we cannot decide, since we know nothing in either case as to the length of time that parthenogenesis has prevailed among them, nor have we any method of computing the number of generations that must elapse before a superfluous organ begins to vacillate. We only know that the parthenogenetic generations of Aphides no longer possess a receptaculum, while other forms with alternating bi-sexual and parthenogenetic modes of reproduction, which are in this respect possibly more modern, e. g. some of the gall-wasps, possess one similar to that of the Ostracods. [Illustration: FIG. 79 (repeated). The two maturation divisions of the 'drone eggs' (unfertilized eggs) of the bee, after Petrunkewitsch. _Rsp_ 1, the first directive spindle. _K_ 1 and _K_ 2, the two daughter-nuclei of the same. _Rsp_ 2, the second directive spindle. _K_ 3 and _K_ 4, the two daughter-nuclei. In the next stage _K_ 2 and _K_ 3 unite to form the primitive sex-nucleus. Highly magnified.] I must refer to one other case of parthenogenesis, since it has been hitherto regarded as a formidable puzzle for the germ-plasm theory, and has only recently found its solution, I mean the facultative parthenogenesis of the queen-bee. As the 'male' eggs of the bee remain unfertilized, and yet undergo two reducing divisions, which must diminish the number of ids in the ovum-nucleus by a half, the number of ids in the germ-plasm of the bee must be steadily decreasing, and this state of things has therefore been regarded by some English biologists as convincing evidence of the untenability of the conception of ids and of the whole germ-plasm theory. Apparently, indeed, it is contradictory to the theory, and we must inquire whether the contradiction is merely an _apparent_ one, disappearing when the facts are more precisely known. It was mainly on this ground that I instituted the researches carried out by Dr. Petrunkewitsch, the results of which I have already in part communicated in a former lecture. These results confirmed the previous conclusions that the 'male' eggs of the queen-bee remain unfertilized, that two reducing divisions occur, and that in consequence the ovum-nucleus only contains half the normal number of chromosomes. That these increase again by division to the normal number does not save the theory, for only _identical_ ids can arise in this way, while the significance of the multiplicity of the ids lies mainly in their difference. The halving of the number of ids in each 'male' ovum would necessarily lead, if not to a permanent diminution in the number of ids, at least to a monotony of the germ-plasm, since the number of _different_ ids would be steadily decreasing and the number of _identical_ ids as steadily increasing. This too would be a contradiction of the theory. But Dr. Petrunkewitsch's investigations have shown that, of the four nuclei which are formed by the two reducing divisions, the two middle ones (Fig. 79, _K_ 2 and _K_ 3)