320 Forestry Quarterly. 



Ever since Weber's efforts to express the 



Mathematics experience figures of yield tables in mathe- 



of matical formulae, this subject has from time 



Tree Grozvth. to time been investigated, the object being 



eventually to reduce the work on yield 



tables. 



Dr. Wimmenauer proved that the progress of height growth, as 

 well as of acre-production, as a function of age x can be expressed 

 in the general formula y=a.\r^-\-bx--\-cx=f (x) . 



By introducing three empirically determined heights with their 

 corresponding ages the constants a, b, c, can then be calculated. 

 Comparing this theoretical height curve with empirically deter- 

 mined ones, while culmination of both current and average incre- 

 ment in the former coincided approximately well with the latter, 

 other discrepancies made the usefulness of the formula still doubt- 

 ful. 



Glaser attempts the solution of the constants by the method of 

 least squares, which is based on determining the unknown con- 

 stants in such a manner that the sum of the squares of the differ- 

 ences between calculated and empirically determined values be a 

 minimum. He comes to a closer approximation to the empiric 

 curve, the theoretical heights up to about the 40 year being some- 

 what larger, from 40 to 80 years somewhat smaller than the 

 empiric ones. 



In a second article, Glaser applied this formula of third degree 

 to a number of empiric curves and found that the same relation 

 as above prevailed, but with decreasing site quality the differences 

 became less ; also that Wimmenauer's procedure was sufficiently 

 accurate to substitute for the more circumstantial method of least 

 squares. Yet, altogether the results are not accurate enough to be 

 used for yield table construction, hence the author investigated 

 first whether any equation of the third degree could express, and 

 finally whether an equation of the fourth degree would more 

 closely approximate the actual growth conditions. 



The first inquiry gave negative results. 



A closer practically sufficient approximation up to about the 

 150 year was secured by the use of a fourth degree equation, but 

 the practical use of the formula on account of the necessary ex- 

 tended calculations is doubtful. 



