History of Metrology

Данная работа является продолжением нескольких более ранних работ автора, посвященных оценке размеров русских путевых мер длины, вёрст. В работе рассматриваются данные «Выписи из Новгородских изгонных книг» о протяженности дорог на территории бывшей Новгородской республики. На основе сопоставления этих данных с оценками протяженностей современных дорог предпринята попытка выявления тех типоразмеров версты, которыми могли пользоваться в Новгороде и его окрестностях в XV…XVII вв.
15.09.2019: статья дополнена разделом о типовых расстояниях между населенными пунктами Новгородчины.

Early modern scholars and statesmen were acutely aware of the need for improved standards of measurement, albeit for differing reasons. The variety of man-made units across territories and histories was, by the seventeenth century, already a sceptical commonplace, and was understood in terms of the mutability of human institutions. The late seventeenth century saw many scholars advance possible candidates for a universal standard. The most promising of these was the use of a seconds pendulum as a standard for length, a project which was actively pursued by the French Académie Royale des Sciences in the 1670s and 1680s, and remained a goal cherished by savants through the eighteenth century. This paper’s first section places the Académie’s early metrological projects in the context of the scholarly community’s ideal of a universal measurement standard, which was often expressed in ways combining political, theological, and humanistic concerns. Melchisédech Thévenot’s ludic proposal that honeycombs might be a length standard is explored as one example. The second section examines the Académie’s attempts to test the seconds pendulum as a universal length standard, by taking the missions to Uraniborg (1671) and to London (1679) as case studies in the practice of metrological work.

"Приведено описание старинной русской системы мер длины за исключением саженной системы (см. материал "Система русских саженей: мифы и загадки") в динамике ее развития.
25.05.2013 в статью внесены небольшие дополнения и стилистические доработки"
16.01.2014. В статью внесены существенные изменения.
12.10.2014. Сделаны небольшие уточнения по данным. Добавлен раздел про предшествующие исследования русской метрологии. Раздел про версту выделен в отдельную статью (и принципиально переработан).
19.10.2014, 04.11.2014, 24.11.2014, 15.12.2014, 24.02.2015, 13.04.2015, 27.04.2015 - внесены небольшие уточнения и дополнения.
03.06.2015 - доработана тема турецкого влияния на русскую метрологию.
27.07.2015 - небольшие доработки
07.12.2015 - небольшие доработки и уточнения

Estudos de história metrológica. Medidas de capacidade portuguesas, Lisboa, Centro de História da Universidade de Lisboa, 2015, 180 p.
Conteúdos principais:
1. A história metrológica portuguesa. Breve roteiro ideográfico
2. Medidas de capacidade medievais portuguesas. Uma revisão
3. As medidas de capacidade nas inquirições de 1258
4. Para a história da metrologia em Portugal: um documento de 1353 relativo a Bragança
5. Para a história da metrologia em Portugal: dois documentos de 1358-1360 relativos a Coimbra
6. A regulação metrológica em Portugal nos séculos XV e XVI
7. As medidas de capacidade nos Açores em 1868

The evolution of the legal systems of weights and capacity measures used in Portugal from the end of the 11th century to the 16th century is described. Unlike previous literature on this subject, this paper pays particular attention to studying the structure  of the ancient Portuguese metrological systems and the equivalences of the ancient units to the current international system of units.

В статье собрана и проанализирована информация о так называемых "бытовых" мерах длины, применявшихся русскими.
Под "бытовыми" понимаются меры, которые не входили в официальные системы мер, не имели строго установленных размеров и эталонов.
В основу статьи положены две работы Г.Я. Романовой: "Наименование  мер  длины  в  русском  языке" и "Объяснительный  словарь  старинных  русских  мер".
15.09.2019: статья немного дополнена

A medição faz parte da actividade humana desde as primeiras civilizações. É necessário medir ou pesar os produtos que se compra, vende ou troca, bem como aqueles que se entregam ao rei ou ao templo a título de imposto ou tributo. É necessário medir as distâncias e as superfícies dos terrenos. É necessário definir as medidas dos edifícios que se pretende construir. É necessário definir escalas temporais. A história da metrologia está, como é óbvio, intimamente ligada à própria história da matemática. A metrologia, em Portugal como no resto da Europa, evoluiu lentamente, desde uma situação de extrema diversidade, na idade média, até à actual uniformidade, resultante da adopção do sistema internacional de unidades. A diversidade metrológica medieval devia-se, naturalmente, à extrema fragmentação do território em diferentes senhorios, bispados, etc., cada um com a sua própria autonomia e percurso histórico. A uniformização era promovida pelos soberanos, não só porque facilitava as trocas comerciais e a cobrança de impostos, mas também pela importância simbólica que tinha submeter-se todo o país à utilização dos padrões de pesos e medidas do rei.

Доклад был сделан дважды: короткая версия - 31 октября 2019 г. на конференции в филиале ИИЕТ (СПб), а полная - 1 ноября на Факультете географии СПбГПУ им. Герцена.
История метра показана с первых научных разработок, приведших в итоге к его появлению.

In this paper, the value of the modius (modio, moyo, moio) in Portugal in the 11th to the 13th centuries is studied. By this time, the modius was both a measure of capacity and a unit used in the specification of prices. The author concludes that, while the modius-measure had a capacity not under the horse charge (210 to 220 litters) in the legal systems used in Portugal from the end of the 11th century onwards, some smaller modii continued to be used in rural areas far away from the main urban centers. These smaller modii had a capacity around 50 to 75 litters. With respect to the modius, as a unit used in prices, the information gathered by the author indicates a value between 25 and 55 litters of cereal. Therefore, it becomes clear that the modius-price was not equivalent to the standard modius measure. The gathered evidence also suggests that, from the 10th to the 13th centuries, independently of inflation, the modius-price remained approximately equivalent to the currency unit known as solidus.

English translation of the report presented at the conference "Time of Peter the Great in the people" 11.18.2014 on the role of Peter the Great in the development of Russian measures of length (for example, a arshin). Entire history of the use of a arshin in Russia investigated.

Доклад был сделан дважды: короткая версия - 31 октября 2019 г. на конференции в филиале ИИЕТ (СПб), а полная - 1 ноября на Факультете географии СПбГПУ им. Герцена.
История метра показана с первых научных разработок, приведших в итоге к его появлению.

Ao longo do século XX, generalizou-se a ideia de que, na idade média, a capacidade do alqueire oscilaria entre 14 e 18 litros. No entanto, num trabalho recente, foi possível que: a) os alqueires legais medievais tinham um valor próximo do modius romano (8.667 litros); b) havia outros alqueires bem conhecidos cuja capacidade era bastante inferior à do modius; c) o próprio alqueire manuelino (13.1 litros) estava fora daquele intervalo. No presente artigo, determino as capacidades de mais alguns alqueires medievais. O tema central deste artigo já não é, porém, a unidade do sistema de medidas, mas sim o conjunto de medidas que compõem o sistema e a forma como se relacionam entre si. Serão estudados nesta perspectiva mais global os sistemas legais medievais e ainda os principais sistemas do arcebispado de Braga, bispado do Porto e cidade de Lisboa. É dada particular atenção ao problema da filiação dos sistemas portugueses, essencial para enquadrar a multiplicidade de sistemas usados nas várias regiões.

Доклад был сделан на Конференциях «Советская наука и техника в годы Великой Отечественной войны» 22 апреля и «Историческая география России: ретроспектива и современность комплексных региональных исследований» 19 мая 2015 года соответственно.
На основе анализа данных о протяженностях более чем 1000 российских дорог выявлены вероятные варианты протяженности русской версты.
(Der Bericht (russisch).
Auf der Grundlage der Daten über den Ausmaßen von mehr als 1.000 russischen Wege wurde man die wahrscheinlichen Varianten der Größe Russischen Werst beurteilen.
The report (Russian).
It was assess the likely variations of sizes of Russian verst, based on the data on the distances of more than 1,000 Russian roads.)

Novos estudos de história metrológica, Ponta Delgada, Centro de Estudos Humanísticos, 2016, 180 p.
Conteúdos principais:
1. Os sistemas metrológicos ibéricos na Idade Média. Um diálogo entre o Mediterrâneo e o Atlântico
2. Sociedades portuárias e técnicas mercantis. A metrologia do transporte marítimo (séculos XIV-XV)
3. Medidas agrárias (medievais) portuguesas. Problemas de método
4. Economia e metrologia na Idade Média
5. Os regimentos do almotacé-mor (1483-1603)

Since the early 20th century, and especially during the last few decades, interdisciplinary
research has strengthened the evidence that during earlier prehistory (35,000–9,000 BP)
people observed certain celestial phenomena and reflected about the spatiotemporal structure
of the world they perceived themselves as dwelling within. What appear to be traces of very
early systems of time-reckoning and visions of the cosmos can be found in depictions on both
fixed and transportable objects (parietal/mobile art) within and outside of caves or related to
other distinctive natural or man-made places. While interpretations of such evidence have
often proved controversial, in broad terms there is little doubt that astronomy played an
important and integral part in the early cognitive development of humankind.
The evidence suggests that there existed during earlier prehistory an archaic form of
astronomy that included such components as simple natural calendars, more complex ‘palaeoalmanacs’,
and the knowledge of certain asterisms. The motivations for watching the sky may
have been both practical and philosophical: a suitable ‘cosmovision’ would have helped give
meaning to life. In order to transform basic astronomical knowledge into suitable systems of
time-reckoning and cosmographic models, people would not only have needed a first-rate
imagination and the ability to conceive abstractions, but also a degree of technical ingenuity.
Table 1.0.1 presents a brief chronology of earlier prehistory from the Lower Palaeolithic to
the Epipalaeolithic. The available archaeological evidence and the hitherto discussed palaeoastronomical
evidence restrict the geographical area of interest to Africa, Australia and Eurasia.
The archaeological record from earlier prehistory in general can be divided into fixed and
mobile artefacts. Rock-art—paintings, engravings, and sculptures—exists within deep caves
as well as at particular places outdoors, such as river valleys and rock shelters. Thematic
‘maps’ have been identified on bones and in caves, demonstrating that people were aware of
landscape features. Caves and rock shelters, as well as other landscape features, had both
practical and symbolic significance. The construction of dwellings, the structure of open-air
campsites, tools, and mobile artwork set up further cognitive categories. Among the graphical
representations found in parietal and mobile artwork there exist both abstract symbols and
naturalistic depictions.
From at least the Aurignacian period (c. 32,000–26,000 BP), hunter-gatherer cultures
depicted the periodic annual phenomena of flora and fauna, both in fixed contexts and on
mobile objects. As hunters, they were surely well aware of the biological rhythms of animals,
such as their diurnal and nocturnal activities, the mating season, the duration of their
pregnancy, their time of birth and incubation, their change of fur, the formation and dropping
of their antlers, their annual migration (particularly in the case of birds), and the production of
spawn. And as gatherers they could not fail to be familiar with the periodic rhythms in the
development of plants. The seasonal change between summer and winter camps is clear from
the remains of the fauna and flora that were either consumed or used in other ways. Some
local cave-sanctuaries also seem only to have been visited at certain times, since the creation
and renewal of graphic art only occurred during ‘special’ time periods. In addition, there exists
some evidence that the illumination of caves and rock shelters by sunlight on certain days of
the year may have been significant, an example being the solstitial illumination of the
innermost chamber of El Parpalló, a cave-sanctuary near to Gandía in Spain that was occupied
in the Solutrean and Magdalenian periods.
Palaeoastronomical research has indicated the existence, within both parietal and mobile
art, of astronomical/natural calendars using systems of images and signs to denote certain
time periods. Observations of the moon appear to have been particularly important, with both
its phase cycle and its changing position along the horizon recorded over periods up to several
years. People not only reckoned time using the moon; there are also notations that evidently
related to solar cycles and even luni-solar cycles. An example of the latter is the elaborate
Thaïs Bone (Case Study 1.1). Among mobile objects dating from the Aurignacian to the
Azilian have been found several tally sticks and tally pebbles (Azilian) that illustrate different
kinds of time-reckoning.
Earlier prehistoric parietal and mobile art contains many representations of animals
(mammals, birds, reptiles and even insects), as well as occasional depictions of plants. Many
of these representations appear to have correlated the biological rhythms of certain animals
and/or human women (menstruation, pregnancy) with astronomical periods. The term
‘almanac’ is probably appropriate. An example comes from the Geißenklösterle cave in
Germany, where an ivory plate dating to 35,000–32,000 BP contains one of the oldest known
representations of a human figure. This appears to relate to the constellation Orion and a lunar
and pregnancy calendar (Case Study 1.2). In some of the more complex examples, especially
those that span longer periods, a clearly structured system of counting—a so-called
Earlier prehistory 15
‘arithmetical’ notation—has been used to indicate astronomically significant time units (for an
example see Case Study 1.3).
There is evidence that during the Upper Palaeolithic certain asterisms, including Corona
Borealis, the Pleiades and the Hyades, were not only recognized but were important for time
reckoning or well-suited for the purpose of determining orientation. Perhaps the best publicised
examples of possible representations of the Pleiades and Hyades are from the aurochs
(no. 18) in the Hall of the Bulls at Lascaux cave in France, although the real significance of
this site is the breadth and complexity of possible astronomical associations amongst what is
undoubtedly a supreme assemblage of Upper Palaeolithic art (see Case Study 1.4).
The astronomical heritage of earlier prehistory is diverse and fragmentary and its
identification, substantiation and evaluation raise a number of serious issues of credibility.
Scientific rigour can only be achieved through the integration of methods from the
humanities, natural sciences and experimental archaeology, but there is also a need for phenomenological
methodology. The interpretation of iconography involves the concurrence of
syntactic, semantic and pragmatic aspects, and the recognition of multiple levels of meaning.
To date, Palaeolithic astronomical heritage has not been promoted or protected in any
consistent way. Some museums specifically point out the astronomical significance of mobile
artefacts in their collections but there is not a single in-situ indication of the astronomical
connotations of fixed items such as rock art; for some years it has been left to broader media
coverage (in the form of printed matter, audio-visual material, electronic media and
planetarium programs) to raise awareness of proto-astronomy (as well as proto-mathematics
and other proto-sciences) during Palaeolithic times. Palaeolithic astronomical heritage is not
explicitly protected, although fixed items are often implicitly included within existing
measures to preserve historic buildings and monuments of broader significance.

In this work, we attempt a philosophical approach to the measurement process motivated by the comments of Martin Heidegger on the poetry of F. Hölderlin about the relationship of the measure with poetry and human dwelling. We start with discussing the question “what is a measurement” in the context of the fundamental human effort to get familiar with the unknown world surrounding him/her. Then we focus on two fundamental features/limitations of the measurement process: a) the inevitable influence of the observation act and the design of measurement process on the results of measurement and b) the unattainable goal of the fully accurate measurement due to the omnipresence of noise.  These two features/limitations motivate us to investigate broader considerations and interpretations of the notion of measure and act of measurement. We initiate such an investigation based on a) the philosophical comments of M. Heidegger on the poetry of F. Holderlin and c ) the concept and role of measure and measurement in art and artistic practice in general. Our ultimate goal is to prepare and cause a cross-fertilization of the scientific with the philosophical/artistic approach to the measure and measurement process.


Keywords: Philosophy of measurement, accuracy, uncertainty of measurement, Heidegger, Poetry

Das ist die Übersetzung des auf der Konferenz "Die Zeit von Peter der Große in den Menschen" vorgelegten Berichts über die Rolle des Peter des Großen in der Entwicklung der russischen Längenmaße (auf Beispiel der Arschin), den am 18. November 2014 in St. Peterburg berichten wurde. Es war gesamte Geschichte der Verwendung eine Arschin in Russland gesucht.

This article discusses the process of formation of Russian historical metrology as scientific discipline during the pre-revolutionary period. Recording of practical metrological knowledge of the second half of the XVI-XVII centuries was replaced by scientific interest in the XVIII century. It was characterized by systematization of information on old and modern measures of the peoples of Russia, Europe and the East. In the first half of the XIX century, generalizing studies on historical metrology appeared. Further development of this field of knowledge needed expansion of historical sources, criticism, development of the conceptual and methodological framework. In the second half the XIX – beginning of the XX century these problems were solved within separate metrological studies, specialized lecture courses and manuals that were necessary for professional training of historians, archivists and archaeographs. Pre-revolutionary authors laid the theoretical, methodological and factual foundation of historical metrology which gained further development in works of the Soviet and modern Russian historians.

J F Fernel's 3 texts are a mixed blessing apropos his subject matter. He has tried to measure a degree of latitude, used the Roman Pes/Passus and sun declination/altitudes but his figures are awry and totally inadequately used. He has even tried to alter Ptolemy's base line to Paris with startling inaccuracies throughout the whole of the 3 texts. He fundamentally has not been able to use his researches with total mis-copying of figures there-in .

Claudius Ptolemy in his Geographike Hyphegesis wrote the same two words, once in chapter7 and then in chapter 11 of Book 1. The word has no actual determinant and thus appears to have been ignored by researchers to the detriment of establishing a logical answer to the conundrum it introduces. Therefore a search through historical possibilities will be but one method to ascertain how the 500 Stade latitude arose.

Practically everything we do in life requires measurement which derives from Metrology. In cartography we use all forms of mathematics and geometry to form measurements for virtually every action we take, particularly scale and proportion. Where they cam from ia a fascinating historical journey which indicates just how adept our forefathers were when faced with necessity.

Рассказывается о ранних математических инструментах в коллекции Музея МГТУ им. Н.Э. Баумана, применение которых относится к XVII-XVIII вв., с целью проследить взаимосвязь между естествознанием и инженерными, сугубо техническими дисциплинами на примере использования научных приборов и устройств в деятельности естествоиспытателей, учёных и изобретателей. Выбор темы продиктован нечастым упоминанием о подобных инструментах в современных российских изданиях и источниках. Материал статьи публикуется впервые и направлен на укрепление междисциплинарных научных связей между Музеем землеведения МГУ им.

During the Palaeolithic epoch parallel to the emerging human mind and self-consciousness the abstracting, logical-mathematical (arithmetic and geometrical) thinking developed from a neural basis, which already was present in the animal kingdom. Moreover, in the evolution of man, processes of counting and calculating, internally running automatically in the brain, had been externalized and stored in various forms on certain “data carriers” of different material. This was closely linked to the emergence of the human form of self-consciousness and, above all, of the specific human language ability, which differentiates the “world” into the respective subject and the objects. Past research in the field of palaeomathematics has made a considerable contribution to the prehistory of counting, calculating and calculating aids in the “Stone Age”. It is shown that the origins of counting already existed in the Lower Palaeolithic (Acheulean: 1.76 million to 150,000 years ago). Numeracy and calculation aids, as well as the beginnings of arithmetic, closely connected to metrology, calendars and astronomy, can be demonstrated in the Neolithic Age, 50,000–10,000 years ago and in
the transition to the post-ice age cultures (Mesolithic, Neolithic) 13,000–5,500 years ago. The beginnings of calculus and abacus are to be found in the Palaeolithic.

Im Paläolithikum hat sich zugleich mit der Ausgestaltung des menschlichen Selbstbewusstseins auch das abstrahierende, logisch-mathematische (arithmetische und geometrische) Denken aus einer bereits im Tierreich vorhandenen neuronalen Basis entwickelt.
Darüber hinaus wurden in der Evolution des Menschen im Gehirn intern
automatisch ablaufende Zähl- und Rechenvorgänge in „externalisiert“ und in verschiedenen Formen auf „Datenträgern“ unterschiedlichen Materials „gespeichert“. Dies war eng mit dem Auftauchen der menschlichen Form des Selbstbewusstseins und vor allem
der besonderen menschlichen Sprachfähigkeit verknüpft, die in das jeweilige Subjekt und die Objekte der „Welt“ differenziert. Die bisherige Forschung auf dem Gebiet der Paläomathematik hat einen beachtlichen Beitrag zur Urgeschichte des Zählens, des
Rechnens und der Rechenhilfen in der „Steinzeit“ geleistet. Es zeigt sich, dass die Ursprünge des Zählens bereits im Altpaläolithikum (Acheuléen: vor 1,76 Millionen bis 150.000 Jahren) liegen. Rechenfähigkeit und Rechenhilfen, sowie die Anfänge der
Arithmetik, eng verbunden mit Metrologie, Kalendarik und Astronomie, können im Jungpaläolithikum, vor 50.000–10.000 Jahren und im Übergang zu den nacheiszeitlichen Kulturen (Mesolithikum, Neolithikum), vor 13.000–5.500 Jahre, belegt werden. Die Anfänge des Kalkulierens und des Abakus liegen im Paläolithikum.

From Eratosthenes' via Claudius Ptolemy to Roman, Arab, Medieval and even Columbus, the latitudinal distance measures have been calculated by researchers writing thousands of words but using distance measures which could not have been applicable given the Form of the Earth. Most texts fail the test of reasonable accuracy as there is only one methodology suitable to quantify such measures; that emanating from ground surveys thus the length of the degree is determined from the latitudinal position of the surveyor. Therefore, with a simple acceptance that the surveyors, be they Greek, Egyptian Cord Stretchers, Agrimensores/geometres, Arab Astronomers or medieval sailors trying to read the Back Staff or similar, were as accurate as possible, and accepting their results, by purely analysing the measurements made, we can determine their basic units and measures. We can even estimate their position when the measure was taken, as the Earth distances vary precisely. This text recalculates, without major comments on previous attempts, the surveys and their measures as they can only have been determined on the face of the earth. Why do this, because the figures used previously are at times incorrect and a standard is required. ChMEA/1; CHARTS, THEIR LATITUDINAL MEASURES REASSESSED FROM HISTORICAL ATTEMPTS TO DEFINE THE DEGREE OF LATITUDE INTRODUCTION The earth is spherical but it is not a perfect sphere it is an oblate spheroid. That is the equatorial circle is greater than the putative polar circle by a ratio of 1:297. Not being perfectly spherical the polar circle exists in name only as it is in fact distorted having two radii. Thus it is a non uniform curve as it leaves the equator and approaches the pole. On the face of the earth at the equator, one minute of latitude is 6046.4 feet/ 1842.9 metres, whilst at the pole the equivalent one minute of a degree is 6107.8 feet/1861.7 metres. At the equator the one minute of longitude is 6087.2 feet/1855.4 metres, any of which x 60 will give the appropriate degree length. In my text ChMES/1, which followed ChMIL/1, I concentrated solely on the possible survey measures applicable to Portolan Charts and balanced the differing measures for 24N, 36N and 50N, the nominal latitudinal spread of a Portolan Chart. But by endeavouring to keep that text as short as possible, it became obvious that a large portion of information for the historical measures and usage of the Latitudinal degree was missing. The Longitudinal measurements were equally a subject of little real discussion and certainly were not the subject of survey measures which is therefore another strand of the research to be discussed at some later date.

A collection of 35 iron weights, currently preserved in the Museu Nacional Machado de Castro, is studied. These weights, dated of the 18th/19th centuries and some of them identified as belonging to the University of Coimbra, do not contribute to validate the widely spread idea that Portugal enjoyed uniform weights throughout the country. On the contrary, they show a crossing of influences leaving little room for the legal system. In particular, the use of libras or arrátels with medieval roots (12.5, 14 and 15 onças) was detected, instead of the legal arrátel of 16 onças. Moreover, foreign weight standards, such as the English avoirdupois standard or the Cologne mark standard, appear to be more important than the Portuguese standard, a variant of the Cologne mark called marco de Colonha in medieval times.

Доклад на Научной конференции «Международные сети как фактор интеграции научного сообщества» (Секция «История географии»), Санкт-Петербург, 13 ноября 2018 года
Рассматривается вопрос о реальной протяженности стадия, которым мог оперировать Эратосфен в своих трудах по географии Земли. А также предлагается гипотеза о происхождении "стадия" в 155...158 м.