July 2, 1908J 



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graphy described in the present paper is of special interest 

 owing to the facility with which it is possible to change 

 over Irom one system to the other, thus, from the ordinary 

 vertical antenna system to the bilateral directive or the 

 unilateral directive, or vice versa. The aerial arrange- 

 ments, moreover, remain exceedingly simple. When a 

 message from a station of unknown position is expected, 

 the vertical antenna or ordinary system would be employed ; 

 on once effecting reception, one can pass to the bilateral 

 or unilateral directive system, and thus determine the 

 direction and on which side the transmitting station lies, 

 at the same time making oneself independent of other 

 transmissions. In the same way, with the transmission, 

 the vertical antenna would be employed for calling up an 

 unknown station or for simultaneously sending to several 

 stations ; on getting a reply the operator can readily 

 determine the position of the receiving station, with 

 the aid of the unilateral system, and thenceforth will 

 transmit solely in that direction. — The lateral vibration 

 and deflection of clamped-directed bars : Dr. J. Morrow. 

 This is an investigation of the problems which arise in 

 connection with the lateral vibrations of clamped-directed 

 bars. The term " directed " is used to describe the 

 e.Ktremity of a bar which is constrained to maintain its 

 original direction, but is free to take up any position of 

 lateral deflection. These terminal conditions are mentioned 

 in Rayleigh's " Sound," but are dismissed on the ground 

 that the directed end cannot be realised experimentally. 

 In the present paper, however, it is shown that the 

 " directed " end is of great importance and of frequent 

 occurrence in engineering practice, and, further, that by 

 the aid of a simple device it can easily be investigated 

 in the laboratory. — The resistance of ' a conductor of 

 uniform thickness whose breadth suddenlv changes, and 

 on the shape of the stream-lines : Prof. C. H. Lees. A 

 knowledge of the resistance of a conductor the section of 

 which suddenly changes is of considerable practical import- 

 ance, but mathematical difficulties have prevented an exact 

 solution of the problem. The paper shows that the resist- 

 ance betw-een two transverse sections through points 

 situated at considerable distance from the change of 

 section on opposite sides of it is equal to the sum of the 

 resistances of the portions of conductor between each of 

 the two sections and the change of section, each considered 

 as part of an infinite length, plus the resistance of a length 

 of either conductor equal to its breadth multiplied by an 

 expression given. — The inductance of two parallel wires : 

 Dr. J. W. Nicholson. When direct and return currents 

 flow in two wires of great length, and the alternation is 

 not rapid, the efl'ective self-induction per unit length of 

 the system may be calculated readily by simple integration. 

 I \i the wires have radii a, h, and permeabilities n, i>, and 

 if C be the distance between their axes, 



L = 2 log c'lab + l{fi + v). 



(This formula is often of little practical use when the fre- 

 quency of alternation is several thousands per second. 

 Such frequencies are of constant use in practical work. 

 For example, in the measurement of small inductances bv 

 Mr. Campbell's method, it is necessarv to employ long 

 leads in order to keep them at some considerable distance 

 from the bridge and other circuits. The self-induction of 

 these loads must be small, and a calculation of its value is 



ivery desirable. The general case presents very great 



• mathematical difficulty, but the solutions given in the 

 paper appear to include most cases of practical utility.— 

 Homogeneous secondary radiation : Dr. Barkia and Mr. 

 Sadler.— (i) Note on 'the amount of water in a cloud 

 formed by expansion of moist air ; (2) an elementary treat- 



[tnent of the motion of a charged particle in a combined 

 I Mic and magnetic field: Prof. Morton. 



I Dublin. 



Royal Irish Academy, Mav ii. — Dr. F. A. Tarleton, 

 president, in the chair.— .A synopsis of Irish alga;, fresh- 

 water and marine: J. Adams. After an historical account 

 of past investigations on Irish algae, and the various 

 attempts to divide the countrv into botanical districts, 

 .there follow complete lists of the genera and species, and 

 'their geographical distribution in each of the four provinces 

 is briefly indicated. For facility of reference the genera 



and species belonging to each of the main groups of algje 

 are arranged in alphabetical order. In all, 2224 species 

 are included, 1379 species being fresh-water and 845 species 

 marine. A summary of the total species recorded for each 

 province is given, followed by a brief description of the 

 local distribution of the rarer or more interesting species. 

 At the end is a bibliography in which all known sources 

 of information on the distribution of Irish algje are 

 indicated. 



May 25. — Dr. F. A. Tarleton, president, in the chair. — 

 Some unpublished work of the late Prof. Charles J. Joly, 

 F.R.S., on geometry, part i. : Rev. W. R. Westropp 

 Roberts. The author discusses curves, both plain and 

 twisted, by expressing the coordinates of such curves in 

 terms of a parameter, and deduces from this point of 

 view the nature of their singularities. — Some general prin- 

 ciples of the theory of dimensions : E. E. Fournier 

 d'Albe. The author discusses the methods of discovering 

 relations between physical quantities by means of their 

 dimensions. He shows that when the quantity investi- 

 gated is purely mechanical, and expressible in terms of 

 length, mass, and time, it can depend upon not more than 

 three independent variables, which are also purely 

 mechanical quantities. When the number of fundamental 

 units is increased, as by adding angle, temperature, or 

 electric quantity, the number of independent physical 

 variables is increased in proportion. The attempts to 

 account mechanically for forces acting at a distance by 

 means of dimensional formulae are criticised. 



Paris. 

 Academy of Sciences, June 22. — M. H. Becquerel in the 



chair. — Study of the phenomena shown by concave wings 

 in the stationary, floating, and hovering flight of birds : 

 Marcel Deprez. A calculation of the horizontal and 

 vertical components of the forces resulting from fdie action 

 of air in motion on the surfaces of wings, supposed 

 curved. The formula arrived at contains no other experi- 

 mental condition than the mass of unit volume of air, 

 thus dispensing with the empirical coefficients commonly 

 employed. — M. Gaillot was elected a correspondant in the 

 section of astronomy, in the place of the late M. Trepied. 

 — The analysis of polymorphic curves : Emile Borel. — 

 The orientation of an anisotropic ellipsoid in a uniform 

 field : Georges Meslin. — The nature of charges of positive 

 electricity and the existence of positive electrons : Jean 

 Becquerel. The recent work by the author on the 

 magneto-optic phenomena of the rare earths over a wide 

 scale of temperature leads to the view that positive electrons 

 exist ; Lilienfeld has also obtained phenomena which he 

 attributes to positive electrons, but these results have been 

 negatived by Bestelmeyer and Marsh. In the present paper 

 an account is given of experiments with a modified form 

 of Crookcs's tube. The results confirm the hypothesis of 

 the existence of positive electrons. — The photographic 

 registration of sound vibrations : Georges and Gustave 

 Laudet. These photographs, which were obtained by 

 purely mechanical means and without the aid of a micro- 

 phone, are distinguished by the clearness of the line pro- 

 duced. Reproductions of the vowels and the sibilants s 

 and = and of the word Laudet are given. No details are 

 given of the method employed. — The relation between the 

 biochemical effects of radiations and the quantity absorbed : 

 H. Guilleminot. In studying the biochemical effects of 

 the X-rays, it is more important to make quantitative 

 measurements on the energy absorbed in the material than 

 to measure the energy of the incident bundle. Fluoroscopic 

 measurements of the incident rays show great divergences 

 between the biochemical effects of the X-rays and the 

 radium rays ; these discrepancies disappear when the 

 amount of energy really absorbed in the two cases is 

 studied. — The heat of neutralisation of acetic and benzoic 

 acids by aniline in benzene solution : L^o Vignon and M. 

 Evieux. .'\niline docs not react to form salts with acetic 

 and benzoic acids in benzene solutions. Aniline benzoate 

 and acetate are destroyed by solution in benzene. — .\ new 

 method of separation of silica and tungstic anhydride : Ed. 

 Defacqz. At a red heat silica is not reduced by hydrogen, 

 whereas tungstic anhydride is readily reduced to lower 

 oxides under the same conditions. The latter are readily 

 removed by heating in a current of chlorine, forming 



NO. 2018, VOL. 78] 



