Of the insects considered in this paper _Aphis_ and _Termopsis_ have no "accessory chromosome" or "heterochromosome" of any kind. The fact that no males develop from the fertilized eggs of _Aphis_ might be offered as a reason for its absence, but such an argument would not apply to _Termopsis_. The sex-character may indeed be represented in the chromatin of some one of the pairs of paternal and maternal chromosomes of the spermatocytes, but there is no evident peculiarity by which one-half of the spermatozoa can be said to be different from the other half. As to McClung's statement ('02) "that if there is a cross-division of the chromosomes in the maturation mitosis, there must be two kinds of spermatozoa, regardless of the presence of the accessory chromosome," it appears to me that in a case like the aphid, where the paired elements of the five bivalent chromosomes are separated in the first maturation mitosis, there may be as many as seventeen kinds of spermatozoa instead of two. If, however, we suppose that the sex characters are segregated in the first maturation mitosis, there would, of course, be two equal classes of spermatozoa with reference to that character. In _Stenopelmatus_ the element _x_ in certain stages closely resembles the "accessory chromosome" of McClung, and especially that described by Baumgartner for _Gryllus domesticus_, but its origin and fate are different. It first appears attached to an end of the spireme in the growth stage of the young spermatocytes, where it is much smaller than in later growth stages. It gradually increases in size, is a conspicuous element in the first maturation spindle, goes into one of each pair of spermatocytes of the second order, and there degenerates during the rest stage between the two maturation mitoses. The whole history of this element suggests that it may be rejected chromatin analogous to that observed in the ovogenesis of many forms. In _Sagitta_, for example, a considerable quantity of chromatin granules is given off by the chromosomes and cast out into the cytoplasm near the close of ovogenesis (Stevens, '03). Rueckert ('92) has described a similar casting out of chromatin material by the chromosomes of the oocytes of _Pristiurus_. The spermatogenesis of _Stenopelmatus_, therefore, differs from that of the other Orthoptera which have been described in having (1) a larger number of chromosomes (46), (2) an even number in the spermatogonia, (3) an accessory chromatin structure in the spermatocytes of the first order, which disappears before the second maturation division.