The author studied on the fittness and the errors among estimated cross-section areas of a tree, calculated by some usual estimation formulae, in which a cross-section figure is assumed as a circle.
1 . Samples were 44 disks taken from shoots of Quercus myrsinaefolia of some coppice forests in Shimane Prefecture.
2 . Measurements were taken at the height of 0.00 m (section I), 0.73 m (section II), 1.46 m (section III), as follows;
i ) Precise cross-section areas, measured by a planimeter.
ii) Diameters in 18 directions, every ten degrees, on a disk, so that he could find a maximum and a minimum diametet and a pair of two diameters crossing at right angle.
iii) Girths, measured by a tapeline, supplemented by a curvimeter.
3 . As a value D in the estimation by a formula ^π_4D^2, he picked up following values,
D_1 : a diameter in a random directon.
D_2 : the arithmetic mean of a pair of diameter crossing at right angle.
D_3 : the geometric mean of a pair of diameter crossing at right angle.
D_4 : the mean of the maximum and minimum diameter.
D_5 : the mean of a pair of the maximum and a crossing diameter.
D_6 : the mean of the minimum and a crossing diameter.
To check the fittness of these of estimations, the author carried a regression analysis, and he found,
i ) When it is a = 0, b = 1, the fitiest index for the section III and II might be the mean of a pair of the minimum and the crossing diameter.
ii) In view of convergency of variances around a regression line, the fittest were the mean of the maximum and the minimum diameter for the section III, and the geometric mean of a pair of diameters crossing at right angle for the section I.