Among the lower Crustaceans also parthenogenesis plays a large rôle, and in many species it even occurs as the sole mode of reproduction, but more often--as is also the case among insects--it occurs alternately with bi-sexual reproduction. For parthenogenesis must not be regarded as asexual reproduction, but rather as _unisexual_, that is, as arising from sexually differentiated individuals (females), and from germ-cells (true ova), but brought about by the agency of individuals of only one sex, the female. These parthenogenetic eggs emancipate themselves, so to speak, from the law that was previously regarded as without exception, that all ova require fertilization to enable them to develop. That this law admits of many exceptions is now universally admitted; thus in the small family of water-fleas (Daphnids) there are even two kinds of eggs, the summer and winter eggs we have already mentioned, which are produced by the same female, and yet the former kind develop without fertilization, while the latter require to be fertilized before they can develop. It was obviously important to learn the state of affairs in regard to reducing divisions in parthenogenetic ova, to find out whether here also, three, or, in some circumstances, two polar bodies were formed, and whether the second polar division reduced the number of chromosomes to half. If the theory previously advanced as to the importance of the chromatin, and especially of the reducing effect of the second maturing division be correct, we should expect the second division to be wanting in parthenogenetic eggs, since otherwise the number of chromosomes would be reduced to half in each generation, and would thus gradually disappear or sink to one. Having directed my attention to this problem, I succeeded in establishing for a Daphnid, _Polyphemus_, that the second polar division does not occur, and that only one polar body is formed. Blochmann found the same in the parthenogenetic eggs of plant-lice or Aphides, in which, moreover, the eggs requiring fertilization exhibit, like the winter eggs of Daphnids, two polar divisions. It was thus established that at least those eggs of Aphides and Daphnids which are wholly parthenogenetic retain the full number of chromosomes of their species, as is represented in the diagram, Fig. 78. When parthenogenesis set in the polar divisions were limited to one, and that this could happen justifies us in concluding _a posteriori_ that it could have happened also in the case of ova which required fertilization if that had been necessary or even merely indifferent. The polar divisions are thus not mere 'vestigial' processes; they have an immediate significance, and it lies in the reduction of the number of chromosomes.