The Calculating Forester: Quantification, Cameral Science, and the Emergence of Scientific Forestry Management in Germany
By Henry E. Lowood
In the second half of the 18th century, few occupational groups rivaled government officials in their attention to numbers. Government officials employed in the duchies, kingdoms, and free cities of German-speaking Central Europe pored over the data on population, imports, and taxes that a growing fiscal apparatus produced in unprecedented volume. Those concerned with the prosperity of the prince and his subjects, from low-level tax assessors to ministers of state, developed an attachment to the quantitative spirit proportionate to the expansion of the state's economic agencies.
Reasons of state and forces of social change brought on the bureaucratization of the state financial apparatus in the 18th century. Rather than dulling their initiative, this bureaucratization created new opportunities for officials, professors, and instructors. In the Age of Englightenment, the improvement of fiscal administration and resource management was seen as requiring a science of state finances, while the proliferation of economic facts and figures raised issues of numeracy and appropriate training for office-holders charged with applying the principles of this new science, which became known as the "cameral sciences" in Germany. The term derived from the Kammer (chamber) in which the prince's advisors tradition-
ally deliberated. The subject matter ranged from economics, finance, and Polizei to mining, agriculture, and trade.
First introduced in Prussia at the universities of Halle and Frankfurt an der Oder in 1727, the Kameral- or Staatswissenschaften were firmly established in the university curriculum throughout Germany by the last third of the century. The call for professional training in cameral science and its gradual emancipation from the faculties of law led to the creation of new professorial chairs and schools for teaching a body of theory and techniques needed for the administration of the state and its domains. It has been argued that these cameral sciences represented a mixed bag of professional training, empirical rules, and warmed-over economic theory. This unflattering characterization overlooks the seminal importance of Kameralwissenschaft in subjecting a variety of economic, administrative, and social practices to rational or "scientific" scrutiny.
Forest management was one aspect of state administration thus scrutinized, in order to fit "scattered pieces of knowledge. . .into systems" and to transform "all sorts of activities previously left to habit. . .into a science." The glue that held these new systems together was economic rationalization. The forest displayed the size of the task of managing the resources from which the prince of the late 18th century ultimately derived his wealth. Discharging the task forged new links between administration and science. The result was quantification and rationalization as applied to both the description of nature and the regulation of economic practice.
German writers on forestry science in the 19th century were struck by the achievements of their compatriots, which "since the middle of the last century can hardly be sufficiently admired." They
touted this example of German cameral science in distinctly national terms: "Compare our literature and the number of our educated foresters to what there is abroad! The beginnings of forestry science are entirely German. " Beginning around 1765, dozens of books and articles published in Germany had established principles and practices of sound forest management; few kindred publications appeared in languages other than German for nearly a century. Theories, practices, and instructional models from Germany provided the starting point for every other national effort in forestry science and management until the end of the nineteenth century.
The work of the classical writers of German forestry science, such as George Hartig, Johann Heinrich Cotta, Johann Hundeshagen, and Friedrich Pfeil, built upon an established tradition of quantitative approaches to the measurement and regulation of the forest. This debt has generally been neglected in the writings of historians of forestry. The origins of rational forest management in the quantitative "forest mathematics" of the last half of the 18th century constitute the subject of this chapter. It will demonstrate that the first advocates of forestry science quantified in spirit in order to bring profits in practice; in the process, they established a tradition of quantitative resource management.
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.
By the end of the 18th century, the new breed of foresters in Germany, those with diplomas from forestry schools or degrees from the university, adopted the methods popularized in the clear prose of writers like Hartig and Cotta. Their appetite for a rational synthesis of calculation and cameralism was whetted by identification of mass and yield as suitable quantities to measure. As in Lavoisier's chemistry, new fundamental measures required new terms of analysis. By 1800, the ideal of the "regulated forest" proclaimed the preservation of the forest's maximum yield under a sound system of forest economy. Three regulae silvarum found throughout the writings of the Forstwissenschaftler linked the desideratum of the regulated forest and the methodological focus on measurement and calculation: "minimum diversity," "the balance sheet," and "sustained yield."
Direct measurements of wood mass or volume would have provided the forester with the data he needed for determining fellings or predicting monetary yield, but such numbers were hidden in the diversity and complexity of vegetation in the forest. New units of analysis gave categories better suited to forest computation than the vast, green sea of individually appreciated trees: the "standard tree" (Normalbaum ), the "size class" (Stärkeklasse ), the "sample plot" (Probemorgen ), and the "age class" (Periode, Altersklasse ), as used in textbooks and instructions.
Johann Wilhelm Hossfeld typifies the Forstmathematiker as leveler. His precocious fondness for mathematics, combined with an argumentative temperament, made him unpopular with his teachers; he turned the tables and became an instructor of mathematics at schools specializing in commerce and forestry at Eisenach, Zillbach (under Cotta), and Dreissigacker, where he finally settled in 1801 with the title of Forstkommissar . Here he moved his mathematical skills from the lectern to the forest. Hossfeld made his name among foresters as a leading proponent of stereometrical and geometrical methods in the determination of wood volume and as the inventor of methods to calculate the value of the forest. His writings are a train of
mathematical exercises, with solutions. Hossfeld worked his way from the volumes of cubic forms representing ideal tree trunks through growth, yield, expected demand, costs, and the budget to an all-encompassing "integral of all results pertaining to the value of a forest." He defended his mathematical approach on the basis of economy of effort: a purely empirical assessment counting every tree in a forest might take one observer several years, whereas a mathematician could produce a useful formula after a dozen or so careful observations. Nature "makes no leaps," he claimed, so that a series of multiplied averages based on one or two easily observed characteristics, such as the height of a stand of trees, is as good as an exact and painstaking summation of all the individual cases. The mathematician need not fear hidden pockets of diversity.
Minimizing nature's diversity and reconstructing the forest to make life easier for foresters and assessors were typical of the authoritative writings of the Forstklassiker . Hartig advocated strict adherence to results drawn from a few sample plots. He recommended that the forester keep things simple by following a small number of general rules and reliable methods. With characteristic dogmatism, Hartig ruled that one should always cut out "arbitrary" details of nature that might distract from the systematic Taxation . Cotta agreed with Hartig on the need to ingnore disparate details and concentrate on useful numbers derived from a sample plot. Cotta argued that selective measurements generate acceptable values for quantities like typical yield or growth, which then become the characteristics of ideal types presented in tables and other summations and
multiplications of data from test plots: "the assumed quantum of growth is really abstracted from many trees of the same kind; the sum of the whole is always the basic measure." These sums cannot be directly measured by any practical method; they can only be determined "mathematically, that is, with the aid of an inference based on single values that are known." The source of the values did not really matter; measurements in sample plots, geometrical deductions, or experience-tables were equally acceptable if the method produced a standard—the "single value." One need not worry about the cumulation of errors; individual differences cancel out in the aggregate. This assumption brought freedom from the need to poll every tree, without increasing the risk of error. The new science rewarded the forester who did not see the trees for the forest.
The Balance Sheet
Although cameralists had in common with forest scientists a faith in numbers as worth a thousand words of old forestry, their underlying assumptions differed. Oettelt, Hossfeld, and Cotta saw management as dependent on mathematics, not the reverse: "the workings of nature and mathematical truths do not subjugate themselves to words of authority." Even kings and ministers had to bow to this ruler of the kingdom of reason.
Officials in the fiscal bureaucracy with broader responsibilities than the forester's showed less enthusiasm for the ultimate rule of mathematics in forestry science. They clearly appreciated numbers as the rudimentary facts of accurate inventory and accounting. Sophisticated forest management provided efficient tools for monitoring the quantities that the state bureaucracy sought to control from year to year. If expressed coherently in numbers, represented clearly in charts
and tables, and placed in the hands of the cognizant minister at court, these vital signs eased the task of keeping the body economic healthy, much as a thermometer aids the physician. To the cameralist, the role of quantification in forestry science was descriptive, not prescriptive.
A common denominator nonetheless related the disparate values that scientists and cameralists attached to quantitative information. The annual accounting of the bureaucrat had to be linked with a long-term plan of resource management based on scientific principles. One prominent Forstwissenschaftler , Friedrich von Burgsdorf, called the common problem "keeping the forest's books," and defined procedures to follow in terms of the quantities of interest to forestry science. The bond between forestry science and cameralism was the conversion from an amount of wood to its value. From that point, the practitioners could go their separate ways, the cameral official to the preparation of the Geld-Etat , or monetary budget, and the forestry scientist to the Forst-Etat , the budget that compared the yield to what the forest could bear over time.
Hartig described the task of creating the Forst-Etat as seeking an equilibrium, as opposed to the bottom line in a fiscal budget. "Where a sure balance sheet of forest use, based on mathematics and natural philosophy, is lacking, wood will always be over- or underutilized." In the former case, balance would have to be restored through conservation, raising more land for the forests, or abandoning a less vital productive arm of the economy; in the latter, by exporting lumber or founding new industries. Hartig used terms like "forest use budget" and "natural forest budget" to describe the related components of planning and biological growth that concerned the forester in his effort to balance supply and demand. Hossfeld likewise spoke of budgets and balances. He explicitly identified forestry assessment with the process of evaluating disturbances to the equilibrium of the forest, whether natural (fires and pests) or artificial (management). After calculating the magnitude of these disturbances, the forester
could prescribe means for restoring the equilibrium of growth and yield over time. The image of the budget, whether of nature or gold, linked forestry, cameralism, and quantification, as foresters learned to manage both the Forst-Etat and the Geld-Etat according to the books.
As we have seen, the books themselves consisted largely of numbers. Hartig wrote hundreds of pages on the gathering of data, calculations, and organization of charts and tables necessary for the production of ledgers; the charts mimicked the columnar arrangement of the accountant's books. Hartig and Cotta both offered book-length examples of their methods of forest bookkeeping, complete with templates for the tables they had used. In general, journals and records kept by low-level foresters were to be turned in quarterly to the supervising forester in each district, who compiled and summarized. A Forst-Rentmeister would calculate the monetary budget from these and parallel records according to prescribed forms, while the Forest Commission, consisting of higher financial officials, would review, analyze, and summarize. According to Ernst Friedrich Hartig, Georg's younger brother and colleague, the results concerning consumption, production, and distribution of wood could thereby be arranged so that "the balance in every forest, district, administrative region, and province can be easily reviewed at a glance." The recurring themes of equilibrium and the balance sheet harmonized with those of administrative convenience and scientific resource management.
The third quantitative principle in German forestry science was sustained yield (Nachhaltigkeit ). Chopping down enough trees to meet immediate needs satisfies the balance sheet. The bureaucratic
annual cycle and associated methods in forestry management deal with immediate and short-term record-keeping and assessment. Year after year, cuttings reduce the wood mass according to ephemeral prices, needs, and the conditions of nature. All can be precisely measured and monitored. But the life of individual trees, let alone the forest as a whole, contains dozens and dozens of annual cycles. Long after the incompetent forester is gone, his mismanagement and irresponsibility survive. As Johann Matthäus Bechstein proclaimed in 1801 to students entering his forestry school, the forester must be capable of calculating "more than one or two generations into the future." Planning the growth, cutting, and replenishment of a forest over the longue durée requires an idea more powerful than the balance sheet. Foresters found it in sustained yield.
The rudimentary concept of sustained yield appeared in one of the earliest texts on forestry mathematics, Johann Ehrenfried Vierenklee's Mathematical first principles of arithmetic and geometry, to the extent they are needed by those who wish to devote themselves to the most necessary subject of forestry , which appeared in the first of three editions in 1767. Vierenklee judged that the forester must know "how to divide up a forest into a definite number of annual cutting areas, from which he obtains a definite amount of wood each year." Vierenklee relied on mathematics for the formulas to achieve this division, and based his work on growth calculations for high timber.
A full generation of Forstwissenschaftler later, sustained yield figured as the cornerstone of Hartig's dogmatic system of forestry management: "always deliver the greatest possible constant volume of wood." The grail of sustained yield has guided the quest for rational forest economy ever since. With this concept, time entered forestry science. How much wood can the forest deliver over a century or two? How should this yield be harvested in one year so as to ensure that the same yield will still be available 100 years hence?
Questions like these redefined the forester's task as curator of the forest, not simply its measurer. As Hartig put it, "no lasting forest economy is conceivable if the output of wood from the forests is not calculated according to sustained yield."
The proper way to ensure the "permanence, certainty, and relative equality of the yield" is not immediately obvious. Yield, unlike wood mass or forest area, is not a "quantity determined by nature"; it cannot be measured, save for the year at hand. A system of forestry based on sustained yield requires prediction and planning. Some relevant factors, like the present mass of wood in the forest, can be measured; others, such as growth rates, must be extrapolated from the performance of sample plots, and the assumption of "good," "average," and "bad" soil. From this blend of quantities and qualifiers, the scientific forester can determine a schedule of cuttings for the forest of standard-trees under the "particular aspects of each system of culture," such as timber forest, coppice, or a mixed form. Conditions such as the present state of the forest and expected growth rates must then be factored in; these, as Cotta pointed out, cannot be calculated according to "algebraic formulae." Inconsistencies in soil, weather, and natural devastations complicate the application of the method. Moreover, equating annual yield to the expected biological growth is a risky proposition. "How can man presume to determine such events of the future in advance, when they are dependent on a thousand accidental events?"
Undaunted by the obstacles to accurate prediction, the Forstklassiker specified procedures for "forest regulation" (Forsteinrichtung ); before long, many foresters throughout Germany adopted these methods. Unlike descriptive assessment, forest regulation was predictive and prescriptive. It offered a framework of long-term seeding and cutting based on the mathematical forest and standard practices
for application in the wooded forest. Scientific forest regulation also exercised many aspects of the forester's art, from cartography, description, and techniques for regeneration to silviculture and assessment. The role and authority of the vigilant chief forester who oversaw and adjusted the plan to circumstances, were reinforced by the scientific principles of forestry management.
Approaches to forest regulation multiplied quickly and differed considerably. Hossfeld and Cotta used geometry and arithmetic to construct flexible systems based primarily on wood mass and areal divisions of the forest; plans derived from their methods could be adjusted as local conditions dictated. Heinrich Christoph Moser, Commissar of Forests in Bayreuth, published a method of determining the "periodic yield" based on "proportion constants" and sample plots. Johann Leonhard Späth, Professor of Mathematics and Physics at Altdorf, proposed a detailed algebraic method. The result of these investigations in almost all cases was a visual arrangement of age-classes and plots, linked with the quantities of wood and cuttings over time. Fold-out tables were common; Hartig used one to extend his plan into the 21st century (fig. 11.1). Like the business plans of a later day, attention to graphic clarity propped even the most chimerical of schemes against the firm oak of faith in numbers.
During the 19th century, the tradition of German forestry science persisted as cameralism gave way to economic liberalism. It produced the monocultural, even-age forests that eventually transformed the Normalbaum from abstraction to reality. The German forest became an archetype for imposing on disorderly nature the neatly arranged
constructs of science. Witness the forest Cotta chose as an example of his new science: over the decades, his plan transformed a ragged patchwork into a neat chessboard (fig. 11.2). Practical goals had encouraged mathematical utilitarianism, which seemed, in turn, to promote geometric perfection as the outward sign of the well-managed forest; in turn, the rationally ordered arrangement of trees offered new possibilities for controlling nature. For example, the technique of periodic area allotment (Flächenfachwerk ) favored by Cotta generated the now familiar checkerboard scheme of growth periods. The mathematical exercise that generated the pattern could be modified to order the sequence of cutting so that older stands protected younger trees against prevailing winds. In the hands of a suitably trained forester, mathematical order and practical utility became one enterprise.
During the 19th century, Forstwissenschaft advanced along the lines established by the early forest mathematicians: sustained yield, regulation according to age-classes and wood mass, and construction of the "normal forest" as an artifact of mathematical reasoning applied to quantitative data. By the end of the 19th century, reformers of forestry in other natiøns—France, England (via the Indian Forest Service under Sir Dietrich Brandis), and the United States—had also discovered the need for conservation and forest management based on professional training and scientific principles. In each country, beginning with France during the 1820s and culminating with the American conservation movement, the inspiration and example was German Forstwissenschaft .
In Germany, however, resistance to the mathematically formulated forest economy began to grow, spurred by natural devastations caused largely by strict reliance on monocultures. By the end of the 19th century, foresters such as Karl Gayer, inspired by new-found loyalty to the natural diversity of species, called for turning "back to nature." Careful consideration of the forest as a multi-faceted biological ecosystem came into vogue. Even in the face of this opposition, quantitative techniques elaborated by the Forstklassiker survived in practice. Above all, the doctrine of sustained yield remained sacrosanct. Franz Heske, writing in 1938 for American foresters, reaffirmed the legacy of 19th-century Forstwissenschaft based on the work of the classical writers:
For all time, this century [the 19th] of systematic forest management in Germany, during which the depleted, abused woods were transformed into well-managed forests with steadily increasing yields, will be a shining example for forestry in all the world. German experience over a century makes it considerably easier for the rest of the world to pursue a similar course, because the attainable goal is now known, at least in principle. The sponsors of sustained-yield management in countries where forestry is still new can find in the results of this large-scale German experiment a strong support in their battle with those who know nothing, who believe nothing, and who wish to do nothing. This experiment and its outcome have rendered inestimable service in the cause of a regulated, planned development and use of the earth's raw materials, which will be an essential feature of the coming organic world economy.