Some 500,000 acres were regulated according to this plan in Prussia, probably very superficially.
In 1789, Bavaria also ordered a division into annual felling areas.
In all these methods of regulating the yield or budget, the area played the main role, the volume being only a secondary consideration.
The first elaboration of a pure volume division was made by Beckman in 1759. He estimated stock on hand by trees and guessed more or less at the increment, allowing 2.5, 2, and 1% for the different sites, and then made a year to year calculation of stock for 125 years. How the felling budget was finally determined is not known.
Two methods were simultaneously devised in Württemberg in 1783, which form the transition to the so-called _allotment_ methods, making periodic age classes of an equal number of years and allotting either felling areas or volumes to each period of the rotation. Incapacity of the officials prevented the application of the one method, while the other, devised by Maurer, remained also only a proposition.
But, in 1788, Kregting in his Mathematical Contributions to Forestry Science teaches a pure volume allotment method with ten year age classes and nearly all the apparatus which was afterward developed by Hartig, who in the next period dominated to such a large extent the development of forestry in all its branches.
9. _Improvements in Methods of Mensuration._
In scientific direction, the mathematical disciplines were the first to be developed; the natural sciences received attention much later.
A considerable amount of mathematical knowledge was required for this work of forest organization. The mathematical apparatus of the foresters even at the end of this period was rather slender, but its development went hand in hand with the development of these methods of regulation; and even elaborate mathematical formulæ for determining felling budgets were not absent.
Until nearly the middle of the 18th century, surveys of exact nature were almost unknown; only when the division into equal or proportionate felling areas became the basis for determining the felling budgets, did the necessity for such surveys present itself.
Plane table and compass were the instruments which came into use in the beginning of the 18th century. But not until the latter half of that century were extensive forest surveys and maps of various character made, especially in Prussia under Wedell, Kropff and Hennert.