When two or more sex-linked factors are present in a male they are always transmitted together to his daughters, as must necessarily be the case if they are carried by the unpaired X chromosome. If such a male carrying, let us say, two sex-linked factors, is mated to a wild female, his daughters will have one X chromosome containing the factors for both characters, derived from the father, and another X chromosome that contains the factors that are normal for these two factors (the normal allelomorphs). The sons of such a female will get one or the other of these two kinds of chromosomes, and should be expected to be like the one or the other grandparent. In fact, most of the sons are of these two kinds. But, in addition, there are sons that show one only of the two original mutant characters. Clearly an interchange has taken place between the two X chromosomes in the female in such a way that a piece of one chromosome has been exchanged for the homologous piece of the other. The same conclusion is reached if the cross is made in such a way that the same two sex-linked characters enter, but, one from the mother and the other from the father. The daughter gets one of her sex chromosomes from her mother and the other from her father. She should produce, then, two kinds of sons, one like her mother and one like her father. In fact, the majority of her sons are of these two kinds, but, in addition, there are two other kinds of sons, one kind showing both mutant characters, the other kind showing normal characters. Here again the results must be due to interchange between the two X's in the hybrid female. _The number of_ {8} _the sons due to exchange in the two foregoing crosses is always the same, although they are of contrary classes._ Clearly, then, the interchange takes place irrespective of the way in which the factors enter the cross. We call those classes that arise through interchange between the chromosomes "cross-over classes" or merely "cross-overs." The phenomenon of holding together we speak of as linkage. By taking a number of factors into consideration at the same time it has been shown that _crossing-over involves large pieces of the chromosomes_. The X chromosomes undergo crossing-over in about 60 per cent of the cases, and the crossing-over may occur at any point along the chromosome. When it occurs once, whole ends (or halves even) go over together and the exchange is always equivalent. If crossing-over occurs twice at the same time a middle piece of one chromosome is intercalated between the ends of the other chromosome. This process is called double crossing-over. It occurs not oftener than in about 10 per cent of cases for the total length of the X chromosome. Triple crossing-over in the X chromosome is extremely rare and has been observed only about a half dozen times.