i April 30, 1908J 



JVA TURE 



23 



Morth. — The triazo-group, part iii., bistriazo-derivativcs of 

 { thane and of acetic ester : M. O. Forster, H. E. Fierz, 

 ) ind W. P. Joshua. 



■• Physical Society, April lo.— Dr. C. Chree, F.R.S., 

 presideiil, in the chair. — .\n experimental investigation of 

 the nature of 7 rays : Prof. W. H. Brags and Mr. 

 Madsen. The view that the 7 rays are not ether pulses, 

 but are material and consist of neutral pairs of one nega- 

 tive with one positive electron, developed in previous 

 'papers {PMl. Mag., October, 1907), is held to be estab- 

 'lished by the experiments described in this paper with the 

 secondary radiation produced by the 7 rays of radium. — 

 Experiments on artificial fulgurites : Miss D. D. Butcher. 

 The first part of the paper deals with natural fulgurites, 

 and the second with the production of artificial fulgurites. 

 The experiments show : — (i) The tubes are formed by 

 ,' fusion of the powder which surrounds the column of air 

 ( in which the spark passes. The length and thicliness of 

 the tube depend on the energy of the spark, and also on 

 the character of the spark, i.e. whether it is unidirectional 

 or oscillatory. (2) There is no appreciable difference in 

 the two ends of a tube provided that the two electrodes are 

 jlike. When 3ne electrode is a point and the other a flat 

 pl.ite, any branching that may occur will be towards the 

 plate, whichever electrode is made positive. In nature, the 

 I flit plate would be represented by the moist lower strata 

 of the soil. Therefore we cannot say from the character 

 of the tube whether the lightning discharge was from a 

 positive or negative cloud. (3) The difference between 

 thick and thin tubes is due probably to a difference in the 

 I sharpness of the flash and the resulting explosive effect. 

 c\\'hen the explosive effect is great and the quantity of 

 1 material melted is small, the result will be a large-bored, 

 tthin-walled tube. Whether this remains circular or be- 

 'comes pressed together and distorted depends merely on 

 1 whether the fused matter has time to cool before the out- 

 ward pressure of the blowing has been overcome by the 

 inward pressure on the surrounding sand or not. In 

 nature, the damp sand or soil probably acts as the damp 

 string in these experiments, and consequently causes many 

 lightning discharges to be unidirectional. In the experi- 

 mental tubes the outward pressure was so great, and the 

 quantity of fused material so small, that the walls were 

 broken through and left as a mere network. — Short-spark 

 phenomena : W. Duddell. The paper deals with two 

 elTects which the author has observed in connection with 

 some measurements of the current in the secondary circuit 

 of an induction-coil. The apparatus in use consisted of a 

 12-inch Nevi'ton induction-coil, which was supplied from 

 the 200-volt direct-current mains. A large resistance was 

 placed in series with the primary of the coil to limit the 

 current, and the current was interrupted by means of a 

 mercury-jet interrupter. The secondary circuit contained 

 a galvanometer to measure the mean current, and a 

 thermo-ammeter to measure the root mean squared current. 

 \\'hen there was no spark-gap in the secondary circuit 

 and the coil was in action, the mean current, as read by 

 the galvanometer, was zero, and the root mean squared 

 current about 38 milliamperes. If, now, a microscopic 

 spark-gap, say between two aluminium points, was intro- 

 duced into the secondary circuit, two curious effects took 

 place. Firstly, the R.1VI..S. current enormously increased 

 in value, and, secondly, a very large deflection w-as pro- 

 duced on the galvanometer in the direction corresponding 

 to that due to making the primary circuit. The introduc- 

 tion of a spark-gap i/io mm. long caused the R.M.S. 

 current to rise to 38-5 milliamperes, and this continued to 

 increase with increasing length of spark-gap until it 

 reached a maximum with a gap about 1-4 mm. The 

 author thinks that this effect is due to very high frequency 

 oscillations set up in the wires connected to the secondary 

 circuit of the coil when a spark-gap is introduced. He has 

 observed the effect with brass, iron, zinc, and aluminium 

 electrodes, but the latter metal is the best to use. 



Mathematical Society. April 30.— Prof. W. Burnside, 

 president, in the chair. — A general convergence theorem 

 and the theory of the representation of a function by a 

 series of normal functions : Dr. E. W. Hobson. .\ 

 general convergence theorem is established, which, when 

 applied to series of .Sturm-Liouville functions, suffices to 



NO. 2010. VOL. 781 



show that the question whether the series converges, or 

 not, at a particular point, depends only upon the nature 

 of the function in an arbitrarily small neighbourliood of 

 the point, whilst the nature of the function throughout the 

 whole interval of representation is restricted only by the 

 condition that it must possess a Lebesgue integral in the 

 interval. The theorem is further employed to show that, 

 subject to the same condition as regards the nature of the 

 function, the question whether the series converges 

 uniformly, or not, in an interval in which the function is 

 continuous, depends only upon the nature of the function 

 in an interval which encloses the interval of continuity in 

 its interior, exceeding it in length by an arbitrarily small 

 amount. — The ordering of the terms of polars and trans- 

 vectants : L. Isserlis. Between any two non-adjacent 

 terms T,, T, of a polar or a transvectant a series of 

 terms Tj,,, T,,,, . . . T,,; can be placed so that any term 

 in the series T,, Tj,,, . . . T^,,•, T„ shall be adjacent to 

 the terms on either side of it. In the paper a method is 

 developed for actually ordering all the terms in this way. 

 — Oscillating successions of continuous functions : Dr. 

 W. H. Young. The paper deals with the theory of series 

 which neither converge nor diverge to a definite limit. In 

 such cases the sum function is replaced by two functions, 

 the upper and lower functions of a sequence. The theory 

 of uniform convergence and divergence is extended to 

 scries of functions which oscillate at every point. — The 

 relation between the convergence of scries and integrals : 

 T. J. I'A. Bromwich. It is proved that when <^(.v) tends 

 steadily to infinitv. as x increases, but more slowly than x, 

 the behaviour of the integrals 



/CO r CO 



f\,r) sin ipiA^dx, I f(x) cos ^{x)dx, 



determines the character of the series 



%f(n) sin <p{n), 2.fi.") cos (>>(«V 



— The multiplication of series : G. H. Hardy. — Porisms : 

 H. Bateman. — The influence of viscosity on wave motion : 

 W. J. Harrison. — Informal communications were made 

 as follows: — (i) Mersenne's nurnbers ; (2) Quartans with 

 numerous quartan factors : Lieut. -Colonel A. Cunning- 

 ham. In the first a factor 150287 was reported of the 

 number 2'"-!. This result reduces to 18 the number of 

 Mersenne's numbers (of the form 2'-!) which have not 

 yet been verified, and none of these 18 numbers Contains 

 any factor less than 200,000. In the second it was shown 

 how to construct numbers of the form x' + y*- which shall 

 have any desired number of divisors of the same form. 



Paris. 

 Academy of Sciences, April 27. — M. H. Becqiierel in the 

 chair. — A problem relating to the theory of left-handed 

 curves : Gaston Darboux. — The application of wireless 

 telegraphy to the improvement of meteorological warn- 

 ings : G. Bigourdan (see p. 14). — The zoological 

 relations of the shrimps of the order of Stenopida; : 

 E. L. Bouvier. — Entropy : M. Auric. An expression 

 for entropy derived from the density of the ether, 

 assuming its pressure to represent the absolute tempera- 

 ture. — The ionisation of air by ultra-violet light : Eugtee 

 Bloch. On repeating the original experiments of Lenard, 

 it was found that the greater part of the Lenard 

 effect could be traced to the presence of particles in the 

 gas. When the gas is completely freed from dust, the 

 Lenard effect, if it exists, represents only a small fraction 

 of the effect due to the dust. — The velocity of transport of 

 the ions H, CI, and OH in the electrolysis of solutions of 

 hydrochloric acid : E. Doumer. From the experiments 

 described the author concludes that the ionisation of water 

 takes an active part in the electrolysis' of solutions of 

 hvdrochloric acid, and the velocity of transport of the 

 CI and H ions is sensibly the same. — The detection of 

 helium in minerals containing uranium : F. Bordas. The 

 method described in a previous paper (selective absorption 

 with charcoal at low temperatures) has been applied to 

 numerous minerals containing uranium. Its delicacy is 

 sufficient to detect helium in i milligram to 2 milligrams of 

 broeggerite, liebigite, or asschynite. Minerals containing 



