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.