SECTIONAL TRANSACTIONS. 



SECTION A.— MATHEMATICAL AND PHYSICAL 



SCIENCES. 



Thursday, September 1. 



(Communications on Textiles, received at special sessions, will be found on p. 411 seq.) 



(For references to the publication elsewhere of communications entered in the 

 following list of transactions, see p. 430.) 



Prof. K. A. Millikan. — The Relations between the Spectra emitted by the 

 Atoms of the First Row of the Periodic Table in all Stages of Ionization. 



Mr. A. C. Menzies. — Regularities in Fuse Spectra. 



Dr. W. Heisenberg. — Recent Progress in Quantum Mechanics. (Followed 

 by Discussion. Mr. R. H. Fowler, F.R.S., Dr. H. T. Flint and 

 others.) 



Mr. H. Jones. — Electron Impacts. 



Department oi Mathematics. 

 Prof. H. W. Turnbull. — Non-commutative Algebra. 



The fundamental laws of algebra which provide axioms of the subject can be 

 dealt with much in the same way as those of geometry. Experience has shown that 

 the surrender of the law axb=bxa for multiplication leads to interesting results, 

 notably in the theory of matrices and of (^-numbers. The finite matrix, as discovered 

 by Cayley, is a powerful symbol in discussing such questions as orthogonal trans- 

 formations and (what is nearly the same thing) those of the restricted relativity in 

 physics. The infinite matrix, which has many properties in common with the finite, 

 introduces other possibilities also, which it shares with the g'-number. For example, 

 the formula 



pq—gp= constant 



is impossible for the Cayley matrix, but possible for the infinite matrix if certain tests 

 for divergency are satisfied. Differentiation can be extended in at least two ways to 

 functions of variables in this non- commutative field. Dirac has discovered one type 

 of differentiation which has immediate place in quantum physics. Another type 

 yields results more directly applicable to functions of a finite matrix. 



Friday, September 2. 



Joint Discussion with Section B on The Structure and Formation of 

 Colloidal Particles. (See p. 317.) 



Report of Committee on Seismological Investigations. (See p. 215.) 



Dr. C. R. Davidson. — The Determination of Stellar Temperatures. 



Department of Mathematics. 



Prof. W. P. Milne and Mr. F. P. White. — Noether's Canonical Curves. 



Noether has shown that the general plane curve of genus p can be represented 

 point by point on a curve of degree 2p — 2 in space of p — 1 dimensions. The object 

 of the communications is to describe as far as possible the fundamental properties 

 of the Canonical Curves for p=3, 4, 5, 6. 



