Many years ago, after a short experience in collecting crinoid cups at the localities herein noted, especially that of Invertiel, it became evident to me that there was considerable variation in the disposition and shape of the anal plates in the cups of Eupachycrinus and in a lesser degree in those of Zeacrinus and other genera. From this I thought it might be possible, in a large number of specimens, to trace the evolutionary stages in the passage of these plates upwards in the cup, and perhaps even their elimination from the limits of the cup. With thoughts such as these in mind, I have in subsequent years laid aside the majority of the cups I have found, and in 1918 (Trans. Geol. Soc. Glasgow, vol. xvi, pt. iii, p. 376) gave a short account of an examination of 200 cups of Eupachycrinus, 45 of Zeacrinus, and 50 of Hydrieonocrinus. This examination was necessarily hurried, owing to the circumstances of the time, but it convinced me that some interesting results would be obtained from a larger series. It was not, however, till recently that I was able to begin this work, my original intention being not only to deal with the cups of the three genera already mentioned but also with a considerable number belonging to Ulocrinus and Woodocrinus. As the sorting and cleaning of the specimens proceeded it became evident that this would occupy considerable time. I have accordingly thought it advisable, in the first instance, to confine attention to Eupachycrinus and Zeacrinus, and in this communication propose only to give the results of the study so far as it has gone.