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The investigation of the properties of groups of homozygous lines by meand of diallel crosses as proposed by HULL (1945) has subsequently been discussed in growing detail in a series of papers by JINKS and HAYMAN (1953 and later). With certain assumptions, the genetic variation present can be described in terms of the biometrical concepts of MATHER (1949) and accurate estimates obtained of the additive, dominance and environmental components. The distribution of genes in the parents is also revealed. The important result of these papers is that the diallel table of results can be tested (by the uniformity ofWr-V,) for conformity to the biometrical model before applying the model to the description of the genetic variation present. The genetic systems controlling many characters do not fit this simple model and it is the purpose of this article to study more general genetic systems using new methods and more generations. This paper concerns parental, F, and F, data and contains an investigation of gene correlation in the parents together with some consideration of linkage and parental heterozygosity. Data from diallel crosses in maize and cotton will be discussed by kind permission of those who conducted the experiments. Reference to HAYMAN (1954b) is by section number prefixed by H.

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