August i6, 1900] 



NATURE 



3S1 



Heligoland), R. D. Abell, B.Sc. (University of Leipzig), 

 W. Caldwell, B.A. (University of Wiirzburg), W. B. McLean, 

 B.Sc. (Owens College, Manchester), B. D. Steele, B.Sc. 

 (University of Breslau), E. J. Butler, M.B. (University of 

 Freiburg), [. W. Mellor, B.Sc. (Owens College, Manchester), 

 L. N. G. Filon, M.A. (King's College, Cambridge). Four 

 scholarships granted in 1898 have been e.xceptionally renewed 

 for a third year. These scholars and their places of study are : — 

 Dr. A. H. Reginald Buller, B.Sc. (University of Munich), H. T. 

 Calvert, B.Sc. (University of Leipzig), R. L. Wills, B.A. 

 (Cavendish Laboratory, Cambridge), E. H. Archibald, M.Sc. 

 (Harvard University). 



SCIENTIFIC SERIALS. 



American journal of Mathematics, vol. xxii. No. 3. — 

 On continuous binary A linearoid groups, and the corresponding 

 differential equations and A functions, by E. J. Wilczynski. In 

 a previous paper (vol. xxi. 2) the writer has shown that, cor- 

 responding to every group of the form 



2 <^rt 



ar)yk(.\). 



where the r parameters ai are essential, there exists a 

 system of differential equations of order r, whose general solu- 

 tions are given by (i), if j'l, . . . y'n form a fundamental system. 

 The functions <^,k were supposed to be uniform functions of x, 

 and it was found that, if the parameters a, were properly chosen, 

 (pit were uniform functions of the parameters also. In the 

 present paper he discusses these groups, the corresponding 

 differential equations, and their solutions for the case when 

 n = 2. Dr. Lovett, in his note on a property of lines in «- 

 dimensional space, working on the lines of Cesaro's " Lezioni di 

 Geometria Intrinseca," shows that a line of multiple curvature cuts 

 its osculating space of highest dimensions, or lies wholly on one 

 side of that space, according as the number of dimensions of 

 the space necessary to the existence of the curve is odd or even. 

 — Concerning the cyclic sub-groups of the simple group G of all 

 linear fractional substitutions of determinant unity in two non- 

 homogeneous variables with coefficients in an arbitrary Galois 

 field, by Dr. L. E. Dickson (read before the Chicago section of 

 the Mathematical Society, December 1899), leads to a generali- 

 sation to the GF[/"] of results due to Prof. W. Burnside (" On 

 a Class of Groups defined by Congruences," Proc. of London 

 Math. Soc, vol. xxvi. ). Variations from Burnside's method of 

 treatment are introduced, partly to avoid the separate treatment 

 of the cases d= I and ^= 3, and to take in the exceptional cases 

 / = 2 and p — 2, and to reduce the calculations ; and further, on 

 the other hand, to amplify some of the proofs. A few errors are 

 also pointed out and amended. — On some invariant scrolls in 

 collineations which leave a group of five points invariant, by V. 

 Snyder. The writer gives numerous references to memoirs in 

 which the qnadric surfaces which are left invariant by cyclical 

 collineations have been exhaustively treated. There is another 

 simple series of scrolls, viz. those contained in a linear con- 

 gruence, which have not been considered, except one form 

 noticed by Ameseder. The writer confines his attention to 

 such surfaces. There are six collineations which are of essen- 

 tially different type, which project a set of five points into 

 themselves without leaving every point invariant. In the nota- 

 tion of substitution-groups these may be thus represented : 



T3=(AiA2)(A3)(A,)(A5), 



T3=(A,A^)(A3A4)(A5), 

 T, = (A,A2A3)(A,)(Ag), T.,=(A,A2A3)(A,A5), 

 T«=(AiA2A3A,)(A5) and T7 = (AiA2A3A4Ag). 



— On the reduction of hyperelliptic integrals (/ = 3) to elliptic 

 integrals by transformations of the second and third degrees, by 

 W. Gilespie. The point of the paper is an application of cubic 

 involution to the problem of the reduction to elliptic integrals, 

 of hyperelliptic integrals of genus / = 3 and of the first kind, by 

 a rational transformation of the third degree. It is a continua- 

 tion of Prof. Bolza's researches on the cubic transformation ( " Die 

 Cubische Involution und Dreitheilung, &c. ," and " Zur Reduction 

 Hyperelliptischer Integrals, &c.," Math. Ann., Bd. 50, pp. 68 

 and 314). — The closing paper, by Dr. E. H, ^Ioore, was read 

 before the American Mathematical Society at the Buffalo meeting 

 of the summer of 1896, and is entitled "The Cross-ratio Group 



NO. 1607, VOL. 62] 



of n ! Cremona Transformations of Order « - 3 in Fiat Space of 

 « - 3 Dimensions." 



Bulletin of the American Mathematical Society, July. — 

 Some remarks on tetrahedraU geometry, by Dr. Timerding, is a 

 paper read at the June meeting. Several properties of a tetra- 

 hedral complex are given, viz. the pole curves of such a complex 

 of lines form again another such complex among the cubic space 

 curves circumscribed about the fundamental tetrahedron, the 

 complex curves of such a complex of lines form another tetrahe- 

 dral complex, &c. — Prof. H. B. Newson's paper on singular 

 transformations in real projective groups was read at the April 

 meeting. It treats of transformations in real projective groups 

 which can not be generated from the real infinitesimal transforma- 

 tions of certain continuous groups. The discussion, which is 

 limited to one and two dimensions, can be readily extended to 

 three and higher dimensions.— Miss Schottenfels, in a paper 

 read at the June meeting, writes on groups of order 8!/2, and 

 gives a simple proof of a correspondence established by Dr. 

 Dickson (/'/-oc. of London Math. Soc, vol xxx.). — Prof. F. S. 

 Woods continues his notes on Lobachevsky's geometry, — Prof. 

 Pierpont reviews H. Burkhardt's " Functionen-theoretische 

 Vorlesungen " (vol. ii. " EUiptische Functionen "). — A " correc- 

 tion," notes, new publications, list of papers read before the 

 Society, with references to the places of their publication, and 

 a full index, complete the sixth volume of the second series. 



Annalen der Physik, No. 7. — Dispersion of electricity in air, 

 by J. Elster and II. Geitel. Sincethe sun's rays contain ultra- 

 violet light before they impinge upon the atmosphere, this light 

 must ionise the upper strata, and the ions produced will be 

 gradually distributed through the whole of the atmosphere by 

 diffusion and convection. Hence the atmosphere will contain 

 stray ions of both signs, but chiefly negative ones in the lower 

 strata, owing to their superior mobility. The presence of these 

 ions can be made evident by an electroscope. — Influence of 

 slight impurities upon the spectrum of a gas, by P. Lewis. Very 

 small quantities of hydrogen and nitrogen considerably affect the 

 spectra of helium and argon, but the reverse is not the case. — 

 Fluorescence and phosphorescence in the electric discharge 

 through nitrogen, by P. Lewis. When nitrogen prepared fronrb 

 ammonium nitrate and sulphate, and purified over hot copper is 

 pumped through an H-shaped vacuum tube, the whole wall of 

 the tube shows a brilliant fluorescence lasting a few seconds, 

 which extends for a length of about a yard into the supply 

 and exhaust tubes. The light can be made permanent by keep- 

 ing the pump at work and thus supplying a continuous stream of 

 fresh nitrogen. Spectroscopic examination shows that the 

 fluorescence is dependent upon the presence of a number of 

 bands in the extreme ultra-violet, due to a combination of nitro- 

 gen with a trace of oxygen. — Production of very high notes by 

 (ialton's whistle, by M. T. Edelmann. The author gives tables 

 for the pitches of pipes of various dimensions, and instructions 

 how to test the pipes by Kundt'sdust figures. He has succeeded 

 in constructing a pipe of only 2 mm. diameter, which gives the 

 enormously high pitch of 170,000 complete vibrations per second, 

 or over two octaves beyond the extreme limit of audibility. — The 

 magnetic force of the atoms, by R. Lang. Magnetishi is 

 accounted for by the revolutions of negative about positive 

 electrons. — The air thermometer at high temperatures, by L. 

 Holborn and A. Day. The authors further investigate the pro- 

 perties of the air thermometer consisting of a platinum -rhodium 

 vessel filled with nitrogen, and compare its indications with that 

 of a platinium-iridium thermo-couple, paying particular attentioa 

 to their regular expansion of the vessel. The corrected value for 

 the melting point of gold is 1064-0° C— Difference of tempera- 

 ture between the surface and the interior of a radiating body, 

 by F. Kurlbaum. A method is given of determining this 

 difference of temperature by means of two bolometers exposed 

 symmetrically to different surfaces of the same black partition. 



SOCIETIES AND ACADEMIES. 



London. 

 Royal Society, June 14.—" Data for the Problem of 

 Evolution in Man. V. On the Correlation between Duration 

 of Life and the Number of Offspring." By Miss M. Beeton, 

 G. U. Yule, and Karl Pearson, F.R.S., University College, 

 London. 



