Methods of analysing genotype-environment interaction were extensively reviewed by Freeman (1973) and Hill (1975). A large number of papers involving such analyses have been published since then, some of them providing new methods, particularly of the multivariate type.While making no pretensions to be a comprehensive review, the present paper attempts an examination of some of these new techniques. It also offers a critique of some established methods, while pointing out others which have been neglected. The methods considered include the linear regression approach and related stability parameters, cluster analysis, principal components analysis, geometrical methods and stochastic dominance.In all these methods, environments are measured by the mean value of the genotypes grown in them: a case is made for research into the use of environmental variables. LINEAR REGRESSION AND RELATED STABILITY PARAMETERSIn earlier times, methods of analysing genotypeenvironment interaction were associated with the linear regression approach. This was first introduced by Mooers (1921) and was given prominence by Yates and Cochran (1938), who used the mean performance of all genotypes grown in an environment as a suitable index of its productivity.The performance of each genotype was plotted against this index for each environment, and simple linear regression fitted by least squares to summarise the genotype's response, the mean regression slope being 1O.An identical technique was used by Mandel (1959) and Mandel and Lashofl (1959) to compare the results of tests on a number of materials at several different laboratories. The use of this approach as a basis for an analysis of variance and associated tests of hypotheses was discussed by Mandel (1961), who showed it to be an extension of Tukey's one degree of freedom for non-additivity (Tukey, 1949; Scheffe, 1959, pp 129-134 genotypes, he removed a component with t-1 degrees of freedom from the interaction sum of squares. This component represents the sum of squares for heterogeneity of t regression slopes and Mandel proved that if the slopes are identical, it is distributed as chi-squared and is independent of environmental effects. Thus an F-test can be made of the existence of different genotype slopes, the null hypothesis being that the slopes are all the same. Finlay and Wilkinson (1963) used the regression technique in examining the yield stability of various barley genotypes, although they claimed that better fits were obtained with logtransformed yields. In assessing stability, they considered that simply comparing regression slopes was not enough: the overall yield level of a genotype also had to be taken into account. The slope of the regression line for each genotype was, accordingly, plotted against its mean yield over environments. Genotypes with a slope near 10 and a high mean yield were regarded as being well adapted to all environments. As mean yield decreased, genotypes with high or low slopes were regarded as being specifically adapted to favourable or unfavour...

The synthesis of a dual offset reflector system with uniform aperture phase is formulated using mathematically exact equations under the assumptions of geometrical optics. We demonstrate the existence of numerical solutions to problems of practical significance. The key to the numerical method is the ability to solve the Mongc-Ampcre equation as a boundary value problem. It is shown that the complexity of the analysis is no greater than that involved in single reflector synthesis and both reflectors are produced simultaneously. IntroductionThe synthesis of offset dual reflectors under the assumptions of geometrical optics has received much attention recently. Impetus for this work has been derived from satellite communications, radio astronomy and radar where the flexibility of the offset configuration can remove blockage to the output aperture by the subreflector whilst minimising crosspolarisation effects. An exact study of the ray geometry of general dual reflector systems based upon the assumptions of geometerical optics was given by Brickell and Westcott [1] where the authors considered arbitrary aperture phase and power patterns and derived some basic equations. These were applied [2] to obtain an exact analytical solution to the problem of shaping a dual offset system, fed by a linearly polarised conical horn, to produce uniform phase and zero crosspolarisation on the aperture. The aperture shape was governed by the solution and was therefore an output property of this study.The problem of synthesising a system when the size and shape of both feed and output apertures are prespecified, as well as the output aperture phase and amplitude distributions, has received particular attention recently.Most authors deal with a special case, important to antenna designers, in which the feed pattern phase is spherical and the output phase is uniform over a plane aperture. However, the uncertainty [3] surrounding the existence of exact solutions to the problem in the general case seems to have generated a number of methods [4-6] which depend initially on ad hoc assumptions whose justification can only come from their results. At least one paper [5] claims that the problem is insoluble being over specified so that some of the conditions must be relaxed to obtain solutions. We shall show that this is unnecessary.In fact the problem can be formulated using mathematically exact equations and numerical solutions are possible in a number of important cases. In this paper we give the exact formulation and demonstrate the existence of numerical solutions to the problem in which rays within a symmetrical feed cone with tapered power pattern are mapped through two reflections onto a circular output aperture over which the phase is uniform and the power is arbitrarily specified.The exact formulation leads to a nonlinear second-order partial differential equation of the Monge-Ampere type. We have solved [7,8] such an equation in dealing with the synthesis of single reflectors fed by a point source and the method is adapted here to...

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SUMMARYThe major genes for dwarfism in Norm 10 wheat, Rht 1 and Rht 2 are located on chromosomes 4A and 4D. The gene for extreme dwarfness from Tom Thumb, Rht 3, is located close to, or is allelic with Rht 1 on chromosome 4A. An F2 telocentric mapping technique has been employed to locate these genes by using their gibberellin insensitive phenotype. Gai/Rht 1 and Gai/Rht 3 were estimated to be 13 map units from the centromere on the arm of chromosome 4A and Gai/Rht 2 15 map units from the centromere on the long arm of chromosome 4D. These results suggest that the genes are part of a homoeoallelic series.