432 



NATURE 



[February 28, 1901 



relations of the University with its own colleges and students are 

 unsatisfactory, and it is most desirable that a Royal Commission 

 should be issued to inquire into the working of this University as an 

 examining and teaching body in relation to the educational needs 

 of the country at large, and to report as to the means by which 

 University education in Ireland might receive a greater extension 

 and be more efficiently conducted than it is at present." 



An influential committee, headed by the Duke of Devon- 

 shire, the Duke of Argyll, the Earl of Derby and Earl Spencer, 

 have issued an appeal with- the object of raising 150,000/. 

 in celebration of the jubilee of Owens College, Manchester. 

 Fifty thousand pounds are needed to discharge debts that have 

 been contracted and 100,000/. for additional endowment. 

 Among the objects the promoters have in view are the extinction 

 of the debt of 22,000/. on the buildings of the medical school ; 

 special endowments for existing chairs, including chemistry, 

 education, anatomy and philosophy ; the establishment of an 

 institution for bacteriological investigation and for the study of 

 hygiene, and of research Fellowships ; and the creation of a 

 pension fund for members of the teaching staff. 



SCIENTIFIC SERIALS. 



American Journal of Mathematics, vol. xxiii. No. i, January. 

 — The new volume opens with a memoir by S. Kantor, entitled 

 " Die Typen der linearen Complexe rationaler curven im R,.." — 

 E. J. Wilczynski writes on transformation of systems of linear 

 differential equations. It has been shown by Staeckel ( Crelle, 

 band 1 1 1 ) that the most general transformation, which converts a 

 general homogeneous linear differential equation of order m > i 

 into another of the same form and order, is 



where /(I) and <^(|) are arbitrary functions of |. If m = i the 

 most general transformation is 



•*■ =/(!). J = *(l)'?^ (-'^ a constant).. 



The present paper considers a system of linear differential 

 equations, and finds the most general transformation which 

 converts such a system into a system of the same order. The 

 transformation thus formed contains T as a special case. 

 Staeckel's method is adopted in essence. The author is 

 working at a theory of invariants of such systems, based on 

 this general transformation. — Distribution of the ternary linear 

 homogeneous substitutions in a Galois field into complete sets 

 of conjugate substitutions, by L. E. Dickson, and the following 

 paper, " Distribution of the quaternary linear homogeneous sub- 

 stitutions in a Galois field into complete sets of conjugate sub- 

 stitutions," by T. M. Putnam, are in continuation of a memoir 

 by the former writer in vol. xxii. (pp. 121-137). — On the 

 determination and solution of the metacyclic quintic equations 

 with rational coefficients, by J. C. Glashan, is a tardy fulfilment 

 of a promise made in vol. vi. p. 114. — E. O. Lovett contributes 

 a construction of the geometry of Euclidean M-dimensi(mal 

 space by the theory of continuous groups. — A table of class 

 numbers for cubic fields, by Legh W. Reid, is calculated with 

 a view to furnishing for the general algebraic number fields an 

 amount of number material sufficiently great to be of use in the 

 further study of these fields, and in particular in that of the 

 cubic fields. It gives for each of 161 cubic number fields the 

 class number, h, the discriminant A, a basis, and the factorisa- 

 tion of certain rational primes into their prime ideal factors. 

 The method is founded upon a theorem of Minkowski's. In 

 every ideal class there is an ideal, |, whose norm, «(|), satisfies 

 the condition 



«(i) < (i 



v/z 



where m is the degree and A the discriminant of the field, and r 

 the number of pairs of imaginary fields found among the m 

 conjugate fields, ^<'*, /■(-'), ... /^(™). The writer refers to Hilbert, 

 " Bericht uber die Theorie der Algebraischen Zahlkorper " ; 

 Minkowski, "Geometric der Zahlen," and Woronoj, "The 

 algebraic integers, which are functions of a root of an equation 

 of the third degree " (translation of Russian title). The tables 

 lake up ten pages.— On certain properties of the plane cubic 

 curve in relation to the circular points at infinity, by R. A. 

 Roberts, contains an investigation of some methods of generating 

 a plane cubic curve.— With this opening number is presented an 



NO. 1635, VOL. 63] 



excellent portrait of Dr. George Salmon, and a supplement 

 gives a still more excellent one of Prof. Mittag Leffler. — Prof. 

 Frank Morley is the editor in chief. 



Bulletin of the American Mathematical Society, January. — 

 Prof. Lovett gives an account of the proceedings at the Inter- 

 national Congress of Philosophy, which was held at Paris on 

 August 1-5, 1900, and furnishes resumes of the papers read and 

 the discussions occasioned by them, so far as they .bore, more or 

 less directly, upon mathematical questions. The sketch is 

 founded upon the account printed in the September (1900) num- 

 ber of the Revue de Mitaphysique et de Morale. It occupies 

 pp. 157-183. — A demonstration of the impossibility of a triply 

 asymptotic system of surfaces, by Dr. Eisenhart, was read before 

 the Society on December 28, 1900. It is a notelet founded 

 upon Bianchi's Lezioni. — Pfof. E. W. Brown writes short notices 

 of Berry's " Short History of Astronomy " and of H. Suter's 

 " Die Mathematiker und Astronomen der Araber und ihre 

 Werke." This latter, though only a catalogue of over five 

 hundred names of mathematicians and astronomers, and so at 

 first sight not giving promise of much interest, is really, as 

 Prof. Brown shows, a work of considerable interest. He illus- 

 trates this statement by a few extracts. — There are a fair amount 

 of notes and new publications. 



SOCIETIES AND ACADEMIES. 



London. . 



Physical Society, February 22. — Prof. S. P. Thompson, I 

 president, in the chair. — A paper on how air subjected to X-rays ' 

 loses its discharging property, and how it discharges electricity, 

 by Prof. Emilio Villari ( Hon. Fellow), was read by the chair- 

 man. Air made active by X-rays in passing through a long tube 

 coiled in many turns loses much more of its discharging power 

 than it does in passing through the same tube if straight. 

 During this process the tube charges itself to a certain 

 potential. If active air is allowed to stream on masses of wire 

 gauze or wound up ribbons, enclosed in tubes, the metals, inde- 

 pendent of their nature, take a positive or negative charge 

 according to whether the active air rubs against them with force 

 or lightly. Experiments have been performed to prove this. 

 For instance, tubes of copper or lead, if short and straight, take 

 negative charges, but if long and coiled they take positive 

 charges. These phenomena cannot be attributed to chemical 

 actions, but seem to be produced by a special rubbing of the 

 active air upon metallic surfaces, as the result of which they 

 assume one of the charges, and the other charge ought to 

 manifest itself in the air. This is not the case, the charge of the 

 air being ofcen of the same kind as that of the metals. It has 

 previously been shown by the author that active air by streaming 

 against an electrified body is reduced either to ordinary air or to 

 air charged with the electricity which disappears. Hence it may 

 be supposed that the active air in rubbing upon the metallic sur- 

 faces develops the two electricities, one of which manifests itself 

 upon these surfaces, and the other goes to reduce the active air 

 to ordinary air, and therefore does not become manifest. The 

 electroscope used in the experiments consisted of a fixed brass 

 plate and a gold leaf whose position was determined by means 

 of a telescope with an eye-piece scale. — The chairman said he 

 had observed the fact that metals were charged sometimes 

 positively and sometimes negatively by active air. Mr. 

 Watson asked if any experiments had been performed 

 on the viscosity of gases rendered active by X-rays. — 

 A paper on the propagation of cusped waves and their relation 

 to the primary and secondary focal lines, by Prof. R. W. Wood, 

 was read by Mr. Watson. This paper is a discussion of the 

 reflexion of a plane wave by a hemispherical mirror, the reflected 

 wave being likened to a volcanic cone. The cusp of the 

 wave, or the rim of the crater, traces the caustic and is con- 

 tinuously passing through a focus. This accounts for the 

 increased illumination along the caustic. The wave fronts were 

 drawn by constructing the orthogonal surface, which in section 

 is an epicycloid. The evolute of this curve is the caustic, and 

 the reflected wave fronts form a family of parallel curves which 

 are the involutes of the caustic. The wave front bet ween two 

 focal lines is expanding along one meridian and contracting along 

 a meridian at right angles to it ; in other words, the wave is 

 convex along one meridian and concave along the other. The 

 outer slope of the volcanic cone representing ihe reflected wave 

 corresponds to the portion of the wave front between the focal 



