reflect X-rays in an amount roughly proportional to their atomic numbers. 2. The structure of siderite is shown to be so nearly the same as that of rhodochrosite as to be indistinguishable by the means at hand. Magnesite is shown to give the same sort of pattern, and hence to have the same general arrangement of atoms, as the other members of the group. 3. The positions of the oxygen atoms as determined by the present method and by the spectrometer results, are compared. The "normal" decline of intensities is in surprising agreement with the reflections. 4. The use of gnomonic projection in studying Laue photographs is mentioned and a ruler is described, the use of which reduces the time and labor of making such projections. 5. The effect of the voltage impressed on the X-ray tube upon the character of the Laue photograph is considered and the best conditions for operating a tungsten tube for this work are stated. 6. A criterion is suggested for determining, in the case of an hexagonal crystal, whether the fundamental unit is a rhombohedron or an hexagonal prism. 7. Evidence is obtained from these crystal structures to show the existence of groups of atoms, as carbonate groups, in the crystal. 8. It is pointed out that unless every atom in the crystal is electrostatically charged, the outside electrons of the atoms making up these crystals cannot be arranged at the corners of cubes. 9. Some connections are pointed out between the development of faces on calcite and its crystal structure, and a means is indicated of deciding the most probable indices of a plane, when they are in doubt. The bearing of these structures upon the question of what constitutes a series of isomorphous substances is mentioned. Geophysical Laboratory, Carnegie Institution of Washington, June, 1920. ART. XXIV.-Entelodonts in the Marsh Collection; by EDWARD LEFFINGWELL TROXELL. [Continued from p. 255.] PART II. THE GENUS ARCHEOTHERIUM. 3 GENERIC CHARACTERS OF ARCHEOTHERIUM LEIDY. Archæotherium ranges in size from that of A. clavus to that of A. crassum; the known species are limited to the Oligocene, generally Lower or Middle. As distinguished from Entelodon Aymard, it has longer diastemata separating the premolars; premolars more primitive in having double roots (exception: P, of 4. marshi, sp. nov.) and less primitive in their small size and the consequent greater separation; P not so wide posteriorly; P1 not quadrate but invariably with a notch on its anterior face; anterior cusps of the lower molars higher than those posterior. (As to the skull, one finds great difficulty in accepting the published reproductions of the cranium of Entelodon magnus as trustworthy evidence of the very unusual features represented.) As distinguished from Pelonax Cope, the chief features of Archæotherium are the generally double-rooted premolars, the smaller size of the mental tubercles, and the much smaller size of the animal as a whole. As distinguished from Dinohyus, medium incisor never known to be absent; P3 always much longer than wide, anterior and posterior cones unequal in lower molars; dependent process generally large, posterior end of malar bone may end before the glenoid cavity; processes may be relatively large on chin, and the generally long chin and long premaxillary have the incisors separated. Dinohyus is, moreover, twice as large as the smallest species of Archæotherium and is known only from the Lower Miocene. ARCHÆOTHERIUM CLAVUS Group. Archæotherium clavus (Marsh). Holotype, Cat. No. 12035, Y. P. M. Middle Oligocene, White River, Nebraska. Following is the original description of this species (Marsh 1893, p. 409). "Elotherium clavum, sp. nov. "On Plate IX, figure 1, is shown a skull of Elotherium, with the brain-cast in position, which agrees in many respects with the skull figured on the preceding plate, and described above (E. crassum). When first figured, the former skull was referred to E. crassum (Dinocerata, p. 65, 1884), but a more careful comparison proves it to be distinct. It is considerably smaller than E. crassum, and the malar process is quite slender and tapering below. It extends directly downward, and hence is not seen in the top view of the skull. The length of this skull is sixteen inches, measured from the front of the premaxillaries to the back of the occipital condyles. The dentition agrees, in the main, with that of E. crassum, the last lower molar in each having four cones only, and no heel. The malar arch and the dependent angle of the lower jaw will distinguish it from E. mortoni. The type FIG. 1.-Archæotherium clavus clavus (Marsh). Holotype. Cat. No. 12035. Side view of skull and jaws. One-fifth nat. size. specimen here figured is from the Oreodon beds, near the White river, in southern Dakota." 3 Two points are offered in contradiction to the description above, viz: there is a definite heel on M, and the dependent processes from the malar do swing outward. In 1909 Peterson made this a subspecies under A. mortoni Leidy, but here it is raised again to the rank of a full species on the basis of the description which follows: In this species (figs. 1-3), the skull is slender and the framework of the zygomatic arch is light, this being in harmony with the longer, more slender canines. The dependent process from the jugal is very narrow; it seems to point neither forward nor backward, but is of course swung outward; its anterior edge is in line with the middle of the orbit. The posterior process has a notch to receive the end of the temporal bone, and in this species the distance from the orbit to the notch is relatively great. From the notch backward the bone is narrow and extends almost to the glenoid cavity, but the glenoid surface is not cut away to receive it. The temporal in its outward course from the cranium forms a wall reaching to the outer extremity of the glenoid cavity, above which it ends in a straight narrow vertical edge; the corner folds back very slightly and forms a depression posteriorly. Anteriorly from this edge and the border of the glenoid fossa, there extends a rather straight and narrow process to fit into the notch on the jugal or malar bone. The distance from the condyle to FIG. 2.-Archæotherium clavus clavus (Marsh). Holotype. Cat. No. 12035. Palatal view. One-fifth nat. size. the upper side of this process is relatively small, 25 mm., further indicating the slenderness of the general structure. On the anterior wall of the temporal there is no foramen as in A. crassum, but a slight tuberosity may be seen. The occipital condyles are set wide apart, are long and narrow themselves, and are very narrowly grooved on the ends. There is no fossa above the condyle, nor any foramen, as is found in the other species. The alveolar border, especially at the canines, descends well below the palate, arching the latter. The posterior edge of the infraorbital foramen lies over the middle of P3 and opens slightly downward. The upper rim of the orbit has a sharp edge and the frontals, though crushed, show a smooth, deep fossa without evidence of supra-orbital foramina. The frontals anterior are very narrow, because the lachrymal, approximately square, is high in front of the orbit. The jugal occupies a very small area on the face; on the other hand the maxillary forms no part of the arch anteriorly. The vertical position of the orbit is very similar in all the species; its anterior edge lies over the metacone of M2. The upper incisor teeth are pyramidal or subtetrahedral, recurved and slender. They are slightly flattened, with sharp corners postero-externally and antero-internally. The upper canine, already slender and long, is worn on the anterior side in such a way as to emphasize its slenderness. It is recurved. P1 is situated very near, in fact, fairly beside the canine, and therefore assumes a diagonal position. Though A B FIG. 3.--Archæotherium clavus clavus (Marsh). 12035. Crown view of (4) upper, and (B) lower teeth. CDC Holotype. Cat. No. small, it is as large as those found in much larger species. P2 is relatively large, is well separated from P1, but is close to P3 A noticeable thing about the third upper premolar is its concavity internally, and as a consequence the wider posterior heel, which gives the tooth an unusual thickness, 15.4 mm. Both fore and aft are developed cingular edges. A serrated fold runs to the point of the cone, and the heel is very rough. It not only has the platform mentioned by Leidy, but also a cingulum back of that. Postero-internally is a roughened area bordered by ridges running vertically. The third premolar joins the fourth without a diastema. P+, implanted with three fangs, is much more molariform, but is composed of two cusps only. The outer cone, or protocone, which may really be the protocone and tritocone combined, is considerably stronger and points |