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.
The methods of measurement of wood developed still later. Until Oettelt’s time no method of precise determination of volumes was known, everything being estimated by cords or by diameter breast-high and height, or by the number of boards which a tree would make (board feet?).
The diameter was sometimes used as a price maker, the price increasing in direct proportion to the diameter increase. Oettelt calculated the volume of coniferous trees as cones, and Vierenklee, who wrote a book on mathematics for the use of foresters, calculated timbers with the top removed by using the average diameter, to which Hennert added the volume of a cone with the difference of the two diameters as a base, to make the total tree volume.