The first beginnings were, as is usual in similar cases, small and inappreciable, and no one could have foreseen from the first observations of the facts in question what the ultimate development would be. We have said above, that von Mohl observed as early as 1836 the striation of certain cell-walls, and that this led Meyen, on the ground of further but to some extent inaccurate observations, to conceive of vegetable cell-walls as composed of spirally twisted threads. It was also noticed that von Mohl next distinguished true striation from spiral thickenings (1837), the two having been confused together by Meyen, and advanced so far as to form some idea of the molecular structure of cell-walls, without arriving however at any satisfactory conclusion. Agardh, who discovered some new instances of cell-striation, was still less successful in his speculations. Von Mohl resumed the subject in 1853 in the ‘Botanische Zeitung,’ and insisted on the fact that it was not possible to separate the striae or apparent fibres by mechanical or chemical means, but he left it still undecided whether the lines which cross each other in the surface-view belong to the same or to different layers of membrane. The communications of Crüger and Schacht, made shortly after, did not help to advance the question; Wigand also took part in the discussion in 1856, but wandered at once from the right path by supposing the cross-striations to belong to different layers of membrane. As long as botanists adhered to von Mohl’s theory, that the concentric stratification of cell-walls was due to deposition of new layers, it was scarcely possible for them to arrive at a correct decision with respect to striation; it became possible, when Nägeli proved in his great work ‘Die Stärkekörner’ (1858) that the concentric stratification of starch-grains and of cell-membranes generally does not mean, that similar layers lie simply one on another, but that denser and less watery layers alternate with layers that are less dense and contain more water; and that it is not possible to explain this mode of stratification by deposition as understood by von Mohl, but that it may be explained by intercalation of new molecules between the old ones and by corresponding differentiation of the amount of water. That surface-growth in cell-walls does take place by this kind of intussusception had been incidentally suggested by Unger, and the appearance, known as the striation of the cell-wall might now be referred to the same principle as the concentric stratification, namely to the intercalation of more and less watery matter in regular alternation. But Nägeli pointed out a fact which had escaped other observers, namely, that the difference of structure which usually appears on the surface-view as double cross-striation, passes through the whole thickness of a stratified cell-wall. Thus Nägeli arrived at a differentiation in three directions in space of the substance