I found here that the nucleus was hollow, or, better, that it showed a clear space within. For a long time it contains the many chromatin granules, as seen in figs. 39, 40, and 41; but at last the walls seem to attract all these granular masses, and the center is entirely clear, as in fig. 45. In fig. 44 are shown cross-sections of spermatozoa heads, of the stage of fig. 43. In fig. 45 we have a mature spermatozoon head. The _accessory chromosome_ in _Gryllus_ lags behind during the spermatogonial divisions, just as in _Xiphidium_ (McClung, ’99), and retains its identity all through the growth period, in many cases becoming quite large. At first it cannot be distinguished in the spermatid, but soon its stronger stain and exemption from disintegration make it apparent. (Fig. 4.) It is flattened against the nuclear wall and, unlike Paulmier’s “small chromosome,” it does not break up but remains intact, as Henking and McClung have described. (Figs. 14, 18, 32, 37, and others.) It gets larger and then smaller, and is finally lost in the rest of the chromatin, as the latter condenses to form the spermatozoon head. I was not able to see that it occupied one side of the elongating head, as McClung describes it in _Xiphidium_. The darker stain and regular contour, and sometimes its greater size, made it in most stages quite evident. (_b_) CYTOPLASMIC STRUCTURES. It is in the cytoplasmic structures that _Gryllus_ shows some things that have not been described, so far as I know; yet I almost hesitate to enter the discussion concerning the nebenkern, the mitosome, the idiozome, the archoplasm, the attraction sphere, the acrosome, the “mitochondrion körper” and other bodies which have been described in the extra-nuclear parts of the germ-cell. But because I have been unable to find in any of the papers a description of a structure like the one in _Gryllus_, I shall proceed to describe the nebenkern as I find it. I shall interpret the appearances as far as possible, leaving to others, or to later efforts, the complete harmonizing of this element with the structures of other species. Before I proceed, I would add my protest against the name “nebenkern,” as voiced by Calkins (’95), Erlanger (’96), Meves (’00), and others. It is inapt and not at all descriptive or distinctive. But since we have the word, and investigators will use it to mean something, I think it would be best to restrict the word, as Calkins and Erlanger suggest, to the remaining spindle fibers and connective fibers which go to each spermatid and which have an important part in forming the tail membrane. I shall retain the name for a further reason, which St. George (’97) gives for first using it, “weil sie die Frage nach der Herkunft dieses Gebildes offen lässt.” A comparison of the literature will convince any one that the origin of this element is still a much-disputed question. 1.—_Nebenkern._