During the past seven years I have published several papers based upon preliminary investigations on the anatomy of the Holectypoida, an order of the Euechinoidea which, by general consent, is regarded as transitional between the Regular and Irregular sections of the class. Continued study, aided by increased mental and technical experience, has revealed an ever-increasing number of interesting features in the order, and has made possible more definite and confident surmises as to its affinities with other groups. The series of contributions here commenced is intended to amplify, and in some cases to correct, the statements made in my earlier papers. With very few exceptions the actual descriptions that are given in the former work still seem to be essentially correct, but every fresh examination, even of the same specimens, testifies to the incompleteness of most of the observations hitherto published. New material, better or differently preserved, often draws attention to features overlooked or discarded as unimportant in the examples already studied. No apology is needed for the publication of incomplete descriptions of natural objects, since complete knowledge is as yet nowhere attained. When inaccuracies of observation have been detected, their nature and cause will be stated frankly, accompanied, verbally or not, by suitable contrition.