SECTIONAL TRANSACTIONS.— A. 315 



Monday, September 5. 



Presidential Address by Prof. E. T. Whittaker, F.R.S., on The 



Outstanding Problems of Relativity. (Seep. 16.) 



Prof. P . Deb ye. — The Polar Properties of Molecules. 



Dr. W. Kolhorster. — Some Experiments on Penetrating Rays. 



Prof. J. J. Nolan. — Ionization in the Lower Atmosphere. 



Afternoon Lecture by Prof. R. Whiddington, F.R.S. — Luminous Dis- 

 charge in Rare Gases. 



Department of Mathematics. 



Prof. S. Brodetsky. — The Equations of the Gravitational Field in Two and 

 in Three Dimensions of Space-Time. 



Experience has shown that in order to deduce gravitational fields in fewer than 

 four dimensions of space-time care has to he taken to avoid obtaining what is merely 

 a Galilean field. This question is discussed in regard both to the original equations 

 of the gravitational field and to the modified form recently suggested by Einstein. 



Tuesday, September 6. 



Prof. C. G. Barkla, F.R.S. — The Coherence of X-rays and the J pheno- 

 menon. 



Dr. F. W. Aston, F.R.S. — A New Mass Spectrograph and the Whole Number 

 Rule. 



Prof. E. N. Da C. Andrade. — Note on a Molecular Theory of Liquid 

 Viscosity. 



Mr. D. Brown and Dr. E. F. Brett. — Secondary Emission from Metallic 

 and Metallic Oxide Targets. 



Reports of Committees on Tides, Upper Atmosphere (see p. 255), and 

 Earth's Gravitational Field. 



Department of Mathematics. 



Prof. W. E. H. Berwick. — The Arithmetic of Cubic Number-Fields. 



It was known as far back as Euclid's time that every whole number can be 

 decomposed, in just one way, into a product of prime factors. When a renewed 

 interest began to be taken in mathematics, after the Renaissance, interest was again 

 directed to the science of whole numbers. One of the first steps taken was the 

 enlarging of the conception of the term ' number ' by introducing first a root of unity 

 and secondly a quadratic surd into the field of operations. The general stage was 

 reached by considering the system of numbers containing, in any arithmetical 

 combination, an assigned algebraic irrationality. It was soon seen that there was 

 a difficulty in defining the integral elements of such a system of numbers. No 

 definition, in fact, could be constructed permitting every integer of an algebraic 

 field to be uniquely expressed as a product of similar prime factors. The next step 

 was the widening of the conception of the integral elements to render factorisation 



