The adjustment of the growth and increment formulas from BACKMAN in the case of missing data for the first years of growth - In the present paper, that starts with a critical evaluation of the method of Thomasius, The parameters from the growth-formula of Backman (a, b) are determined to work out the equalities (g), (h) and (i), by using the incrementformula (c). When the parameters k0, k1 and k2 are known, they are substituted in the equalities (d), (e) and (f), from which the parameters for the growthformula can be recovered. This method was tested on data for height (Yh) and diameter (Yd) of Populus euramericana cv Marilandica (2nd quality) from the yieId tabIes of Wiedemann- Schöber. (Tab. I). The results are summarized in table 3. In tables 2 and 4 the comparison is made between the calculated results and the data for increment and growth from the yield tables ofWiedemann-Schober. It thus appears that a very good similarity exists between the given data and the results obtained by use of the increment-formula. This is not the case for the growth formula on account of inadmissible systematic errors. These errors result from the indirect determination of the growth formula, that, in fact, may not be used when data for the first years are unavailable. To avoid these errors a 'grafic method' is developed by the author. This method requires less arithmetic work to to test the asymptotic values. In principle this method is based on the fact that in representing growth progress in an axes system (absis t for time and ordinate y/J), all coordinated points (t; y/J) will be situated on a straigh line, when the axes are graduated respectively in a logaritmic and probability scale. This means, practically, that the value of J has to be estimated till nearly all the points are on a straight line. By adapting a line through these points, using the terms (m) and (p), it becomes possible to determine c1 and c2, while (q) gives the value for c0. On the other hand, when the parameters of the growth formula are known, the parameters of the increment formula can be determined by calculating (r), (s) and (v). A comparison between data thus obtained and the data from table 1 is made in table 6. By a similar procedure as was used for the evaluation by the method of Thomasius, the author was able to clearly prove that a good similarity exists between given and calculated data on growth and increment for height and diameter of Populus euramericana cv Marilandica (Tab. 5 and 7). In conclusion, a comparison is made between both methods (Thomasius/graphic method) (tabIe 8) by determining for diameter and height, the average deviation between the calculated and given values for increment (∆y') and growth (∆y). A t-test for P = 0,01 proves that no essential difference exists between the precision of the increment formula, calculated according to either method. This can not be said for the growth formula as the average errors, for height and diameter are near zero, while these errors are respectively 4,6 m and 7,9 cm for the method of Thomasius.
Optimal synthesis of a four-bar linkage by method of controlled deviation