which it is possible to con- 

 struct the science by rigid mathematical reasoning." Then 

 follow short notices of an 8-figure logarithm table, published 

 " par ordre du Ministre de la Guerre, Paris, 1891," and of " An 

 Introduction to Spherical and Practical Astronomy, by Dascom 

 Greene (Boston, 1891)." The usual " Notes" and list of new 

 publications close this number and also No. 7. This last-named 

 number opens with a review of " The Laws of Motion, an Ele- 

 mentary Treatise on Dynamics, by W. H. Laverty." The writer's 

 object in this, and similar articles that are to follow, is "by 

 reviewing somewhat at length a few of the better recent works on 

 elementary mechanics to ' fix the ideas ' and arrive at some con- 

 clusions, at least, as to what is the best modern usage in treating 

 the subject" (pp. 145-50). The next contribution, by Dr. C. 

 H. Chapman, entitled " Weierstrass and Dedekind on General 

 Complex Numbers" (pp. 150-56), is one of those that makes 

 this Bulletin so interesting and valuable to the student. The 

 last article is a translation (pp. 156-68) by Prof. Ziwet of an 

 eloge by M. Duhem on " Emile Mathieu : His Life and Works." 



Memoirs of the St. Petersburg Society of Naturalists, vol. 

 xxi. (Section of Botany). — Besides the proceedings, the volume 

 contains the first part of an excellent monograph, by M. 

 Aggeenko, on the flora of Crimea, being a description of the 

 botanical geography of the peninsula. The orography and 

 hydrography of Crimea, and its various soils, are shortly de- 

 scribed, as also its climate. The periodical phenomena of 

 blooming and fruit-bearing are next dealt with. The foUow- 



NO. II 77. VOL. 46I 



ing chapter is devoted to the analysis of previous exploration, 

 and the remainder of the work is given to the description of the 

 character of vegetation in the Steppes of Crimea, on the northern 

 slope of the highlands, the flat summits of the Yaila highlands, 

 and especially the southern slope. The influence of man and of 

 the fauna on vegetation is briefly treated, and a new species, 

 Alyssum rotundatum, as well as a new variety of Orchids 

 {Ophrys aranifera, Hudson, var. taurica) are described and 

 figured on plates. A very interesting geo-botanical map of 

 Crimea is given. — A paper on the pigments of Pungi, by A. 

 Nadson, must be rather considered as a preliminary communi- 

 cation, containing many valuable data on the pink, yellow, red, 

 and orange pigments of some fifteen species.— On the crystals 

 in the leaves of the Anonacece and- Fio^ariecz, by Prof. Borodin. 

 Vol. xxii. (Section of Zoology and Physiology). — Ornithologi- 

 cal observations in the middle course of the Amu-daria in the 

 Tcharjui-kelif region, by A. Yaschenko. A list of 161 species 

 of birds and their distribution in various regions (cultivated, 

 mixed, deserts, and mountains) is given, each of the regions 

 being described separately as to its most characteristic birds. — 

 On the hybrids between Butydes flava and Butydes campes- 

 tris, by N. Zaroudnoi. — On the embryonal development of 

 Phyllodromia {Blatta) Germanica, by N. Kholodkovsky, being 

 a very elaborate and valuable contribution to comparative 

 embryology. It is the fruit of a four years' laborious research, 

 and is accompanied by five large well-drawn plates. 



Bulletin de VAcadcmie des Sciences de St. Petersbourg, 

 Nouvelle Serie, t. ii., No. 3. — The ephemeris and the approxi- 

 mate elements of the comet of Encke for the year 1891, by 

 O. Backlund (in German). The ephemeris is calculated from 

 July 2 to November i, 1891, after having taken into 

 account the perturbing influences of Venus, the Earth, 

 Mars, and Jupiter in 1884-88, and Jupiter alone from March 

 7, 1888, to May 31, 1891.— Additions to the Flora of the 

 Caucasus: i. Two new varieties of Rhamnus, byN. Kuznet- 

 soff" (in German, with two plates). — On the radiants of the 

 Andromedides, by Th. Bredikhine (in French), with a plate. 

 The meteoric current of November 27, 1872, and 1885 is 

 studied, the former on the ground of the observations of the 

 Brera Observatory at Milan. The positions of the radiants are 

 given on a map, upon which the orbit of the comet of Biela 

 (for 1859) is also traced. The positions of the radiants being 

 taken into account, the author compares the probable elements 

 of the meteoric current with the orbit of the Biela comet. 

 Taking further into account the meteoric currents observed 

 on December 7 and 8 in 1798, 1830, 1838, and 1848, the 

 author concludes that those currents must have belonged to the 

 orbit of the same comet before the severe perturbations it 

 suffered through the influence of Jupiter in 1794. ^Obser- 

 vations of 51 double stars, followed by a research into sys- 

 tematic errors, by F. Renz, of Pulkova (in German). The 

 observations and the catalogue based upon them are given.— 

 On some old and new catalogues of stars, by J. Seyboth (in 

 German). Before the printing of Romberg's catalogue a 

 comparison of its data with those of previous catalogues was 

 felt to be necessary. A series of comparative measurements 

 has been undertaken for that purpose, and their results are given 

 in the introduction to Romberg's catalogue. Further com- 

 parison is now made with the catalogues of Struve, Argelander, 

 Pulkova (3542 stars), Becker, and Gould, and reduction tables 

 are given. — A new Bacterium, Nevskia ramosa, by A. Famintzin 

 (in German), with a plate. This strange organism, so widely 

 different from all known Bacteria, but not unlike to Metchnikoff"'s 

 Pasteuria ramosa, consists of a jelly-like ramified growth, the 

 Bacteria cells appearing upon the ends of the branches. It 

 forms colonies similar to those formed by some Algse and 

 Infusoria ( Urococcus, Gomphonema, Epistylis). — On the libration 

 of Hyperion, by H. Struve (in French). The last years' obser- 

 vations of this satellite of Saturn, which have been made with the 

 aid of the great Pulkova refractor, having disclosed considerable 

 discrepancies from the ephemerides calculated by Mr. Marth, 

 the Pulkova astronomer tried to explain them — and succeeded to 

 a great extent — by a libration which has a short period of 641 

 days, and an amplitude of 9° in the average longitude. — Revision 

 of the Hymenopteresof the Zoological Museum of the Academy, 

 by A. Semenoff: i. Genus Cleptes (\n Latin). The following new 

 species are described : Cleptes flamniifer, obsoletus, Buyssonis, 

 and Mocsarii ; ii. Genus Abia (new species) : A. symballoph- 

 thahna. — New Gentianoe from Asia, by N. Kuzneisoff'. The 

 following new species, some of which had already been recog 



