I will begin my comparison of all Echinoderms with an analysis of the Star-Fishes and Sea-Urchins, because I think I can best show the identity of parts between them, notwithstanding the difference in their external form; the Sea-Urchins having always a spherical body, while the Star-Fishes are always star-shaped, though in some the star is only hinted at, sketched out, as it were, in a simply pentagonal outline, while in others the indentations between the rays are very deep, and the rays themselves so intricate in their ramifications as to be broken up into a complete net-work of branches. But under all this variety of outline, our problem remains always the same: to build with the same number of pieces a star and a sphere, having the liberty, however, of cutting the pieces differently and changing their relative proportions. Let us take first the Sea-Urchin and examine in detail all parts of its external structure. I shall say nothing of the internal structure of any of these animals, because it does not affect the comparison of their different forms and the external arrangement of parts, which is the subject of the present article. On the lower side is the mouth, and we may call that side and all the parts that radiate from it the oral region. On the upper side is a small area to which the parts converge, and which, from its position just opposite the so-called mouth or oral opening, we may call the _ab-oral region_. I prefer these more general terms, because, if we speak of the mouth, we are at once reminded of the mouth in the higher animals, and in this sense the word, as applied to the aperture through which the Sea-Urchins receive their food, is a misnomer. Very naturally the habit has become prevalent of naming the different parts of animals from their function, and not from their structure; and in all animals the aperture through which food enters the body is called the mouth, though there is not the least structural relation between the organs so designated, except within the limits of each different branch or division. To speak of these opposite regions in the Sea-Urchin as the upper and lower sides would equally mislead us, since, as we have seen, there is, properly speaking, no above and below, no right and left sides, no front and hind extremities in these animals, all parts being evenly distributed around a vertical axis. I will, therefore, although it has been my wish to avoid technicalities as much as possible in these papers, make use of the unfamiliar terms oral and ab-oral regions, to indicate the mouth with the parts diverging from it and the opposite area towards which all these parts converge. [Footnote: When reference is made to the whole structure, including the internal organs as well as the solid parts of the surface, the terms _actinal_ and _ab-actinal_ are preferable to oral and ab-oral.]