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.
Most measurements of standing trees were, of course, made on the
circumference, for, in the absence of calipers, the diameter could be
directly measured only on the felled tree. Doebel had already measured
the height by means of a rectangular triangle, and the first real
hypsometer with movable sights was described by Jung in 1781; and a
complete instrument, which could be used for measuring both height and
diameter at any height, similar to some more modern ones, was
constructed by Reinhold.
Determination of the real wood contents in a cord of wood and of the
volume of bark by measurement was taught by Oettelt, and the method of
immersion in water and measuring the displaced volume, by Hennert
(1782).
In 1785, Krohne first called attention to the variation of the increment
in different age classes and the need of determining the accretion for
each separately.
In 1789, Trunk taught how to determine average felling age increment,
and also the method of determining the change of diameter classes, which
is now used by the United States Forest Service: “On good soil a tree
grows one inch in three years, on medium soil in four years, on poor
soil in five years.” With this knowledge, the attainment of a given
diameter, or the change from one diameter or age class to the next could
be calculated.
Volume tables were at Trunk’s command, and Paulsen in 1787, Kregting in
1788, mention periodic yield tables; but generally speaking “ocular
taxation” or estimating was the rule, checked by experience in actual
fellings, the method of the American timber looker. Generally, of
course, only the log timber was estimated as with us, and only the very
roughest estimating or rather guessing was in vogue until near the end
of the period.
The first attempt at closer measurement was made by Beckman (1756), who
surrounded the area to be measured with twine, drove a colored wooden
peg into each tree, one color for each diameter class, when, knowing the
original number of pegs that had been taken out, the difference gave the
number of trees in each diameter class, and by multiplying the average
cubic contents of a measured sample tree in each class by the number in
the class its volume was found.
The method, often employed at present, of ascertaining by tally the
diameter classes on strips forty to fifty paces wide, the so-called
strip survey, was described by Zanthier in 1763.
These measurements were usually confined to sample areas, the use of
such being already known in 1739. The contents of the sample area, if a
special degree of accuracy was desired, were ascertained by felling the
whole and measuring.
Oettelt, of mathematical fame, was the first to publish something about
the determination of the age of trees by counting rings, although the
practice probably antedates this account. He knew of the dependence of
the ring width on the site and on the density of the stand.
It seems that long before this time the French had made the
determination of yield in a more scientific manner, Réaumur reporting in
1721 to the French Academy comparative studies of the yield of coppice
and of volumes of wood.
Oettelt, too, laid the foundation of forest financial calculations when
he ascertained the value of a forest by determining the value of an acre
of mature wood--the oldest age class--and multiplying it by half the
acreage of the whole forest, suggesting the well known expression for
the normal stock (I r/2) soon after to be developed by an obscure
Austrian tax collector.
Even the first forest finance calculations with the use of compound
interest, and a comparison of the profitableness of the different
methods of management, are to be recorded as made by Zanthier in 1764,
bringing the beginning of forestal statics into this period.