Summary. The variation of the chromosome number within a systematic group obeys fixed laws. These laws seem to be different in the plant and animal kingdoms. Polyploidy plays a major part in the plant kingdom; it is rare in the animal kingdom. Fragmentation of the chromosomes is frequent in the animal kingdom, and it is this which constitutes the principal method of evolution of the chromosome garnitures. In many cases all the elements of the chromosome garniture are divided simultaneously each into two fragments, so that the number of chromosomes is doubled. The arrangement resulting from this process of fragmentation strikingly brings to mind the arrangement brought about by polyploidy. Several examples of this are given in Section IV. The augmentation of the chromosome number seems nearly always to go along with the evolution and the specialization of the phylum. Most of the cases in which compound heterochromosomes have been observed, made up of two or more distinct elements, are met with in forms in which there has occurred a bipartition of the whole or of the greater part of the chromosome stock. This shows that the process of fragmentation relates both to the heterochromosomes and to the autosomes. The heterochromosomes usually react en bloc after the manner of a single element, but exceptions exist (Tegenaria domestica). Dimcious polyploids, in animals and plants alike, are rare. The list of known cases is given in Section III. (a). Among unbalanced polyploids, triploids in particular, one of the sexes (the heterozygous sex) is intersexual or sterile. However, exceptions to this rule exist (Trichoniscus elisabethæ, Antennaria carpathica), which are a sign of the appearance of the process of stabilization. The method of disjunction of the sex genes is particularly interesting to follow in polyploids:— Very rarely the segregation occurs according to the laws of chance. This is met with only among some experimental polyploids (Sphærocarpus Donnellii). Very generally segregation does not follow laws of chance, but it has been proved that certain types of segregation are favoured compared with others (Rumex acetosa, Drosophila). These cases are understandable for, by a progressive regulation, the recent polyploids have been able to produce stabilized polyploids of the type of those which make up natural species, and among which the distribution of the sexes occurs absolutely regularly. Disjunction appears in certain polyploids quite regularly (Empetrum hermaphroditum); this is an example of perfect regulation. The most extreme case of regulation is that in which the polyploids possess only one pair of heterochromosomes. Several explanations which are able to account for these conditions are given.

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