This paper is a modest first step towards establishing a non-linear quantum electrodynamics, that is to say, an attempt at a quantum mechanical description of the electromagnetic field, based on Born's non linear electrodynamics rather than on Maxwell's theory. No great revelations with immediate bearing on experiments can be expected from this first step, which deals with the charge-free electromagnetic field in the first approximation (as regards amplitudes) after the linear Maxwellian case. Yet it is a step necessary for further progress. Covering ground, which in the linear approximation is still entirely trivial, it illustrates well the complexity entailed by this - or any other - non-linear theory and thus, very probably, the true complexity of the problem of quantum electrodynamics.

I am greatly indebted to Professor E Schrödinger for many valuable discussions and suggestions. My thanks are also due to Professor W Heitler, who suggested the introduction of radiation damping.

Very much the same as in the case of Einstein's field-equations of gravitation in empty space, Maxwell's equations likewise admit of a term expressing that the potentials act also as sources of the field-the "cosmical term," as it is usually called. While in the case of gravitation anything but an extremely low order of magnitude of this term is excluded by observation, the widespread 'belief that the corresponding Maxwellian term must be of the same low order, neither rests on direct experimental evidence, nor are there strong theoretical grounds for it.

Its object was to enable those who had no previous acquaintance with relativity or quantum theory to acquire sufficient knowledge of quantum mechanics, quantum electrodynamics and meson theory to understand the main features of the theory of elementary particles.

Some 250 pages offer rather cramped accommodation for the development from introductory wave-mechanics to strange particle theory via quantum electrodynamics. Particularly in the earlier chapters, on Special Theory of Relativity, Introductory Quantum Theory, Wave and Matrix Mechanics, Angular Momentum, Many-particle Systems, the reviewer feels that a reader for whom these chapters are necessary will find parts of the treatment too facile to avoid perplexity. ... One can only regret that the author did not develop part or all of his subject matter much more fully.

In this clearly written concise survey of Sir Edmund Whittaker's writings on the philosophy of physics, the author divides Whittaker's work in this field for convenience into five divisions: neo-Cartesianism, Eddington's principle, determinism and freewill, cosmology, natural theology. With regard to Eddington's Fundamental Theory, the author makes the point that in recent years Eddington's work would have been ignored had not Whittaker focussed attention on it, and he claims that both for this and for pointing out the epistemological defects he has placed both philosophers and mathematical physicists under a debt.

After a few ad hoc words on elementary particles in general, the $SU_{2}$ group is briefly discussed and the notion of a Lie group is introduced. The next five chapters contain a simple, readable account on the general notions concerning semi-simple Lie algebras, their root diagrams, weight diagrams, and the reduction of product representations. Chapter 8 presents a detailed explicit treatment of the $SU_{3}$ group. Chapter 9 is devoted to the 5-dimensional rotation group, and includes mention of the possibility of applying it to leptonic symmetries. The concluding chapter reviews some of the major applications of $SU_{3}$ for strong, electromagnetic, and weak interactions.

The first half of this brochure is devoted to a detailed and elaborate discussion of the weight diagrams of representations of the simple Lie groups of rank two: $A_{2}, B_{2}$ and $G_{2}$. A graphical method is developed for obtaining the multiplicities of the weights in an irreducible representation starting from a dominant weight. In the remainder the author studies representations of the general linear group over the complex numbers, $GL(n, \mathbb{C})$ for $n > 2$, and the reduction of such representations when the group is restricted to a subgroup of rank two.

This book has a dual interest; one, according to the foreword, is to give an exposition of the theory of dielectrics that will guide experimenters to set up the critical experiment to test the substantial body of the theory described here. A second use for the book is to provide probabilists with hard but clearly interesting problems in stochastic differential equations and which call for a more rigorous treatment.

In September 1992, my father died. A couple of days later, I walked down the aisle of the same church to where Fr McConnell was standing at the altar-rail. He wasn't looking very well himself. ... I had taken instructions from him some time before to draft his will and I had presented it to him for execution at the Institute for Advanced Studies on Burlington Road. He bequeathed his intellectual property to 'Propaganda Fidei'. Shortly after my father's death, Fr McConnell's descent into dementia commenced. Unhappy was the day I made an application to the High Court to make this mathematical genius a ward of court and myself guardian of his person and property, including intellectual property. I knew his book had been taught in Princeton, in Beijing, in Cracow. Where else? ... What precisely were my duties in the matter? My responsibility did not last long enough to make answers to these questions an obligation. He died soon after. Responsibility for the management of his property passed to his executor.

James McConnell was a friendly, unassuming and generous man, who was full of vitality and had an infectious enthusiasm for all his undertakings. He was sustained in his late years of failing health by his faith and the devoted care of the Carmelite Sisters for the Aged and Infirm at Our Lady's Manor, Dalkey. Requiescat in pace.