ii8 



ATA TURH 



[November 26, k 



analogous to Bezout's rule for forming the eliminant of 

 two quantics in one independent variable. — The Dirichlet 

 series and the asymptotic expansion of integral functions 

 of zero order : J. E. Littlewood. — The norm curves on 

 a given base : Prof. F. Morley. — The arithmetical nature 

 of the coeflicients in a group of linear substitutions 

 (third paper) : Prof. W. Burnside. — The conformal 

 transformations of a sp.ice of four dimensions and 

 their applications to geometrical optics : H. Bateman. 

 — Periodic properties of partitions : D. M. Y. Sommer- 

 wille. — The solution of integral equations : Prof. A. C. 

 Dixon. — Note on the continuity or discontinuity of a func- 

 tion defined by an infinite product : G. H. Hardy. — The 

 energy and momentum of an ellipsoidal electron : F. B. 

 PiddMck. — (i) q-Integration ; (2) q-transformations of 

 power series : Rev. F. H. Jackson. — The complete solu- 

 tion in integers of the Eulerian equation X''-|-Y' = U'-|-V* : 

 Dr. T. Stuart. — Waves of finite amplitude: W. J. 

 Harrison. — .An asymptotic formula for the generalised 

 hypergeometric series: T. J. I'.A. Bromwich. — Satellite 

 curves of a plane cubic : A. C. O'Sullivan. 



Royal Meteorological Society, November iS. — Dr. H. R. 



Mill, president, in the chair. — Investigation of the electrical 

 state of the upper atmosphere, made at the Howard Estate 

 Observatory, Cilossop : W. Makower, Miss M. White, 

 and E. Marsden. There e.\ists under normal atmospheric 

 conditions a potential gradient in the atmosphere surround- 

 ing the earth. The earth being negatively charged with 

 respect to the air, a continuous electric current flows from 

 the upper atmosphere to the earth. It follows, therefore, 

 that a kite attached to an earth-connected wire will tend 

 to assume the potential of the air surrounding it, and an 

 electric current will flow continuously down the wire to 

 earth through the wijiding machine to which the wire is 

 attached. The experiments described in the paper were 

 undertaken with the view of determining the magnitude 

 of this current when the kite was at different heights 

 above the ground. The authors found that in general a 

 high wind produced at a given altitude an abnormally 

 high value of the current flowing down the wire. Whether 

 the action of the wind is to be accounted for by the greater 

 volume of air which passes in a given time over the sails 

 of the kite, so giving a greater volume of air from which 

 electricity is collected, or whether the action of the wind 

 is to be attributed to electrification by friction, the authors 

 find it difficult to say, but there is no question that the 

 velocity of the wind does play an impmrtant part in deter- 

 mining the current flowing down the kite wire. In further 

 confirmation it may be added that observations made with 

 a captive balloon in very calm weather gave abnormally 

 low values for the current. — Balloon observations made ,it 

 Birdhill, co. Limerick, during July and August, iqoS : 

 Captain C. H. Ley. These observations were carried 

 out on behalf of the joint kite committee of the Roval 

 Meteorological Society and of the British .Association. 

 Captain Ley in this paper gave full details of the observa- 

 tions made on twenty-five pilot balloons, seven of which 

 carried registering instruments. The method employed is 

 similar to that known by surveyors as the subtense 

 method, that is, obtaining the range of a known vertical 

 bar by_ observation of the angle subtended bv it at the 

 theodolite with an eye-piece micrometer. In this case the 

 bar is the line joining a hydrogen balloon and a com- 

 paratively heavy air-filled balloon, and the balloons appear 

 as discs to be bisected simultaneously bv the fixed and 

 movable wire in the diaphragm. Several balloons were 

 observed to a horizontal distance of twentv-four miles. 

 Two of the balloons dropped in the river Shannon ; these 

 were sent up in exceptionally calm atmosphere, and Cap- 

 tarn Lry considers that the river had a suction effect upon 

 them. The immediate neighbourhood of stratus or cirrus 

 cloud appears to cause a co!!ap.5e of vertical velocity, and. 

 generally speaking, the highest horizontal velocity of wind 

 appears to occur below the cirrus level. .A feature 

 developed during the course of the experiments was the 

 observation of the balloons at night by means of naked 

 acetylene lights. After some trouble these proved quite 

 successful, gave long runs with less risk of being lost 

 in small clouds, and afforded points of light which could 

 be observed on with gri-.-it accuracy. 



NO. 2o,-;g, VOL. 79] 



Institution of Mining and Metallurgy, November 19. — 

 Mr. .Alfred James, president, in the chair. — Notes on tin 

 dressing : H. W. Hutchin. A record of investigations of 

 dressing operations conducted at South Crofty Mine with 

 the view of determining the losses incurred in tin dress- 

 ing and their nature. The ground covered embraced 

 mainly the first stage of concentration, in preparing con- 

 centrates for the calciner, and comprised a systematic in- 

 vestigation of the battery tailings. The range of the 

 present inquiry was, however, restricted to tin alone of 

 all the metallic constituents, and in this connection the 

 author had collected a mass of valuable data resulting 

 from experiments with different grades of crushing and 

 difi'erent modes of treatment. — Working costs on mines, as 

 practised on the Rand : J. A. Dennison. In this paper, 

 which was originally submitted to the standardisation 

 sectional committee of the institution dealing with mine 

 accounts and cost sheets, the author reviews the practice 

 of the Rand with the object of seeing to what extent 

 it is capable of standardisation in itself and as a guide 

 to other localities. His brief is in favour of standardising 

 general principles and systems rather than details, and of 

 securing the utmost simplicity consistent with a clear and 

 full statement of accounts. — A manganese deposit in 

 southern India : R. O. Ahiers. A description of the 

 manganese deposits in the native State of Sandur, Bellary 

 district, an elliptical basin composed geologically of a bed 

 of the Dharwar (.Archjean) series of schistose rocks, which 

 is surrounded by gneiss, the predominating rock in that 

 part of India. Iron and manganese are intimately 

 associated in the Sandur deposits, which, though of large 

 extent on the surface, go but a short distance in depth. 

 The author inclines to the theory that these ore bodies 

 are the result of metasomatic action, a replacement of 

 the original rock by oxides of manganese and iron, by the 

 agency of meteoric waters. — Extinguishing the fire in the 

 Testasecca Mine, Sicily : F. C. Chrambach. .A brief 

 description of the method adopted in dealing with an 

 incendiary outbreak in a sulphur mine in Sicily, the opera- 

 tion being greatly assisted by the employment of the West- 

 phalia " rescue " apparatus, Avhercby the working party 

 was enabled to penetrate and carry on its labours in the 

 highly vitiated air of the undergroimd sections. 



Manchesier. 

 Literary and Philosophical Society, Oriober 20. — 

 Prof. H. B. Dixon, F.R.S., president, in the chair. — 



Further notes on the separation of cobalt .and nickel : 

 R. L. Taylor. 1 he author referred to a former paper in 

 which he described a modification of Rose's method 

 (barium or calcium carbonate in presence of chlorine or 

 bromine). In that paper he pointed out that various con- 

 ditions caused a remarkable retardation in the precipita- 

 tion of the cobalt. He now proposes the use of magnesium 

 carbonate instead of calcium or barium carbonate, and 

 finds that with this there is practically no uncertainty in 

 the action. — Some questions connected with the constitu- 

 tion of the atom : H. Bateman, It is shown that a con- 

 tinuous succession of infinitesimal conformal transforma- 

 tions of space can be derived by steroographic projection 

 from a figure on a hypersphere which moves as a rigid 

 body in .a space of four dimensions. I'his gives ten 

 degrees of freedom, so that the model atom would have 

 at most ten degrees of freedom. It is suggested that the 

 number of degrees of freedom possessed by an atom in 

 given circumstances is equal to three /)!ii5 the valency 

 exhibited in those circumstances. When two atoms are 

 in a state of chemical combination there is, in general, a 

 loss of three degrees of freedom for a single bond and 

 five degrees of freedom for a double bond. By means of 

 this rule it is possible to calculate the number of degrees 

 of freedom of a molecule. In the case of a molecule con- 

 sisting of several atoms there are additional restrictions 

 due to the atoms arranging themselves at equal distances 

 from one another or in a plane. The ratio of the specific 

 heats calculated from the numbers 11 obtained in this 

 way and the formula 7 = 1+2/11 agree with the results 

 of observation. — A collection of fossil insects from 

 Shiobara, Japan, collected by Dr. Marie Stopes : C. 

 Gordon Hewitt. In the collection there were a large 

 nimiber of the aquatic larv^ of ephemerids. There were 



