SUMMARY The crown pattern of the tooth is essentially that of the surface of the dentine (dentine‐enamel junction), modified by the deposition of enamel which may be uneven in thickness. The dentine‐enamel junction preserves in the completed tooth the form of the membrana praeformativa, the basement membrane of the inner enamel epithelium of the enamel organ. Folding of this membrane creates the crown pattern. The inner enamel epithelium is subjected to pressure from both sides. On the basal side there is the rapidly growing mesenchyme of the dental papilla, and on the occlusal side there is the stellate reticulum, which swells by the accumulation of fluid. The stellate reticulum prevents distortion of the epithelium by growth of the papilla, and thus ensures that folding of the epithelium is due to its intrinsic growth pattern. This makes for more accurate control of the crown pattern, the details of which are of importance in the function of chewing. The enamel knot is a region of the inner enamel epithelium from which cells are contributed to the stellate reticulum. It represents the tip of the primary cusp. The enamel cord (‘enamel septum’) which consists of cells which are in process of transforming into stellate reticulum, has been confused with two other structures that develop later: a cleavage septum, preparatory to the formation of crown cementum, and an epithelial septum, found in marsupials and crocodilians. The epithelial nodules of monotremes are probably degenerate relics of an epithelial septum. The inner enamel epithelium is a diaphragm passing across the interior of the dental follicle, and folding to adapt its increased area to a confined space. The cement organ, which in some mammals develops from the follicle, probably plays no part in the deformation of the epithelium, but the follicle as a whole may be subject to compression by adjacent follicles. A cusp is a centre of precocious maturation of the cells of the inner enamel epithelium. Here growth ceases (perhaps after a transitory burst of mitosis) and eventually the hard tissues are deposited. The process starts at the tip of the cusp and extends basally, so that growth continues longest in the valleys, intensifying the crown relief. Dens in dente is due to retarded maturation of an area of the enamel epithelium. Throughout the development of the crown there is a marginal zona cingularis, where growth continues. The crown pattern depends upon the position and the stage of growth in which cusps are differentiated from the zona cingularis, by accelerated maturation of groups of cells. Cusps which appear late in development stand low on the crown and frequently form part of a cingulum. Changes in the timing of cusp formation play an important part in serial modifications of pattern, as well as in phylogeny. Ridges are probably produced by tensions set up in the epithelium by the relative movement of cusps, owing to unequal growth or to changes in the shape of the follicle. They form in areas where growth has slowed down but the apposition of ...

Summary. 1. The theory is developed that teeth are repeated organs that occupy different positions in a continuous morphogenetic field. The field can undergo changes in structure and position in the course of evolution, and thus changes in the differentiation of the dentition may be explained. 2. The differentiation of teeth in size seems to be to some extent independent of their differentiation in form. 3. The characteristics of the field or gradient can be described by plotting dental form against the numerical position of the tooth in the series. Two main types of evolutionary change can be detected: (a) retardation of the gradient in the molar region, so that some mammals have more molariform teeth than others; (6) shifting of the molar region backwards and forwards along the dentition. 4. The upper molar patterns of Cenozoic mammals are considered to be of four types–zalambdodont, dilambdodont, tritubercular, and quadrituber‐cular. The serial differentiation of a number of dentitions of which the molars belong to each of these types is described. 5. Each element of the molar has its own peculiar mode of change as it is traced along the series of teeth, and different elements reach their maximum development on different teeth. 6. Some variations are distributed along the gradient in such a way that they appear most frequently on certain teeth and less frequently on teeth lying farther away from the point of maximum incidence. 7. Other variations, in form and dental formula, can be interpreted as due to changes in the degree and position of the gradient. 8. In dentitions that differ in molar pattern, homologous (or homodynamous) elements show similar serial changes and the mode of serial change can be used as a test of homology (or homodynamy). Marsupials and Placentals are similar in this respect. 9. In evolution the serial change of one element can get out of step with that of another, so that changes can take place at one point in the series that occurred at several different points in the ancestor and vice versa. 10. In evolution, new types of change can be superimposed upon the old, e. g., the reduction of the paraconid in the lower molars. 11. The premolars differ from the milk‐molars in a limited number of ways, and the relation between the two series can undergo evolutionary changes. 12. The two jaws are usually similar in the degree of differentiation between corresponding adjacent teeth, and between the premolars and milk‐molars. 13. A description of'Potamogale has necessitated certain corrections in the interpretation of the Centetoid molar pattern as described in the previous paper. 14. This study makes very improbable the view that individual teeth are independent of each other in variation and evolution.

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SUMMARY. A survey is made of the milk‐molars of Perissodactyla and Condylarthra with a view to determining the evolutionary trends. Molarization of the milk‐molars takes place in a variety of ways, which may be grouped into three main types: (a) the condylarthran type, found also in Plagiolophus, (b) the type found in the Equidae and Brontotheriidae, and (c) that found in the Tapiroidea and Rhinocerotoidea. Each of these types has a characteristic order of development of the cusps. The condylarthran type is considered to be the most primitive. From a study of the wear of the teeth, it is concluded that the occlusal movement in all Perissodactyla is transverse (ectal). The characteristic features of occlusion in the various families are discussed. During molarization the talonid becomes intercalated between two trigonids, the intercalation taking place at a relatively late stage in type (a), earliest in type (b) and at an intermediate stage in type (c). The buccal parts of the trigonid and talonid become functional before the lingual parts. The Palaeotheriidae (excluding Pachynolophus and Propachynolophus) are regarded as a distinct family that retains condylarth features of the milk dentition to a late date, and cannot be derived from Hyracotherium. With the exception of Plagiolophus, they show in their milk‐molars transitional stages leading to the conditions found in other perissodactyls. The hypothesis is put forward that the order of development of the cusps depends upon their different sensitivities to the graded morphogenetic conditions in the developing jaw. Correlated evolution of the upper and lower teeth suggests that occlusion has a morphogenetic basis which affects both jaws. The concepts of homology due to descent from a common ancestral structure, homology due to parallel evolution, and serial homology are considered to be closely related and not sharply separable in practice.