DIFFERENTIATION, ORGANOGENESIS, AND THE TECTONICS OF CELL WALL ORIENTATION. II. SEPARATION OF STRESSES IN A TWO‐DIMENSIONAL MODEL

This paper describes a polarographic technique for the separation of tension and compression stresses in a two-dimensional plastic model of a sectioned cotton ovule. Compression and tension stress trajectories in the model comprise two families of lines which are mutually perpendicular and which, in the "nucellar" region of the model, coincide with cell wall patterns seen in sectioned ovules. This arrangement of stresses is demonstrated, by direct manipulation of the model, to be dependent on the pressure of the integuments. The integuments insure that compressive stresses generated during the growth of the nucellus do not collapse the embryo sac but pass around it, leaving it as a compression-free space within the growing ovule. THE TECHNIQUE of photoelastic stress analysis makes it possible to obtain relatively accurate information on the direction, magnitude, and sign of the principal stresses in an appropriately loaded plastic model. The technique is founded on the work of Sir David Brewster (1816) and relies on the property of certain otherwise isotropic materials which become birefringent under stress. Since at any point on a stressed two-dimensional model the two axes of maximum birefringence can be determined in polarized light, the direction of the two principal stresses can also be determined. A multiplicity of well-documented and easily applicable visual techniques exists in the literature on experimental stress analysis. Most of these techniques, including the use of birefringent coatings and brittle lacquers as well as the more commonly used three-dimensional techniques, such as frozen stress analysis, have been specificially developed for the evaluation of design prototypes and the localization of stress concentrations in critically loaded structures. Some of these techniques can be enhanced by the application of optical-fringe multiplication, which increases the accuracy of quantitative measurements severalfold. A variety of different materials is available for the construction of photoelastic models, including plastics of several kinds, epoxies, gelatin, and glass. These materials provide the experimenter with a variety of different Young's moduli, Poisson ratios, and stress-optical coefficients to work with, each with its own limitations and ad1 Received for publication 27 October 1972. The author wishes to express his thanks for the critical assistance and equipment provided by Dr. William Godden of the Department of Mechanical Engineering, University of California, Berkeley, and for the graphical assistance and encouragement of Mr. James Crawford. 2 Present address: Department of Biology, Stanford University, Stanford, California 94305. vantages. These techniques are well described and coherently presented with an extensive bibliography in Photoelasticity for Designers by R. B. Heywood (1969). For this investigation two-dimensional techniques were employed, since this provided the most direct analogy with two-dimensional sectioned material. There are several qualifications which should be placed on the mechanical analogy between living thin-walled plant tissue and a nearly perfectly elastic and homogeneous plastic, although in general the stress distribution in a model is unaffected by differences in Young's modulus and Poisson's ratio (Heywood, 1969). One of these qualifications is that the analogy only holds true for small amounts of stress which do not result in structural failure of the living tissue; and secondly, information derived from a two-dimensional sectional model can only be generalized to the three-dimensional case to the extent that the latter can be considered its volume of rotation. Despite these limitations, however, information which clarifies considerably the structure and the development of the cotton ovule and the role of the integuments in this process can be obtained from the two-dimensional model. MATERIALS AND METHODS-The shape of the plastic model was derived from a tracing of an axial section of an immature cotton ovule (Fig. 3) modified by rendering it symmetrical about its axis and eliminating space between the integuments due to specimen shrinkage. It can be considered to represent a generalized crassinucellate ovule. The outline was transferred to a sheet of 1/8 in. clear urethane plastic (Photolastic Inc. Malvern, Pa.). This is a rubbery material which is difficult to cut smoothly; after freezing in liquid