The transfer matrix method of structural analysis was used to examine the hypothesis that tree stems grow to a shape that tends to equalize the average bending plus axial stresses to which they are subjected along their length. The method and computational procedures were checked by comparing computed height-diameter profiles with those calculated using elementary stress theory for trees with simple force distributions in the crown. Measured height-diameter profiles for trees were then taken from the literature and shown to be well-fitted by profiles calculated to give uniform stress along the stems, using the most realistic average forces and force distributions within the crowns. At high wind speeds, the height-diameter profile giving uniform stress was more tapered than the profile giving uniform stress at low wind speeds. The profile giving uniform stress was similar over the normal range of average wind speeds of 2.5 to 10.0 m s(-1) (at the top of the canopy). But a tree that had grown to give uniform stress along its stem in an average wind of 5 m s(-1) showed markedly decreased stress with height at wind speeds of about 15 m s(-1) or more, and increased stress with height (to the crown base) at wind speeds of about 1.25 m s(-1) or less. The fact that tree stems develop shapes in response to average conditions, but show varying stress distribution in extreme conditions, may help to explain some of the apparent evidence for non-uniform stress distribution in the literature. In general, our analysis supports the above hypothesis for the stem region above the butt swell.

For imore than 150 years reports have appeared in the literature indicating that a wide diversity of plants can lose mineral nutrients from their leaves through the leaching action of rain, mist, and dew. With the adlvent of radioisotopes the phenomenon was conclusively dlemonstrated (4,5, 13) and in recent years, has been the subject of several reviews (7,9, 12). Not only are mineral nutrients leached, but also large anmounts of organic metabolites are lost from many plants. Chromatographic and electrophoretic analysis of the leachate from bean leaves (Phaseolus 7ulgaris L.) demonstrated the presence of several amino aci(ls, carbohydlrates, and organic aci(ds (11, 12).Since leaching is such a widespread natural phenomenon (12), it is of interest to characterize more conmpletely the nature of the organic fraction of plant leachates. This paper reports the results of analyses of the leachates from several plant species. reagent (8) and (leveloped at 1000 for 10 minutes. Materials and MethodsThe neutral fraction was again passed over anion and cation resins to remove possible contamination and the eluate was concentrated under vacuum. Separation and identification of the sugars was carried out by 1-dimensional descending chromatography, using butanol: acetic acid: water (9: 1: 2.9) and 590 www.plantphysiol.org on May 9, 2018 -Published by Downloaded from

Young's modulus along the grain (elasticity, E) was measured on 10 sections of branches and three tree trunks, with bark, of Picea sitchensis (Bong.) Carr., Pinus contorta Dougl. ex Loud., Larix decidua Mill. and Betula pendula Roth. syn. verrucosa Ehrh. The sections were simply supported and corrections were made for taper and deflection due to shear. The E values for trunks were at the lower end of the range reported for green timber (2.4-7.5 GPa), and those for branches were still lower (0.7-4.6 GPa). Values of E for branches decreased with decrease in specific gravity, which corresponded with an increase in percentage water content. When E values were calculated using underbark diameters they fell more closely within the range reported for green timber.

Measurements were made on branches and trunks of Picea sitchensis (Bong.) Carr. to determine the relationship between (i) the bending moment at the bases of branches that cause breakage, and (ii) midpoint diameter cubed. The theory for cantilever beams was then used to calculate the basal bending moments and midpoint diameters of branches with different numbers of laterals and endpoint deflections, given previously measured values of Young's modulus, taper and weights of foliage and wood. Snow and ice loads (equal to 2 and 4 g cm(-1) of shoot, respectively) were then included in the calculation to determine whether the basal bending moments exceeded the breakage values. The likelihood of breakage increased with an increase in (i) number of laterals, and (ii) endpoint deflection under self weight (without snow or ice)-features that had previously been shown to lessen the amount of branch wood required to support a unit of foliage. However, branches which deflected moderately (> 10% of their length) under their own weight deflected greatly under snow or ice loads and might shed powdery snow before breakage occurs.

The dimensions, deflections and support costs of tree trunks and branches can be deduced using the structural theory for cantilever beams. However, elementary theory applies only as long as deflections are small, and complex analytical solutions are required to account for complex taper and patterns of loading. This paper describes a method that copes with large deflections, any patterns of taper, and any patterns of distributed loading, point loading or externally applied bending moments. A beam is considered to be composed of a series of short segments, such that each has only a small deflection, and each can have specified dimensions, Young's modulus and loading. The transport matrix method of structural analysis is used to determine the end conditions of each segment and of the whole beam. The method is verified by comparing predicted deflections with deflections (a) calculated using an analytical solution by Bisshopp and Drucker (1945), (b) calculated and measured for sapling tree trunks by Leiser and Kemper (1968), and (c) measured on tapered and untapered plastic rods.