To summarize, we may say, that resulting from the division of each first spermatocyte are two second spermatocytes, one of which contains an accessory chromosome while the other does not. The second spermatocyte containing the accessory divides, and with it the accessory, so that each of the spermatids derived from it contains a chromatid from the accessory. The other second spermatocyte, not containing the accessory, also divides, producing two spermatids in which the accessory is absent. Thus half of the spermatids contain accessory chromosomes while the other half does not.

(e) Number of Chromosomes.

The enumeration of the chromatic elements, while a very important part of any study upon the nucleus, is unsatisfactory at the best. If there is any great number of chromosomes in the cell, it is impossible to secure a determination of it in a lateral view of the metaphase, because the elements overlie one another so as to render their distinction very uncertain. A polar view is much more desirable, but even here one is never certain that all the elements are represented, or that only entire chromosomes of one cell are present. The first of these contingencies arises from the fact that, in the event of a cell being cut in two, some of the chromosomes may drop out and not appear in the sections; or, if still on the slide, and in a small group, they may lie so close to a mass of chromosomes in another cell as to be confused with them. An excess in number may be found if a portion of the chromosomes have already divided in the equatorial plate, while the remainder are still united (cf. fig. 19), or if one or two from the fragment of another cell are in the neighborhood. All these embarrassments are increased when an independent structure like the accessory chromosome is present. These difficulties exist when the conditions are most favorable, i. e., when the chromosomes are arranged in the equatorial plate; they become practically insurmountable during any other stage of mitosis by the intertwining of the chromatic segments or by fusion of chromosomes in later stages.

Because of these considerations, I do not put implicit confidence in conclusions drawn from numerical relations when they involve the question of whether or not there is a difference of one chromosome between two cells. What I have to say, therefore, concerning the numbers of chromosomes in the different cell generations of the Locustid testis, I must state as my best judgment in the matter, based upon the most careful observations I could make upon cells showing the elements with the greatest clearness. While I regard them as in all probability correct, I do not rely so thoroughly upon them as I do upon observations of structural details, and have therefore based no conclusions upon numerical relations alone.

As is stated elsewhere, the number of chromosomes in the spermatogonia appears to be thirty-three. This was ascertained by selecting the clearest possible cases of the metaphase that could be found and drawing them under the camera lucida. Subsequent countings were made, and in most of the cells thirty-three chromosomes were found. An inspection of figure 1 will show that there is a characteristic arrangement of the chromatin bodies, the larger ones being on the outside of the group, the smaller within. Amongst the large ones, it was impossible to distinguish the accessory chromosome, but a lateral view of the anaphase shows it clearly. From the fact that it was a single element in the spermatogonia, it was to be expected that an uneven number of chromosomes would appear in this cell generation.

In the spermatocytes, as in the spermatogonia, the polar view of the metaphase was the stage selected for use in counting the chromatin elements. A large number of cases showed that sixteen and seventeen were the prevailing numbers. The smaller of these is easily accounted for when it is recalled that the accessory chromosome is at one pole of the spindle, and would very often lie in another section, where it would not be possible to be sure of its relations. I am convinced from these counts that seventeen is the reduced number in the first spermatocyte, sixteen of the elements being ordinary chromosomes, the other one being the accessory chromosome which has come over unaltered from the spermatogonia. This coincides with the theoretically expected number, deduced from the independently determined number of spermatogonial elements.

In view of the divergences found in insect spermatogenesis, the established theory that the reduced number of chromosomes is exactly half the normal or somatic number is not a strictly accurate one, for in this case the reduction is from thirty-three to seventeen. Similar instances may be found in the forms investigated by Montgomery and de Sinéty.

When we come to consider the second spermatocytes, spermatids, and spermatozoa, it is necessary to divide them into two classes, because of the unequal apportionment of the accessory chromosome consequent upon its remaining undivided in the first spermatocyte mitosis. There are formed, accordingly, two numerically equal classes of second spermatocytes—those containing sixteen chromosomes plus the accessory chromosome, and those with merely the sixteen chromosomes. The members of each of these classes divide and double their kind, forming spermatids marked as were the second spermatocytes—one class with seventeen chromatic elements, and the other with sixteen. From these, by the usual transformations, are derived the mature male elements, which are thus of two distinct kinds.

(f) Spermatids.

The limits set to this paper preclude anything more than passing mention of the spermatids. As stated above, cells at this stage of development are of two classes, depending upon the presence or absence of the accessory chromosome. The distinction thus set up continues to exist visibly far through the transformation stages of the spermatid, by reason of the persisting independence of the accessory chromosome. Of the dual nature of the spermatids I was very early convinced, because the accessory chromosome is so strikingly displayed by the nuclei in which it exists that it is impossible to overlook its absence in a large proportion of the cells. As to the certainty of this partial distribution in the transforming spermatozoa, I am rendered positive by the most careful and painstaking study. This is valuable corroboration of the observed fact that the accessory chromosome remains undivided in one of the spermatocyte mitoses.