Experiments in diffraction microscopy, previously described, are here continued. Special emphasis is now laid on verifying the theory by the production of an “artificial” hologram, by non-diffractive means, from data calculated for a relatively simple object. The assumed object is then reconstructed in the usual apparatus.

A type II linear zone plate of limited width is studied as a particular case of an artificial hologram. It gives rise to an unexpected black artefact, which is explained by a detailed analysis of this particular zone plate, and is shown to be due to its limited extent.

Experiments on twisting the linear zone plate skew to the reconstructing beam show that the effective focal length is affected astigmatically by a factor proportional to cos2θ, where θ is the angle of twist, for lines parallel to the axis of twist. Lines perpendicular to the axis of twist are unaffected.

The production of a hologram in an astigmatic pencil and its subsequent reconstruction while skew to a parallel beam is described. It is found that the focal length differences can be corrected in this way, but that the lateral scale factors are only partially rectified.

Since taking up a temporary appointment at the Sir John Cass College, the author has had the opportunity of checking the artificial hologram discussed in the main paper on a non-recording microphotometer. The result is interesting in demonstrating both the points of agreement between the actual and theoretical holograms, and the points where the technique of production has failed.

The division of one polynomial by another is studied with the object of ascertaining the errors produced in the coefficients of successive remainders by small errors in the coefficients of the divisor. It is shown that the matrix which effects this transformation of errors is a polynomial in the rational canonical matrix for which the divisor polynomial is characteristic. The theory gives rise to a numerous class of iterative processes for finding an exact factor, such as the extant method based on the penultimate remainder, Bairstow's iterative method of finding a quadratic factor, and many others. Some new suggestions are made for accelerating convergence.

Analytic solutions of the functional equation f[z, φ{g(z)}] = φ(z), in which f(z, w) and g(z) are given analytic functions and φ(z) is the unknown function, are investigated in the neighbourhood of points ζ such that g(ζ) = ζ. Conditions are established under which each solution φ(z) may be given as the limit of a sequence of functions φn(z), defined by the recurrence relation φn+1(Z) = ƒ[z, φn{g(z)}], the function φn(z) being to a large extent arbitrary.

In very olden days chemists did not forgather merely as chemists; they merged themselves in broader organizations such as the Royal Society. The “chemical revolution”, which had its real beginning with the work of Joseph Black and which culminated in the overthrow of the phlogiston theory by Lavoisier, aroused for the first time a popular interest in the special science of Chemistry. Until recently, world priority among the chemical societies that resulted therefrom was by general agreement conceded to the Chemical Society of Philadelphia, founded by James Woodhouse in 1792. The distinguished chemical historian Edgar F. Smith (I), late Provost of the University of Pennsylvania, may be quoted in this connection:

A study is made of the propagation of elastic and plastic deformation in a thin plate, initially unstressed, and of infinite extent, when it is penetrated normally by a cone moving with uniform velocity. The work is an extension of unpublished researches by Sir G. I. Taylor on the corresponding problem for a thin wire, and a summary of his results is included.

The relaxation technique of R. V. Southwell is developed to evaluate mixed subsonic-supersonic flow regions with axial symmetry, changes of entropy being taken into account. In the problem of a parallel supersonic flow of Mach number I·8 impinging on a blunt-nosed axially symmetric obstacle, the new technique is used to determine the complete field downstream of the bow shock wave formed. Lines of constant vorticity and Mach number are shown in the field, and where possible a comparison is made with the corresponding 2-dimensional problem.

A derivation is given of a sum rule which may be useful in the discussion of line intensities of molecular spectra.

Since the delivery of my presidential address (1) in July I have assembled an amount of supplementary information regarding “the Chemical Society instituted in the beginning of the Year 1785”. This, together with a brief description of some other chemical societies of the revolutionary period, forms the basis of the present paper.

First of all, it will be expedient to furnish a complete list of the dissertations read before the Society during 1785–86 and included in the first volume of its Proceedings, appending short comments with respect to the communicators or their topics when anything of special interest arises.