340 SECTIONAL TRANSACTIONS.— A. 



Department of Mathematics. 



19. Dr. A. M. OsTROWSKi. — A General Theorem on Zeroes of Functions 



connected by a Linear Relation. 



20. Prof. W. R. VON Dyck. — On Graphical Algebra. ' 



21. Prof. V. VoLTERRA. — Mathematical Problems in Competitive Popu- 



lation. 



Tuesday, August 10. 



22. Prof. M. Born. — The Quantum Mechanics of Electron Collisions. 



23a. Prof. W. WiEN. — On the Direction of Electrons emitted by the Photo- 

 electric and Compton Effect. 



It is well known that the number of photo-electrons expelled by polarised Rontgen 

 Tays has its highest value in the direction of the electric force of the incident wave. 

 This result is in accordance with the electro-magnetic theory of light. 



On the other hand, the emission of electrons by the Compton effect is a quite 

 different phenomenon. Kirchner has made observations by stereoscopic photographs 

 made of the tracks originated by Compton electrons in a Wilson case. By the 

 stereoscopic observation it is possible to settle the direction in space of the electrons. 

 Kirchner found that the number of electrons has its maximum at right angles to the 

 ■jlectric vector. Though this result can be derived from the geometrical constella- 

 tion, it seems paradoxical, because the classical theory shows no force at all in that 

 direction. 



23b. Prof. W. WiEN. — On the Asymmetry and Intensity of Spectral Lines 

 split in the Electric Field connected with the Direction of Impacts 

 originating the Emission of Light. 



The Balmer lines of canal rays, split by the Stark effect, show a remarkable 

 asymmetrj' of intensity, which is reversed with the field. In some recent new work 

 Wierl has shown that, if the observation is made in a high vacuum, the asymmetry 

 disappears. Therefore the asymmetry is effected by collisions of the moving atoms. 



If canal rays of hydrogen are shot in a vessel fiUed with nitrogen, one has only 

 moving atoms of hydrogen. Then one finds an asymmetrical intensity. If canal 

 rays of nitrogen are going in hydrogen, the asymmetry is opposite, the impact on 

 the hj'drogen atoms having now the opposite direction. 



This result shows that only the direction of the impact in relation to the direction 

 of the field is responsible for the asymmetry of the lines. The asymmetry does not 

 last any appreciable time, for it vanishes if the atoms pass after the coUisions into 

 a high vacuum. 



24. Mr. R. d'E. Atkinson. — On the Mechanism of Light Emission from 



Atoms. 



25. Prof. L. Vessot King. — The Gyro-magnetic Electron. 



A charged sphere in rotation was shown by Maxwell as long ago as 1870 to give 

 a uniform internal field, and an external field equivalent to that of a magnetic doublet. 

 The writer has considered the problem of determining the fields due to a spinning 

 electron moving with uniform velocity v making any direction with the axis of spin, 

 taking into account the deformation or contraction of the electron boundary into an 

 ellipsoid of axes a and a(I — ii'Vc^)*, the short axis being in the direction of motion. 

 Regarding this as a real, physical deformation, the energy of the electrostatic and 

 magnetic fields, internal and external, separates into two terms, one translational, 

 the other due to components of spin (wiCOitOa). The final result is 



T=mc2+i(Acoi2+BcOi2-l-Cw,,2)+constant (1) 



