Analysis and Composition of Stem Growth in Form

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Year by year, the stem adds a layer of wood around it. On the other-hand, we can strip off those layers which have grown so far in the year or in the past several years, just as we can strip off the coat of an onion. Hereinafter, we will call the layer as "stem increment". In Fig. 1, the heights of stem increments are located on the y-coordinate, and the cross section areas of stem increments on the x-coordinate. Therefore, if we see the height and diameter growth of a stem for each of the past years, we can understand the continuous change in shape of the stem up the present, by way of putting one stem increment upon another. From the above mentioned, we may suppose that the shapes of stem differ because the height growth and the diameter of breast height growth of the past differ from one another, even though the height and the diameter breast high for the present may be the same with one another. The cross section area of each part of the stem increment can be shown by the next formula: z=K(eAx-e-Bx2)+Le-cy where z is the cross section area, x is the distance between the top of the stem and the cross section, y is the distance between the base and the cross section, K and L are the constants.
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