How to be a Wine Gauger

In the world before widely standardized measurements, that is, before the Industrial Revolution, standards were set locally. The need for standards was driven by economics and commerce, not science. Things that could be counted, like the number of baskets of porcelain dishes on a boat or the number of threads in a fabric, were not the problem. Merchants had been counting and weighing for thousands of years. As an apprentice merchant in Amsterdam around 1650, Leeuwenhoek probably learned to use a low-power lens to count threads.

The problem came from liquids in barrels. How much liquid was in this barrel compared to that barrel when the barrels were different sizes, different thicknesses, and only partially full? Increasing the complexity, barrels were round. That made them easier to move, but quantities inside curves are harder to measure than quantities inside rectangles. The barrels could not be opened and unpacked like a basket.

When Leeuwenhoek was young, knowledge of the appropriate mathematics, what we now call plane and solid geometry, was uncommon. It was not taught in school because it was seen as too advanced and specialized for children. It was not taught in the university because it was too practical. In that atmosphere of uncertainty if not mystery, with money at stake, the perceived trustworthiness of the person doing the measuring and calculating was a significant factor.

What drove the need to quantify the uncountable was taxes. An important source of tax revenue for the Dutch Republic were excise taxes (accijns) on the movement of goods. During Leeuwenhoek's time, Delft collect about fifty thousand guilders annually. Most important to Leeuwenhoek were the taxable liquids in barrels that required more complex mathematical calculations: beer, wine, brandy (distilled beverages), vinegar, and soap. The city employed men to do the measuring, and Leeuwenhoek was appointed in 1679 as wine gauger (wijnroeier).

His training as a surveyor was a common precursor for those who held his job as a gauger (peilder). The mathematics used for surveying long distances, heights, and irregular parcels of land were the same as those for measuring the size of containers and the volume of liquid inside. The techniques differed. A surveyor used chains for shorter distances, levels for differences in height and elevation, and a theodolite on a tripod for angles. The gauger had one instrument, a marked stick (peilstok or wijnroede), what we now call a measuring rod or a yardstick.

Where did Leeuwenhoek learn the techniques, especially the mathematical algorithms, for measuring liquids in barrels? Just as surveyors had to be certified, so did gaugers. While we have the document certifying Leeuwenhoek as a surveyor in 1669, all we have for his gauging is his appointment in 1679 as recorded in the city's archives.

Leeuwenhoek may have learned as an apprentice or assistant for an experienced gauger. In addition, several books were commonly used as texts for training gaugers.

Three volumes come from the 16th century, all published in Antwerp:

• Gielis Vanden Hoecke's In Aritmetica een sonbderlinge excellent boeck (1545)
• The anonymus Die waerachtige const der Geometrien...Hoemen maken sal die wijnroede, om daer mede te roeden alderhande tonnen vaten cuypen backen ende dier ghelijcke (1547)
• Willem Readts' Pracktijcke om lichtelijc te leeren visieren alle Vaten metter Wisselroede (1566)

By Leeuwenhoek's time, these books were a century old. Johannes Kepler, the astronomer, published a book in 1615 titled Nova stereometria doliorum, 1615 (Latin: solid geometry of wine barrels) and a German version the following year. It is unlikely that Leeuwenhoek, knowing only Dutch, used either of them.

The two books that Leeuwenhoek is more likely to have read were published in Dutch during his lifetime. Click on the images below to enlarge and on the book titles for the full text (Dutch only).

Adriaan Metius' Manuale Arithmeticae et Geometricae Practicae, Amsterdam, 1633		Christiaen Anhaltin's School-Boeck van de Wyn-Royeryen, Amsterdam, 1663