26o 



NA TURE 



[July (2, 1900 



statu pupillari in public secondary schools above the age of 

 fifteen, able and willing to bear arms, should be enrolled for the 

 purpose of instruction in drill, manoeuvre, and the use of arms." 

 At the same time the paper makes it quite clear that the Head- 

 master of Eton thinks mere proficiency in drill is not sufficient 

 — at every step the boy must be taught the reason of everything 

 he is called upon to do, and throughout his training his intel- 

 ligence must be carefully and steadily developed. Approaching 

 the same question from another point of view. Prof. Armstrong, 

 in a letter to the Times, maintains that no amount of mere 

 military training given in schools, or subsequently, will ensure 

 the necessary improvement in our officers, unless the intelligence 

 of boys is more satisfactorily developed in the early years at 

 schools — an end which can best be secured by an adequate 

 training in the scientific method. It may fairly be surmised 

 that the Headmaster of Eton is quite in agreement with Dr. 

 Armstrong as to the paramount importance of early teaching, 

 and that both are equally anxious that intelligent citizens should 

 somehow be produced. Of the value of a familiarity with the 

 methods of science it is here unnecessary to say anything, but 

 it would certainly appear that both contentions are right. 

 What is wanted is Dr. Warre's intelligent military training for 

 public school boys who have all had the advantage of a training 

 in the scientific method for which Dr. Armstrong pleads. 



SCIENTIFIC SERIALS. 



Transactions of the American Mathematical Society, vol. i. 

 No. 2, April. — On the metric geometry of the plane w-line, by 

 F. Morley. The relations which «-lines of a plane exhibit, when 

 considered in relation to the circular points, have not received, 

 in Prof. Morley's opinion, systematic attention .since the im- 

 portant memoirs by Clififbrd, on Miquel's theorem ("Works," 

 p, 51), and by Kantor ( Wiener Berichte, vols. Ixxvi. and Ixx viii. ). 

 He applies certain notions which are fundamental in the 

 geometric treatment of the theory of functions, and especially 

 the notion of mapping. The paper is an interesting exten.sion 

 of Clifford's chain, and adds many curious results. — On relative 

 motion, by A. S. Chessin. A memoir extending to 54 pages. 

 The theory developed in it originated in a memoir by Bour in 

 1863 {Journal de Liouville, Ser. 2, vol. viii.). It deals mainly 

 with the so-called " second form " of differential equations of 

 Lagrange, and with the canonical system of differential equations 

 of Ilamilton-Jacobi. The first part of the paper deals only with 

 the theory ot relative motion. The differeniial equations are 

 derived from one fundamental principle embodied in the so- 

 called " theorem of Coriolis." This enables the author, not only 

 to write down the differential equations of relative motion im- 

 mediately from the corresponding equations of absolute motion, 

 but to obtain equations as general as those kno7vn for absolute 

 motion. In this first part there are eleven chapters. The 

 second part (promised) is to contain applications of the 

 theory. Among the problems to be discussed is the problem 

 of Foucault's pendulum when the oscillations are not 

 infinitely small, and the problem of Foucault's. top, 

 which Gilbert was unable to solve (sur I'application de 

 la m^thode de Lagrange a divers problemes de mouvement 

 relatif). The two problems, our author states, can be easily 

 solved by the theory and formulas given in this first part. — Plane 

 cubics and irrational covariant cubics, by H. S. White. — The 

 paper considers cubics invariant under /a:;-/?'a/ transformation by 

 covariants (2, 2), and those invariant under complete transforma- 

 tion by covariants(3, 3). There remain for further treatment 

 the two sets of conies invariant under the third transformation 

 (2, 2), and invariant curves of order higher than the third {cf, the 

 author's paper in No. i). The new covariant cubics are 

 eight in number, all of the type called equianharmonics. — A 

 purely geometric representation of all points in the projective 

 plane, by J. L. Coolidge. After some definitions, the writer 

 gives a representation of all points in a real line by lines in a 

 real plane, and then extends the representation so as to include 

 all points in a real plane, noticing in particular those systems of 

 lines which represent points on an imaginary line. He then 

 takes up the subject of chains of points, showing their applica- 

 tion to the general theory of projectivity. Finally, he glances 

 briefly at the system of lines which represent points on a real 

 conic, and concludes with remarks as to other possible solutions 

 of the problem and its extension to three dimensions. — The 

 decomposition of the general collineation of space into three 



NO 1602, VOL. 62] 



skew reflections, by E. B. WiUon. The paper discusses the 

 question, " Is it possible to decompose the general collineations 

 of space into the product of a number of skew reflections ; and 

 if .so, what is the least number of skew reflections involved in 

 such a decomposition?" — A new method of determining the 

 differential parameters and invariants of quadratic differential 

 quantics, by H. Maschke, exhibits in a preliminary way a 

 symbolic method in close analogy with the symbolism used in 

 the algebraic theory of invariants, for the construction and 

 investigation of invariants of quadratic differeniial quantics. — 

 On the extension of Delaunay's method in the lunar theory to 

 the general problem of planetary motion, by G. W. Hill, shows 

 that the tediousness of Delaunay's method disappears when the 

 greatest generality is given to the procedure. — Mr. J. E. Camp- 

 bell writes on the types of linear partial differential equations of 

 the second order in three independent variables which are 

 unaltered by the transformations of a continuous group. 



Bulletin of the American Mathematical Society, June. — 

 Prof. Cole furnishes an account of the Proceedings at the New 

 York April meeting of the Society, and abstracts several of the 

 papers read ; and Prof. Holgate performs a like office for the 

 April meeting of the Chicago section of the Society. — J. G. 

 Hagen gives a short sketch of the history of the extensions of 

 the calculus. The abstract is confined to those theories that 

 are in close relation to the infinitesimal calculus and the theory 

 of functions, and excludes geometrical methods and methods of 

 demonstration. To name one or two points discussed, they are 

 Cauchy's " Calcul des Residues," S^hell's " Quotial and In- 

 staural," the exponential function of higher order, the 

 logarithmic methods of Bergbohm and Oltramare, and the ex- 

 tension of the calculus of finite differences. — Reviews are given 

 ot Burnside's "Theory of Groups," by Dr. G. A. Miller; of 

 D'Ocagne's " Traite de Nomographic," by Prof. Morley; of 

 Barton's "Theory of Equations," by J. Maclay ; of Rice's 

 "Theory and Practice of Interpolation," by Prof. E. W. Brown; 

 of Von Braunmiihl's " History of Trigonometry," by Prof. 

 Cajori ; of M. Boyer's interesting " Histoire du Mathe- 

 matiques," by the same writer ; and of FrischauTs " Vorlesungen 

 uber Kreis- und Kugel-Functionen-Reihen," by W. B. Ford. — 

 Varied information is supplied in the "Notes" and "New 

 Publications." 



The numbers of the Journal of Botany for May, June, and 

 July are almost entirely occupied by articles descriptive of new 

 species, or relating to the geographical distribution of plants, 

 chiefly in the British Islands. Mr. H. N. Dixon records the 

 detection of an addition to British mosses in Amblystegium 

 compacium, and Mr. S. M. Macvicar an addition to British 

 Hepaticae, in Pellia neesiana. 



SOCIETIES AND ACADEMIES. 

 London. 

 Chenriical' Society, June 21.— Prof. Thorpe, President, in 

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

 morphine, I., by S. B. Schryver and F. H. Lees. Morphine 

 readily exchanges an alcoholic hydroxyl group for halogen, 

 yielding the bases chloromorphide, CnHjaO-jNCl, and bromo- 

 morphide ; when heated with water these substances give iso- 

 morphine, CnHiaOjN, and on reduction chloromorphine yields 

 desoxymorphine hydrochloride (Ci7Hi<,02N,HCl)2,3H20. These 

 four new bases are not narcotics. — On the oxime of mesox- 

 amide and some allied compounds, by M. A. Whiteley. 

 Nitrosyl chloride converts malonamide into the isonitroso- 

 derivative, CONH2.C(NOH).CONH2 ; nitrous acid converts 

 the latter into a pseudonitrole, CONH2.C(NO)(N02).CONH2, 

 and hydriodic acid reduces it to aminomalonamide, 



CONH2.CH(NH2).CONH2, 



— On dimethyldiacetylacetone, tetramethylpyrone and orcinol 

 derivatives from diacetylacetone, by J. N. Collie and B. D. 

 Steele. Disodiodimethylpyrone and methyl iodide react, 

 giving dimethyldiacetylacetone, C7H803(CH3)2, which is 

 converted into tetramethylpyrone, Q,^l\^0,^{Q,\i.^,2. by hydr- 

 iodic acid ; the residues from the preparation of dimethyl- 

 diacetylpyrone contain trimethylpyrone, CgHigOo, and an 

 orcinol derivative, CgHijOj. — Dehydracetic acid, "by J. N. 

 Collie. The author has succeeded in preparing dehydr- 

 acetic acid from triacetic lactone. — The decomposition of hydr- 

 oxyamidosulphates by copper sulphate, by E. Divers and T. 



