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The work describe in this thesis is concerned with the vapour-phase pyrolysis of sulphonate esters resulting in 1,3-elimination with or without rearrangement. This process is seen as going through a seven-membered transition state as in (1): the C--O and C--H bonds that cleave are coplanar while the C--C bond that migrates from the intermediate carbon is anti-periplanar to both. In order to test how rigid are the steric requirements for elimination to proceed, other systems have been pyrolysed in the course of this work. This thesis describes the pyrolysis of the two epimeric 2-noradamantyl mesylates (2) and (3) giving triaxane (4) and brendene (5), and the epimeric 10-protoadamantyl mesylates (6) and (7) giving adamantane (8) and the olefin (9). The cis-ggamma-deuterium kinetic isotope effect in the pyrolysis of 2-adamantyl esters has been investigated. This thesis describes the synthesis of (10), (11), and (12) and the analysis of the products obtained from their pyrolysis. Two methods were used for analysing the partially labelled protoadamantene (14) and dehydroadamantane (13) products obtained from the pyrolyses, namely, g. c. m. s. and 13C n. m. r. spectroscopy. The results thus obtained indicate that the pyrolyses do not go through a simple concerted mechanism as depicted in (1). The pyrolysis of (11) and (12) gave products with the same deuterium content, indicating an ion-pair intermediate causing an epimerisation of the ester function prior to or during pyrolysis. The subsequent elimination with or without rearrangement then proceed stepwise. A deuterium isotope effect is not observed for fission of the gamma-C--H bond, so that this process presumably plays no part in the rate determining step.

This thesis describes a new method of measuring dielectric constants and loss tangents using an open resonator. The dielectric constant measurement method consists basically of perturbing the resonant frequency of an open resonator by placing a dielectric sample at the centre of the resonator normal to its axis. By measuring the resonant frequency of a symmetrical mode and of the adjacent lower-frequency asymmetrical mode, the dielectric constant can be determined. Based on the Gaussian beam theory, a pair of transcendental equations, one for each mode, are derived by assuming first the surfaces of the dielectric sample are spherical and coincident with the phase fronts of the resonator modes. These equations can easily be solved for the refractive index n, by using a computer. When sample in sheet form is measured, the results can be corrected to account for the error so introduced. The formula giving this correction is derived by using the perturbational technique. From these two equations, two sets of approximate formulas are also derived for the determination of the dielectric constant. An important feature of these formulas is that they are algebraic expressions, but reduction in their accuracy occurs if the sample is nearly a multiple of half wavelengths thick. The loss tangent is determined by the measurements of Q of the perturbed and the unperturbed resonator. Based on the usual definition of Q, an algebraic-expression is derived relating the loss tangent to the experimentally measurable quantities. Measurements of dielectric constants and loss tangents of polystyrene and perspex have been made at X-band frequencies and the results are presented. It is on these results that the accuracy of ±0.25% for measuring dielectric constant is claimed. The accuracy of the loss tangent measurement is estimated to be about ±10%. The method is applicable to the measurements of both low-loss and high-loss materials, and becomes more accurate at shorter wavelengths.

This thesis describes an experimental and theoretical investigation of the stresses and deformations in a square-based pyramidal-sheet roof. Four perspex pyramids were tested, and one beam of five perspex pyramids and one of seven pyramids. A larger steel model of seven pyramids was also tested to give a better idea of the behaviour of the thin metal structure. Single pyramids were loaded at the apex, and strains and deflections measured when the base was fixed and simply-supported. Deflection measurements were taken with perspex trusses. The stress distributions in a pyramid of the steel truss and its base plate were obtained from strain measurements; the position of this pyramid in the span being varied. Deflect-ions of the truss were also measured. The theoretical work was divided into three parts, (i) an approximate method was used to calculate the deformations of single pyramids and trusses. In this method, an equivalent skeletal system was used to replace the actual structure. (ii) the stress distributions in a single pyramid having its base simply-supported and fixed and subjected to a vertical load at its apex were calculated. In both cases, the walls were considered as plane stress problems having certain assumed boundary conditions. (iii) an approximate method for calculating the buckling load limits of a pyramid was suggested. The pyramid wall was treated as a trapezoidal plate uniformly compressed along its two parallel edges. The calculated deflections for the five exploratory models and the steel truss compared well with measured values. The theoretical stress distributions in the simply-supported pyramid were close to the experimental distributions but were lees accurate in the fixed pyramid. The buckling load calculated for a pinned trapezoidal plate compared well with that obtained from test on one of the exploratory models.

This thesis is concerned with the beneficiation and agglomeration of standard grade chromite concentrate with low chromium:iron ratio by a sequence of processes including pelletizing of the finely powdered concentrate, selective reduction of the iron oxide by carbon and removal of iron by leaching with acid. Fundamental principles which control or influence the various stages of the process were examined and are appraised here, k process of pelletizing fine chromite concentrate was evolved with a laboratory pelletizing drum. The following variables affecting the pelletizing process were investigated: (1) Seeding of the load in the drum (2) Moisture content of the feed and seeds (3) Loading of the drum (4) Drum diaaeter and drum velocity (5) Rolling time. The mechanisms deduced from these observations are Sintering and reduction of the pellets were examined and the influence of various binding agents on this process was investigated. Reflected light microscopy and I-ray microradiography were used to elucidate the mechanism of sintering and to detect textural and laineralogical changes in the agglomerates. The relationship between sintering temperature, amount of reducing agent incorporated and efficiency of removing iron by leaching are explained.

This thesis reports a study of the quantization of generally covariant and nonlinear field theories. It begins by reviewing some existing general theories in Chapter 2 and Chapter 3, Chapter 2 deals with general classical theories while Chapter 3 examines various quantization schemes. The model field derived from the Lagrangian density ℓ = 1/4 ℇ[super]lkμλ (A [sub] k,t – A [sub] k,t)(A, {sub{ A[sub]μ,λ – A[sub]λ,μ). is proposed in Chapter 4 especially for the study of general covariance. It is demonstrated that for this field general covariance alone does not appear to bring in anything physically new, a discussion is given on the differences between general covariance and Lorentz covariance. In subsequent chapters a generally covariant and nonlinear model field, a 4-surface of stationary 4-volume embedded in a 5-dimensional Pseudo-Euclidean space, is investigated. Firstly a manifestly covariant quantization programme is carried out. The model field is then examined in a special coordinate frame for the study of its nonlinearity. Various treatments of the intrinsic nonlinearity are examined starting with conventional perturbation theory in Chapter 6. The usual divergence problem in quantum field theory appears, in particular in the self-energy calculation of a one-particle state. A new variational method is proposed in Chapter 8 which is able to lead to finite results for one-particle states. The thesis is concluded with a chapter discussing some general problems involved and a chapter containing suggestions for further work.