278 SECTIONAL TRANSACTIONS.—A*. 
ideal metal; conductivity ; thermoelectric phenomena; the transverse 
effects in a magnetic field. Meaning of the sign of the Hall coefficient. 
Next stages in the elaboration of the theory. Electron states in a periodic 
field of force. Brillouin’s zones. Metals as insulators and semiconductors. 
Prof. C. G. Darwin, F.R.S.—The quantum theory of the free path 
(10.50). 
The formal free path of Sommerfeld’s theory is replaced by a properly 
calculated free path by studying the interaction between the electron waves 
of an ideal metal and the elastic waves (thermal agitation) of the ionic lattice. 
Bloch’s integral equation for the distribution function. 
Dr. H. Jones and Prof. N. F. Motr.—Further developments of the 
theory (11.20). 
The form of the Brillouin zones for a number of crystal structures asso- 
ciated with well-known metals and alloys is discussed and illustrated. ‘The 
significance of the form of these zones in relation to the structure is described 
with particular reference to the case of bismuth, and alloys possessing the 
characteristic y and « structures. From these considerations a theoretical 
basis is found for the well-known Hume-Rothery electronic rules. The 
nature of the X-ray emission bands of metals discovered by O’Bryan and 
Skinner is discussed in the light of the Bloch theory. This leads to an 
examination of the optical transition probabilities from the conduction levels 
of the metal to the deep-lying K or L levels. A brief account of the optical 
properties of the alkali metals, including Zener’s explanation of Wood’s 
recent experiments, is given. 
Finally, the electrical resistance of pure metals with reference to their 
place in the periodic table is discussed, and it is shown how the observed 
resistance of alloys leads to a better understanding of the resistance of pure 
metals. 
Prof. G. P. THomson, F.R.S. 
Friday, September 7. 
Discussion on Unified field-theories in physics (11.0) : 
Prof. E. T. WuitTaker, F.R.S.—The problem and some recent pro- 
posals for its solution. 
The problem to be solved. The earlier theories of Weyl, Eddington, 
Einstein, and Kaluza-Klein, compared with the more recent developments 
by Einstein-Mayer, Veblen, and Schouten-van Dantzig. Introduction of 
the fifth coordinate. Interpretation of the coordinates (i) in five- 
dimensional space, (ii) in four-dimensional space-time. Geodesics as 
world-lines of charged and uncharged particles. Interpretation of curva- 
ture. Deduction of the field-equations of gravitation and electricity. 
Dr. W. H. McCrea.—Unified field-theories and the quantum theory 
(11.50). 
The formulation of Dirac’s wave equation in projective relativity ; the 
physical significance of the result. Discussion of the general a priori 
possibility of including quantum theory in existing unified field-theories. 
