One of the arguments against the interpretation of these series of spots as sections across spiral arms is that of probabilities. It is known from flattened specimens that _Neolenus_, _Kootenia_, _Ptychoparia_, _Triarthrus_, and _Cryptolithus_ all have a single type of exopodite, consisting of a simple setiferous shaft. All these genera have been examined in a way that permits no doubt about the structure, and no trace of spiral arms has been detected. On the other hand, Walcott found spiral arms in three unrelated genera, _Calymene_, _Ceraurus_, and _Acidaspis_, all of the trilobites in which he found exopodites by the method of sectioning. What are the probabilities that genera of three different families, studied by means of sections, should agree in having a type of exopodite different from that of the five genera about whose interpretation there can be no doubt? Another argument against the interpretation of the sections as spirals is that in any one line the individual spots are of roughly uniform size. This means of course that the spiral has been cut by a plane parallel to the tangent plane. This might happen once, just as once Doctor Walcott cut all six segments of a single endopodite, but that it should happen repeatedly is highly improbable. Moreover, there is a limit to the diameter of the section which may be made from these slender spirals. Most of the spots have one diameter about one half greater than the other, but others are from three to six times as long as wide. These last could obviously be cut only from a very large spiral, and they are therefore interpreted by Walcott as setæ of epipodites. Yet all gradations are found among the sections, from the long setæ to the short dots. (See pl. 27, 1918.) In referring to one slice, Walcott says (1918, p. 152): In the latter figure and in figure 13, plate 27, the setæ of several epipodites appear to have been cut across so as to give the effect of long rows of setæ. The same condition occurs in specimens of _Marrella_ when the setæ of several exopodites are matted against each other. [Illustration: Fig. 12.--A slice of _Ceraurus pleurexanthemus_ in which the exopodite happened to be cut in such a way as to show a part of the shaft and some of the setæ in longitudinal section. Specimen 80. × 4.] This is certainly an apt comparison, and equally true if _Neolenus_, _Triarthrus_, or _Cryptolithus_ were substituted for _Marrella_.