Irradiation data involve sampling distributions which are binomial and depend on probabilities less than .01. The chi-square test has been shown to be valid for such data even when the expected numbers are as low as 0.5, whereas it is known that the normal theory breaks down under these conditions;New data were obtained on visible mutations at nineteen loci on the first three chromosomes of Drosophila melanogaster. These data were analysed by the chi-square test on the basis of these hypotheses: (1) that the genes within the sets observed have the same basic mutation rate, (2) that the mutation rate at a specific locus is directly proportional to the dosage of radiation applied, (3) that if the sets of genes used are representative of their respective chromosomes, the fundamental rates of mutation on those chromosomes are the same, and (4) that for a particular gene and a fixed dosage, the wave-length of x-ray used does not affect the mutation rate. Our data indicate that the first hypothesis is inadequate to explain the variation observed when the "ct" locus is among those observed, but the other hypotheses fit the data quite satisfactorily;Other sets of data were analysed by chi-square as illustrations of methodology. These data were on the following subjects: (1) continuous versus interrupted irradiation (from Patterson, 1931), (2) reverse mutations (from Timofeeff-Ressovsky, 1932), (3) the production of mutations by heat (from Buchmann and Timofeeff-Ressovsky, 1936), and (4) comparison of mutation rates among the species Drosophila funebris, Drosophila melanogaster, and Drosophila simulans (from Timofeeff-Ressovsky, 1937).