1. A study was made of the growth of vegetable cells during their differentiation from the meristematic to the mature condition, and of problems connected with it such as the shape of cells and the presence of certain cell wall structures. As the objects studied proved to be excellent material, certain particularities of the submicroscopic structure and the chemical composition of the cell walls were included in the investigation. 2. A discussion was given of various theories of changes in intercellular relationships, of which Krabbe’s theory of “sliding growth” and Priestley’s theory of “symplastic growth” are the most important. 3. It appeared that Krabbe’s conception does not hold true and that it is possible to explain all changes in intercellular relationships which were ascribed to sliding growth in literature satisfactorily without assuming any sliding of cells. 4. It was shown that changes in intercellular relationships are principally brought about by symplastic readjustments of the cells as a common whole associated with an expansion of the cells. In those cases only in which cells form additional contact with other cells another process occurs in which certain walls grow less in width and ultimately are separated by the fusion and subsequent deformation of the angular thickenings of the middle lamellae, but which does not implicate sliding of cells either. 5. A discussion of the various factors determining cell shape was given. It was concluded accordingly that the most probable cell shape in a tissue consisting of cells of uniform size which have been able to expand in all directions is the shape of the figure which was described by Lord Kelvin as the shape formed by liquid films dividing space homogeneously and called the orthic tetrakaidekahedron. 6. It was shown that in meristems the total number of contact faces per cell averages fourteen and the number of sides per cell section averages six. When no additional cell contacts are formed during differentiation, in mature tissues the same average number of contacts per cell and the same number of sides per cell section are found. 7. It was demonstrated that the shape and the arrangement of faces of certain meristem cells are so as to yield mature derivative cells approaching the orthic tetrakaidekahedron much in shape by a general expansion during differentiation. For several reasons many meristem cells do not possess the required shape or the required arrangement of faces, and their mature derivatives therefore do not assume the shape of an orthic tetrakaidekahedron, but more or less different shapes. 8. It was explained that in tissues in which the cells have not been expanding in all directions to the same extent, none of the cells possesses the shape of an orthic tetrakaidekahedron. The cells which might have assumed that form by uniform expansion assume a shape which may be derived from the orthic tetrakaidekahedron by transformation; the remaining cells assume more or less different shapes. 9. Changes in shape and in intercellular relationships occurring during the growth and differentiation of cells were demonstrated by means of experiments. 10. It was shown that Ziegensphck’s amyloid and collose reactions are not to be considered indicative of certain special cell wall substances, but are probably only indicative of a less compact structure of the cellulose framework of the wall, ti. It was proved that Preston’s conception of the cell well as a single spiral complex of cellulose chain molecules does not hold true in many cases and that the direction of the cellulose chains in various lamellae of the wall may be entirely different. Ac- cordingly, Preston’s explanation of the “ballooning” of swollen fibres also has to be rejected. 12. By means of michrochemical reactions Griffioen’s theory of the origin of lignin from pectic substances was completely confirmed inasmuch cell walls of Angiosperms were concerned.