In the location of genes affecting quantitative characters in Drosophila, Thoday has made extensive use of a technique of examining the products of crossovers between tester chromosomes and those from selected lines. The paper considers the validity of inferences which can be drawn from such experiments. The multiplicity of possible models makes this difficult and some efforts have been made, simulating results from given known situations. It seems probable that the shape of the final conclusions would be in terms of the power of the method to discover groups of genes, covering a certain length of chromosome and with a given sum total of effects.