TKANSACTIONS OF SECTION D. 667 



to unequal growth. In bis Text-Book (1874), Englisli translation, 1882, p. 8o3, 

 the author, referring to Hofmeister's work, says: ' I pointed out that the growth 

 of the under surface of an organ capable of curving upwards was accelerated, and 

 that of the upper surface retarded ; I did not at the time express an opinion as to 

 whether these modifications of growth were due to an altered distribution of plastic 

 material or to a change in the extensibility of the passive layers of tissue.' Frank's 

 already quoted paper made valuable contributions to the subject. He showed 

 that the epidermic cells on the convex side of the root are longer than those on 

 the concave side, — that is, they have grown more ; he explained apogeotropic 

 cxirvatures in precisely the same way. He showed, moreover, that the sharp 

 curve close to the tip of a geotropic root, and the long gradual curve of an 

 apogeotropic shoot, are necessary consequences from the manner in which growth 

 is distributed in these parts. He demonstrated that rectilinear growth and 

 geotropic curvature require the same external conditions; that, for instance, a 

 temperature low enough to check growth also puts a stop to geotropism. 



The distribution of longitudinal growth which produces geotropism was after- 

 wards studied by Sachs,' who thoroughly established the fact that the convex 

 side grows faster, while the concave side grows slower, than if the organ had 

 remained vertical and uncurved. 



These facts are of interest in themselves, but they do not, any more than 

 Frank's results, touch the root of the matter. Until we know something of the 

 mechanics of rectilinear growth, we cannot expect to understand curves produced 

 by growth. The next advance in our knowledge did in fact accompany advancing 

 knowledge of rectilinear growth. It began to be established, through Sachs' 

 work, that turgescence is a necessary condition of growth. A turgescent cell is 

 one which is, as it were, over-filled with cell sap ; its cell-walls are stretched by 

 the hydrostatic pressure existing within. In osmosis, which gives the force by 

 which the cells are stretched, a force was at hand by which growth could be con- 

 ceived to be caused. The first clear definition of turgor, and a statement of ita 

 importance for growth, occurs in Sachs' classical paper on growth.- 



As soon as the importance of turgor in relation to growth was clearly put 

 forward, it was natural that its equal importance with regard to growth curvatures 

 should come to the fore, and that increased growth on the convex side (leading to 

 curvature) should be put down to increased internal cell-pressure in those tissues. 

 In the fourth edition of Sachs' 'Lehrbuch,' 1874, Eng. tr. 1882, p. 834, such a view 

 is tentatively given, but the author saw very clearly that much more evidence was 

 needed before anything like a conclusion as to the mechanism of movement could 

 be arrived at. The difficulty which faced him was not a new one — in a slightly 

 different form it had occurred to Hofmeister — the question, namely, whether the 

 curvatures of acellular and multicellular organs depend on the same or on different 

 causes. If one explanation is applicable to both, then we must give up as a 

 primary cause any changes in the osmotic force of the cells. For no change in the 

 pressure inside a cell will produce a curvature in that cell, whereas, in a multi- 

 cellular organ, if in the cells in one longitudinal half an increase of osmotic sub- 

 stances takes place, so that the cell walls are subject to greater stretching force, 

 curvature will take place. 



On the other hand, if the cause of bending of acellular and multicellular organs 

 is the same, we must believe that the curvature takes its origin in changes in the 

 cell-walls. In an acellular organ, if the cell membranes yield symmetrically to 

 internal pressure, growth will be in a straight line ; if it yields asymmetrically it 

 will curve. Thus, if the membrane along one side of a cell becomes more or less 

 resisting than the rest of the membrane, a curvature will result. 



If we are to apply strictly the same principle to acellular and multicellular 

 organs, we must suppose that the whole organ curves, because each individual cell 

 behaves like one of the above described free cells, the curvature of the whole 

 resulting from the sum of the curves of the separate cells. This was Frank's view, 

 and it also occurs in Sachs' Text-Book, 1874, Eng. trans., 1882, p. 842. 



Are we bound to believe that the mechanism of acellular and multicellular 



• Arleiten, i. p. 193, June 1871. * Ihid. p. 104, Aug. 1871. / 



