As a substantial portion of the prince's domain, forests constituted one of the largest sectors of the state economy in central Europe. Other forested lands in Germany belonged to the cities and the landed nobility and provided indispensable products for the local and regional economies under their control. Wood in one form or another was essential for home heating and construction, iron manufacture, glassmaking, shipbuilding, and other crafts and trades, while secondary products of the forest found applications in myriad occupations, such as tanning and agriculture. Before the age of coal, which would not begin in many parts of Germany until the middle of the nineteenth century, wood was king.
After the acute and widespread devastation and neglect that resulted from the Seven Years' War (1756–63), the state fixed its gaze on economic recovery. The specter of shortages of wood fuel caught the attention of a small group of conscientious foresters and enlightened bureaucrats, who saw evidence that the deterioration of the woodlands, reported here and there since the Middle Ages, had dramatically accelerated. In the Palatinate, for example, a survey of the forests carried out between 1767 and 1776 spoke of "woods in places so ruined that. . .hardly a single bird can fly from tree to tree." The state of Germany's forests reached its nadir just when rulers like Frederick the Great sought to encourage population growth and force the expansion of industry and trade, measures bound to increase the pressure of demand for wood and other forest products. The fear of impending crisis in the supply of wood lodged in the minds of government officials throughout the remainder of the century, and was periodically intensified by reports of rapidly rising prices.
Officials vigorously pursued economy in the use of wood. But redesigning fireplaces, door-frames, and spoons offered help only on a limited scale; to expand that scale would be a tedious undertaking. Better understanding of the nature of combustion and material properties of wood offered some hope for greater efficiency in wood burning, and scattered experimental reports on these matters of forest physics appeared before 1800. The alternative of expanding the wood supply promised larger gains. Here a bold innovation might succeed in increasing the amount of firewood and lumber available to an entire town, city, or region. Almost in proportion to the potential payoff, however, the complex problem of proper forest management exceeded the meager qualifications of the vast majority of foresters. As a rule their primary appointments as caretakers, game wardens, and master of the hunt required neither practical nor theoretical training in forestry. In Prussia, for example—even under Frederick the Great—posts in the forest administration, which carried the revealing title of Jäger , served as sinecures for military retirees. In the absence of qualified personnel, how could a new approach to forest management arise?
After the middle of the century, the establishment of private forestry schools and publication of books and even journals devoted to forestry began to raise expectations for the training and competence of future foresters and forestry officials. The last year of the Seven Years' War saw the foundation of the first forestry school (by H.D. van Zanthier, in the Harz Forest), the appearance of the first book to use "forestry science" in its title (Johann Beckmann's Beyträge zur Verbesserung der Forstwissenschaft ), and the first journal devoted exclusively to forestry (J.F. Stahl's Allgemeines oekonomisches
Forstmagazin ). One of the first points to settle was the very definition of forests. Traditional privileges and the continued use of the forest for such agricultural purposes as grazing or mast (windfall nuts) had long discouraged a conceptually precise demarcation of the forest. Beginning in the 1760s, however, better-trained officials, equipped with publications for the exchange of ideas, promoted the notion that the forest could be defined precisely and studied objectively.
The first writers on forestry science were led by men trained in the cameral sciences—financial officials and chief foresters who expected economic disaster if the condition of the forests continued its downward slide. As these officers of the local prince consolidated their control over state-managed economies throughout Germany, they attended to the forests in their jurisdiction. Where bureaucratization and centralization of political authority extended the official's sphere of action, as in Prussia, forestry science flourished. The year 1757 marked the appearance of the first of many books on forestry geared specifically to cameral officials: Wilhelm Gottfried von Moser's Principles of forest-economy . Like other cameral officials, the head forester came to his post after considerable study. Every cameralist learned about forest administration, a subject of acknowledged importance: "First, because they are a considerable source of revenue for the state, and second, because they constitute a vital necessity for the sustenance of its citizens, without which these lands—especially in the north—would hardly be habitable." Cameralist writers such as
George Ludwig Hartig placed the new forestry alongside the "state sciences," since the two "make up a complete whole."
The new breed of officials trained in cameral science described the living forest quantitatively before subjecting it to economic reason. They brought to the task a familiarity with mathematics. Mathematics figured prominently among the required subjects, especially in the first year or two of coursework, in the university curriculum in the cameral sciences and also in special forestry schools. Published curricula and schedules of lectures consistently featured mathematics as a Hilfswissenschaft , both for the work of the future government official and as exercise for his mind. At the Cameral College in Kaiserslautern, for example, mathematics was one of the subjects required of every student, and "empiricists" wishing to proceed straight to practical studies without this preparation were not welcome. Heinrich Cotta's Forest Institute at Zillbach, which originated as a site for private instruction in mathematics during the idle Saxon winters, featured the same progression from theoretical to practical. Forestry had become a "complicated science," and it fell to "patriotic men" to ensure that foresters entrusted with the resources of the state were adequately prepared in this new science.
The program won over skeptics. An anonymous reviewer of one book on mathematics for the forester had questioned whether forestry required its own mathematical literature. Careful reading removed his doubts: forest management presented a set of problems worthy of special attention, which they surely would not receive within the body of mathematical literature. Moreover, the reviewer pointed out,
new sciences need to stand on their own feet, and specialized textbooks help to disseminate new rules and procedures and to establish new sciences as independent disciplines.
Writers on forestry presented problems and applications of special techniques, not elementary mathematical instruction. Their goal was to demonstrate how the forester should proceed mathematically, not to produce a new mathematics. With the exception of solutions to a few obscure problems of stereometry and xylometry (measurement of volume and specific gravity of wood), mathematical virtuosity was not necessary. Cotta argued that the "practiced algebraist," to whom calculating the value of a forest was a trivial exercise, would not be the least bit interested in applying his art to it. Cotta also knew that most foresters, unencumbered by such mathematical sophistication, were likely to faint at the slightest scent of a mathematical problem. A reviewer of another early book on the mathematics of forestry concurred: "[the author] demands from the forester planimetry, stereometry, trigonometry, levelling, transformation of figures, third-order and second-order equations. Terrible demands for most foresters!" A prominent advocate of forestry schools argued that one cannot make "great scholars out of uneducated people." But one could turn trees into thalers by replacing the time-worn "routines" of the old Jäger with Forstwissenschaft , it was generally agreed.
This approach was decidedly German. Reforms under Louis XIV had resulted in plans de forêts for state-owned forests and promoted the concept of dividing the forest into annual cutting areas. Jean-Baptiste Colbert's ambitious plan for improving France's forests in 1669 had prompted new statutes, administrative reorganizations, and inventories throughout the 18th century. But a scientific forest management did not take root in France until it was imported from
Germany in the 1820s. English authorities, ignoring such expressions of concern as John Evelyn's Sylva (1664), did not even inventory the remaining forests until the founding of the Board of Agriculture in 1793. As late as 1885, select committees in Parliament debated the merits of emulating the German model of forestry schools and forest science. In Switzerland and Austria, government officials exerted control over a lesser proportion of the forests than did their counterparts in Prussia and Saxony. Moreover, the physiocratic doctrine fashionable in late 18th-century Vienna and Bern offered a rationale for avoiding the problem by selling off woodland and converting it to farmland.
Doing the Work
In central Germany, particularly in Hesse and Saxony, a few foresters had applied the same enthusiasm to managing the forest as to directing the hunt. These conscientious holzgerechte Jäger of the mid-century set annual cuttings according to easy rules based on areal divisions of the forest. After demarcating and measuring the acreage covered by the woods under their supervision, foresters estimated the number of years that the dominant types of trees should be allowed to grow between clearings or cuttings. They then partitioned the forest into a number of divisions equal to the number of years in this growth cycle, from which they proposed to derive equal annual yields, assuming that equal areas yield equal amounts of wood for harvest each year. This straightforward method worked reasonably
well for relatively short growth periods typical of coppice farming and the periodic clearing of underwood. It permitted limited variations, such as shelterwood (Schirmschlag ) or relative cutting (Proportionalschlag ), in which the harvest from a given section of the forest or the size of individual sections could be adjusted according to soil quality and other contingencies.
These methods may have sufficed for a minimally trained huntsman, but not for the fiscal or forest official imbued with Wissenschaft . The crude assumptions underlying the traditional areal division of the forest proved wholly unsatisfactory for the cash crop of forestry—the long-lived high timber, or Hochwald ; the older the trees, the greater the variation in the timber produced by each of the divisions of the forest. Furthermore, the irregular topography and uneven distribution of German woodlands confounded ocular estimation of area without the aid of instruments. Only in the 1780s did Johann Peter Kling, chief administrator of forests in the Palatinate and Bavaria under Elector Karl Theodor, systematize forest mensuration and cartography into instructions for making forest maps of unprecedented detail.
Other fundamental problems also plagued area-based forest management. First, a division of the forest into equal cutting areas did not provide the most useful information to those responsible for fiscal planning and management. They needed to know the amount of firewood or lumber. Correlation of acreage with actual distribution of lumber and firewood required principles not formulated and measurements not routinely executed under the old forestry. Second, the prudent forester could not easily respond to inevitable quirks of nature over the many decades in a single forest cycle, because the area-based system did not provide a flexible method for directly adjusting the harvest from year to year, let alone predicting annual yields over the long cycle from the outset. The most meticulous forest management under these methods, while an improvement over neglect, fell short of the high principles of Kameralwissenschaft .
After midcentury, an approach to forest economy based on the mass or volume of wood gradually displaced area-based systems. The first prominent advocate of wood-mass as the quantitative basis for sound forestry emerged from the holzgerechte Jäger . Johann Gottlieb Beckmann, a forest inspector in Saxony, gave the forest priority over the hunt; his knowledge of forestry derived from experience, not education. Beckmann's deep concern for preserving the wood supply led him to construct a system of forest economy that rested on a practical technique for measuring the quantity of standing wood in the forest. Beckmann instructed his team of assistants, whom he supplied with birch nails of various colors, to walk side by side through the forest at intervals of a few yards. Each member of the formation fixed his gaze to the same side and noted every tree he passed. He made a quick estimate of the size category in which the tree fell and marked it with a nail of the appropriate color. At the end of the day, unused nails were counted and subtracted from the original supply to indicate the number of trees in each category. The forester and his assistants knew from experience the approximate yield of wood from trees in each size category; with multipliers thus assigned, the number of nails used could be converted through a simple calculation into the quantity of standing wood in the forest. Beckmann's case suggests that the clever quantifier need not be a calculator or mathe-
matician nor carry out detailed measurements or stereometric calculations in order to determine the mass of wood. A vigorous and productive author, Beckmann began around 1760 to campaign for the method of forest economy based on wood mass. Soon Beckmannianer sprang up throughout Germany to propagate his ideas.
Within a few years, a group of mathematically adept foresters followed along the trail cleared by Beckmann. Carl Christoph Oettelt, Johann Vierenklee, and Johann Hossfeld assigned the task of measuring the area of the forest to the Forstgeometer , a surveyor hired to demarcate the borders of the forest, prepare maps, and carry out other prescribed tasks for a set fee. The geometer, along with the army of marching assistants, gathered the data. Forsttaxation , or forestry assessment—a mix of calculation, analysis, and planning—fell to the chief forester and his superiors. Forest mathematicians like Oettelt and Vierenklee were moved by a new confidence in the power of mathematics to solve problems associated with the conversion of the forest into an equivalent quantity of wood mass. Assessment, the scientific component in Forstwissenschaft , required general principles and techniques based on them. Without them the unrelated numbers and observations reported by foresters and surveyors would overwhelm planners and administrators. Forestry science supplied the necessary organizing principle: "evaluation, or the ascertaining of the mass of wood, which is to be found for a given place at a given time." Identifying wood mass as the crucial variable of forestry set the stage for quantitative forest management.
Counts to Calculation
Theoretical computations of tree volume began to appear in the 1760s. In the first definitive work of scientific tree measurement (Holzmesskunde ), Carl Christoph Oettelt's Practial proof that mathematics performs indispensable services for forestry , the problem of estimating the quantity of wood on a tree without felling it figured prominently. Oettelt was an experienced surveyor and had held the title of "Forest-Geometer" in the civil service of Saxony-Gotha before taking over the forest department in Ilmenau, where he would later serve under Goethe. In the Practical proof , Oettelt criticized the crude techniques commonly used to estimate the quantity of wood. Most foresters used the so-called Bruststärke , or a stack of wood piled to chest height, to veil their wild guesses as to how many boards a tree had delivered. Estimating in this way, they commonly made the value of a tree proportional to its diameter. Heinrich Wilhelm Döbel, one of the most conscientious writers on forestry around 1750, exemplified the problem. In his influential Gamekeeper's practicum , Döbel struggled to find a simple computation for the problem—in fact, relatively easy—of estimating the volume of a felled trunk. Oettelt invoked geometry: "A tree is the same as a cone with a circular base." With the appropriate formula for the volume of a cone, calculating the volume and mass of trees was not so troublesome.
Oettelt's treatment of wood mass as a mathematical quantity was a radical departure. The holzgerechte Jäger had shown little potential for forest geometry. Döbel argued vehemently that exact calculations of wood mass were unnecessary, "since you don't measure wood like
you do gold." He preferred the simple "farmer's calculation" to disputations and proofs. The mathematically oriented foresters, among them Johann Vierenklee and Carl Wilhelm Hennert, joined Oettelt's cause. They corrected and improved his geometric calculations in a series of books that culminated in 1812 in the definitive work on forest stereometry by Johann Hossfeld. As abstract, mathematics-based forestry gained sway during the 1780s and 1790s, compilations of tables based on controlled measurements replaced the older crude techniques described by Oettelt.
Those who compiled such tables had to bridge the gap between tree conics and precise measurement. Consider the problem of converting from cubic measures of wood mass to Klafter , the unit of stacked cordwood familiar to the forester, and back again. The interstices and warping of real wood might defeat the most exact geometrical analysis of its volume. Since mass or volume constituted the central quantity of the new forestry science, small errors due to branches, warped stocks, and imperfections of nature multiplied rapidly as one reasoned from the tree to the forest. Equating the economic measure—volume of stacks of hardwood—and the computed volume did not work out.
The quantifiers, beginning with Oettelt and Hennert, searched for scientific sandpaper to achieve a greater semblance of precision. Oettelt measured as accurately as possible the volume of the cord, then ordered the wood chopped into small pieces. The volume of each piece could be measured with greater accuracy. He summed these individual measurements, and compared the sum to the original cord. After repeated tests he determined that a typical span of cordwood measuring approximately 110 cubic feet contained 14 to 18 cubic feet of empty space, about 15 percent of its volume. Hennert borrowed Diogenes' barrel: he poured water into a box filled with wood; the volume of the box less the volume of the water yielded the solid content of wood (Derbgehalt ). By 1812 Hossfeld, in his Lower and higher practical stereometry (1812), had replaced Hennert's water with sand and contrived even more accurate xylometers. Such innovations made feasible "measurement and calculation of all regular and irregular bodies, and especially trees in the forest."
In the German tradition, the mathematician's forest was populated not by the creations of undisciplined nature, but by the Normalbaum . Forest scientists planted, grew, and harvested this construct of tables, geometry, and measurements in their treatises and on it based their calculations of inventory, growth, and yield. Writers and instructors gave foresters in the field the tools for reckoning the dimensions of the standard tree. Most treatises contained instructions for averaging measurements made on a test plot, but foresters were happier to use the Normalbaum . Tables of numbers representing measurements and calculations, or Erfahrungstabellen , provided data organized by classes of trees under specified conditions. A small number of variables governed the forester's choice of one or another of these tables. For example, the wood mass of the typical sixty-year-old pine on good soil was given as a function of its height and circumference. These tables, which appeared in every complete manual of rational forestry
practice, generally did not bother with regional variation, the bugaboo of 18th-century agricultural treatises.
By the end of the 18th century, German writers on forest management had worked out steps for determining, predicting, and controlling wood mass. Heinrich Cotta presented the clearest and most widely read exposition of these steps in his Systematic instruction for the assessment of woods , published in 1804; they were elaborated in his Directions for the organization and assessment of the forest , which appeared sixteen years later. Cotta's first book, which consisted of lectures originally prepared for students attending the forestry school under his direction, was an example of systematization induced by the necessity of teaching. In his method, the "geometric survey" of the woods supplied the Taxator with information about the extent of his forests. The next step required calculations of wood mass of individual trees, then of stands, and finally of the forest as a whole; growth rates were computed for each level of organization. Finally, Cotta's forester qua cameralist linked the forest balance sheet to the monetary budget by determining the value of the yield.
If the standing forest is capital and its yield is interest, the forester can complete the chain of conversions from wood to numbers to units of currency: an estimate for the worth of the forest can thus be used to predict income, calculate taxes, assess the worth of the forest, or determine damage to it resulting from a natural disaster. For Cotta, the fundamental problem of forestry management was determining the "standing value" of a forest, given uninterrupted maintenance costs and full harvest some 100 to 150 years hence. Cotta's forestry science thus consisted of sound methods for inventory and prediction: "From summary investigations based entirely on verified
judgment, we go through various stages to more exact investigations, first of individual trees, then of the supply, growth, and yield-determination of individual stands, and finally of whole forests." Similar procedures, from the forest to the tree and back again, also appeared in practical manuals such as Georg Hartig's New instructions for the Royal Prussian forest-geometers and forest-assessors .
In one respect, Cotta differed from Oettelt's line. He preferred careful ocular estimates based on tables to geometrical deduction, which he not only considered impractical in the field, but also inaccurate, since branches and other irregularities confound the comparison of trees to cylinders and cones. For Cotta, the only absolutely sure method was to chop up a tree and measure its volume (or mass) in the same unit of measure to be adopted in the taxation itself. This view did not weaken his allegiance to mathematical forestry. He was skeptical only of geometrical estimates, not of quantification.
The Forstwissenschaftler , and particularly Cotta, championed use of "experience tables." Their use reinforced the notion of a forest filled with standard trees. The forester was to instruct his assistants in the use of these tables so that a mental picture of a tree encountered in a forest corresponded to an entry in the tables. With sufficient repetition, a good forester could make an instant association from the mental picture triggered by the tree to the value of the wood mass contained in the table. The next step was to generalize: every tree of the same height has the same mass (or volume). The standard forester was trained to find the standard tree. For Cotta, the "eyeball measure" could displace the "measuring hand" if every forester learned to see the archetypical. The practiced eye could indeed attain this mechanical perfection, "as subsequent measurements and calculations prove[d]."
The head forester thus trained his assistants to internalize Erfahrungstabellen and become computers of wood mass. He remained at his desk manipulating the Normalbaum and numerical data based on local measurements. He could produce his own tables if necessary; according to Hartig, the Taxator was responsible for all "mathematical preliminaries" of forest assessment—determining growth rates, preparing maps and calculating tables—before delegating to his staff routine measurements and the mechanical application of tables. The assistants marched, tallied, catalogued, and marked under the watchful gaze of their supervisor, who—according to Hartig's directions—never counted with them. Instead, his duty was to "dictate principles, record the results in the Assessment-Register, and make sure that there are no mistakes."
By 1800, the forest assessor trained in the cameral sciences specialized in theoretical principles, mathematical preliminaries, and the cumulation and analysis of data, a far cry from Beckmann with his colored nails and squad of assistants. An array of numbers stood for the quantity of wood in the forest. The forester or cameralist trained in forestry science felt no need to step off every acre with the exactness given to the test plot, the geometrical abstraction, or exact measurements of the volume of cordwood. Instead, he could sample and generalize. The work of the assessment and management of the forest thus required only standard trees and Erfahrungstabellen . As Cotta argued, the crucial quantities of his science were "determined mathematically" from the "premises" of forestry science, not through "direct real measurement ." The scientific forester had abandoned Beckmann's empiricism in favor of "sure mathematical deductions, experiments and experiences in the given and understood units of measure." Under the banner of Wissenschaft , the new breed of qualified forester breathed the quantitative spirit into administrative practice.