Diagram illustrating the behavior of the _x_-element or sex-chromosome in the maturation of the sperm-cell. In one of the two maturation divisions (represented here as in the first) it passes undivided to one pole (_a_, _b_, _c_), in the other it divides. Since the cell without the _x_-element also divides the result is that ultimately from the original primary spermatocyte (_a_) four cells are formed (_f_), two with the _x_-element and two without it. Half of the spermatozoa therefore will bear an _x_-element, half will be without it. In _a_ the ordinary chromosomes, arbitrarily indicated as 10, are supposed to have already paired for reduction so that the original diploid number in spermatogonia and body-cells of the male would be 20 plus the _x_-chromosome.] It has been found, furthermore, that in species in which the males possess this extra element the females have two of them. That is, if the original number in the somatic cells of the male were twenty-three, twenty-two ordinary and one _X_-element, the number in the somatic cells of the female would be twenty-four, or twenty-two ordinary and two _X_-elements. It has been found that when the chromosomes of the female pair for the reduction division, each chromosome uniting with its corresponding fellow, the two _X_-elements in the female pair in the usual way so that every egg-cell possesses an _X_-element. Thus every mature egg has an _X_-element, while only half of the spermatozoa have one. That is, if we assume twenty-three as the diploid number present originally in the somatic cells of the male and twenty-four as the number in the female, then one-half the spermatozoa of the male would contain the haploid number eleven, and the other half, the number twelve, whereas every mature ovum would contain twelve. Since there are equal numbers of the spermatozoa with the _X_-element and without it, and inasmuch as presumably under ordinary conditions one kind is as likely to fertilize the egg as the other, then there are equal chances at fertilization of producing a zygote with two _X_-elements or with but one. Thus, Spermatozoon + _X_ by Ovum + _X_ = Zygote + _XX_. Spermatozoon (no _X_) by Ovum + _X_ = Zygote + _X_. We have already seen that the former is always female, the latter male. It thus becomes possible to distinguish the sex of an embryo by counting the chromosomes of its cells. This has been accomplished in several cases. In some instances[1] the conditions may be much more complex than the ones indicated--too complex in fact to warrant detailed discussion in an elementary exposition--but the principle remains the same throughout, the very complexity when thoroughly understood, strengthening rather than weakening the evidence. In a few forms an interesting reversal of conditions has been found in that the eggs instead of the spermatozoa show the characteristic dimorphism.