Tibetan units of measure
Tibetan units of measurement were used in Tibet to determine the sizes of objects of everyday life, of geometric construction drawings in painting, of subdivisions of the ecliptic in astronomy and of time according to the types of size, length , volume , weight and time interval . Certain objects of daily life, such as quantities of grain, were not weighed in Tibet, but measured with a volume measure.
Length measurements
In terms of length, a distinction was made between units of measurement, the sizes of which were determined on the basis of a fixed measuring rod, that is, which had a fixed absolute size, and proportional dimensions as well as arc or angle dimensions.
Length dimensions with specified dimensions
Measures of length in everyday life
The smallest unit of length practically used in Tibetan economic life was the sor-mo ("finger width"), which corresponded to the assumed width of a finger. 12 sor-mo form a mtho (" span ", in Tibet the span between the index finger and thumb). 2 mtho correspond to a khru ( cubit ) and 4 khru form a rank 'dom or a ' dom ( fathom ).
For this measuring system, we have also received a corresponding measuring stick with a length of 182 cm. The bar is divided into 8 equal parts by circumferential notches. The last of these 8 parts is divided into 12 parts, which are numbered from 1 to 12 consecutively. This is the unit of measurement sor-mo .
Using the length of the measuring stick, a fathom ( Tib . : 'dom ) is 182 cm. The ell (Tib .: khru ) measures 45.5 cm. A span (tib .: mtho ) corresponds to 22.75 cm and a finger width (tib .: sor-mo ) is rounded up to 1.896 cm. Due to the nature of this measuring stick, it can be assumed that the measuring instrument was not used as a ruler for drawing lines.
It can be assumed that the absolute size of these units of length varied in different parts of Tibet.
Length measures of the kālacakratantra
In the length system, which was handed down from India to Tibet by the Kālacakrantra , the smallest unit is given as very fine dust (Tib .: phra-rab rdul ; Sanskrit : sūkṣma ), which is the size of
a finger's width (Tib .: sor-mo ). This corresponds to approximately 0.000072 millimeters. The largest unit is called dpag-tshad (Sanskrit: yojana ). Such a dpag-tshad covers 32,000 cubits, i.e. about 14.56 km.
This system of measurement found practical use in Tibet only to describe the size of the structure of the world, whereby only the unit of measurement dpag-tshad was important here.
Table of units of measurement:
| Conversion factor for the next higher unit | Name (Tibetan) | Name (Sanskrit) | meaning | Approximate length | |||||
|---|---|---|---|---|---|---|---|---|---|
| 8th | phra rab rdul | sūkṣma | very fine dust | 0.000072 millimeters | |||||
| 8th | phra mo | aṇu | fine dust) | 0.000576 millimeters | |||||
| 8th | skra yi rtse mo | vālāgra | Hair tip | 0.0046 millimeters | |||||
| 8th | ske tshe | rāji | Mustard seed | 0.037 millimeters | |||||
| 8th | shig | yūkā | louse | 0.296 millimeters | |||||
| 8th | nas | yava | Stye | 2,368 millimeters | |||||
| 24 | sor mo | aṅgula | Finger width | 1.896 centimeters | |||||
| 4th | khru | hasta | Cubit | 45.5 centimeters | |||||
| 2000 | gzhu | dhanus | Arc length | 1.82 meters | |||||
| 4th | rgyang grags | krośa | Call range | 3,640 kilometers | |||||
| dpag tshad | yojana | 14.56 kilometers |
Proportional measures of Tibetan painting
On design drawings Tibetan thangkas , like a grid are drawn to figures using the distances of the individual lines, the basic size also as sor is called "finger width". However, this is not a fixed length measure that has a fixed length, such as the length measure "meter", but a so-called proportional measure. The basic size to be used for a certain drawing or construction is the width of the middle finger of the representation of the respective person or deity in the drawing. This basic size was accordingly sor called "finger width".
Depending on the size of the drawing, these Sor dimensions had different lengths in absolute terms. However, the size of the sor within a drawing was always the same. The proportions had different names depending on their relative size. The smallest unit was nas called "barley grain". 2 nas corresponded to a rank and 4 rkang resulted in a sor , which was also called cha-chung "small part". The next larger unit was a cha-chen "large part" that comprised 12 sor .
Angular dimensions
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Angular measurements occur in Tibetan astronomy , which deals in particular with the calculation of the positions - called astronomical lengths - of the moon , the sun and the planets Mercury , Venus , Mars , Jupiter and Saturn . Here, in the geocentric worldview of the Tibetans, the sun is a planet .
The great circle created by the projection of the sun's apparent orbit over the course of a year on the celestial sphere is called the ecliptic . From the point of view of the earth, all planets including the moon move on it with slight deviations in the so-called latitude .
The first division of this great circle in Tibet to be mentioned here is that into 12 signs of the zodiac , which in Tibetan were called khyim . As shown in red in the figure above, these zodiac signs had names, but for the astronomical calculations they were counted and designated with the numbers 0 to 11. The same applies to the division of the ecliptic into the so-called 27 lunar houses or lunar stations, which were called rgyu-skar in Tibetan and which were counted from 0 to 26, as shown in the blue color in the figure below.
The arc or angle unit of measurement rgyu skar was divided into 60 chu tshod "arc hours". The chu tshod were divided into 60 chu srang "minutes of arc". A chu srang consisted of 6 dbugs "bow breath", which in turn were divided into "parts". It becomes clear that with this system of angular dimensions the length of a planet could be determined very precisely.
The excerpt from a Tibetan astronomical thangka shown on the right shows the moonhouses 20 chu smad , 21 gro bzhin and 22 mon gre in the fifth circle ; the zodiac signs 8 gzhu and 9 chu srin are drawn in the third circle . The division of the moon houses in chu tshod is shown with the numbers 15, 30, 45 and 60.
Table of angular dimensions:
| Full circle: | 12 khyim | 360 degrees | 27 rgyu skar | 360 degrees | |||||
|---|---|---|---|---|---|---|---|---|---|
| 1. Subdivision: | 1 khyim | 30 degrees | 1 rgyu skar = 60 chu tshod | 13 degrees and 20 minutes of arc | |||||
| 2. Subdivision: | 1 chu tshod = 60 chu srang | 13 arc minutes and 20 arc seconds | |||||||
| 3. Subdivision: | 1 chu srang = 6 dbugs | 13 + 1/3 arc seconds | |||||||
| 4. Subdivision: | dbugs | 2 + 2/9 arc seconds |
Measure of capacity
Cereals, legumes, etc. The like were not weighed in Tibet, but measured with a measuring box. These were called 'bo or bogs' bo . The largest unit of measurement thus given was called a khal . A khal was divided into 20 bre . Each bre comprised 6 phul ("handful"). There were different measuring boxes for measuring the khal and the bre .
The size of this measuring box was very different depending on the part of the country. In the 17th century, the central Tibetan government established a standard measure for the khal that is binding for the treasury with a suitably calibrated measuring box . The associated measuring device was called mkhar ru or gtan tshigs mkhar ru . The weight of the grain, which was measured with such a measuring device, should have been around 15 kg. The statements made by travelers to Tibet about the weight of this Normkhal vary widely. It should also be noted that the weight of a grain quantity, which is measured with a volume measure, can vary greatly depending on the size of the grains and their water content.
Assuming an approximate density of 0.8 g / cm³ for grain, one khal would correspond approximately to a volume of 18750 cm³, i.e. 18.75 liters. A bre would be a little less than 1 liter.
The conversion of the sizes of grain quantities determined with the various measuring boxes to the standard measure of the government was carried out by the officials in the Tibetan Treasury using the abacus with loose stones . In order to get the problem of the formation of leftovers under arithmetic, the size phul was divided into 120 nang gi rdog ma "inner pieces". Further subdivisions led to size units, the size of which was khal .
Table of capacities:
| Name (Tibetan): | khal | bre | phul | nang gi rdog ma | phyi ma'i rdog ma | de´i phyi ma´i rdog ma | yang phyi rdog ma | mthil phyi rdog ma | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Conversion factor for the next higher unit: | 20th | 6th | 120 | 120 | 120 | 120 | 120 |
- |
Weight measurements
In terms of weight units, a distinction was made between units for weighing precious metals and units for the weight of butter, meat, wood, etc.
Units of weight for gold
The smallest unit of goldweights was nas called "barley grain". Two grains of barley are a ma nu . 2 of them are a se ba . 2 of them form a gser tam . 15 gser tam make a zho . The size of these gold weights varied greatly from region to region. For an overview, see the historical currency of Tibet .
Usual measures of weight
For weighing butter, meat, wood, hay, etc., beam scales were used in Tibet, which had sliding weight stones.
The largest unit of weight was also referred to as the khal . This weight khal was equal to 20 nyag . There were 4 spor per nyag .
Time sizes
Time division according to the Tibetan calendar
The time intervals known in Tibet were the year (tib .: lo ), month (tib .: zla ba ), day (tib .: zhag ) and time of day (tib .: dus tshod ). See the Tibetan Calendar for details of this complicated time division .
Astronomical schedule
The three different types of day listed in the Tibetan calendar, namely the zodiac day , the lunar day and the natural day , were used for astronomical calculations analogous to the division of the ecliptic into the time intervals chu tshod "hour", chu srang "minute" and dbugs "Length of a breath" divided. One day consisted of 60 chu tshod . One chu tshod was divided into 60 chu srang . A chu srang consisted of 6 dbugs .
For the natural day (Tib .: nyin zhag ) with 24 hours this results in the following:
| Tibetan name: | nyin zhag | chu tshod | chu srang | dbugs | |||||
|---|---|---|---|---|---|---|---|---|---|
| Meaning: | Natural day | Tibetan hour | Tibetan minute | breath | |||||
| Conversion factor for the next higher unit: | 60 | 60 | 6th | ||||||
| Length: | 24 hours | 24 minutes | 24 seconds | 4 seconds |
literature
- David P Jackson , Janice Jackson: Tibetan Thangka Painting. Methods & Materials. Second and Revised Edition. London 1988
- Loden Sherab Dagyab: Tibetan Religious Art. Part I-II. Wiesbaden 1977
- Winfried Petri: Indo-Tibetan Astronomy. Habilitation thesis to obtain the venia legendi for the subject history of natural sciences at the high natural sciences faculty of the Ludwig Maximilians University in Munich . Munich 1966
- Dieter Schuh: Studies on the history of the Tibetan calendar calculation . Wiesbaden 1973
- Dieter Schuh: Studies on the History of Mathematics and Astronomy in Tibet, Part 1, Elementary Arithmetic . Central Asian Studies of the Department of Linguistics and Cultural Studies of Central Asia at the University of Bonn, 4, 1970, pp. 81–181
- Ngag-dbang chos-'byor: rDe'u'i rtsis-rig la mkho-re'i byis-pa mgu-ba'i long-gtam . Old Tibetan block print of a treatise written by an officer of the Treasury of Trashilhünpo Monastery.
Individual evidence
- ^ Precious Deposits, Vol. Four, Beijing 2000, p. 272
- ↑ Based on an Armenian trader's diary from the end of the 17th century, Levon Khachikian gives the following information about the weight units for gold used in Lhasa at that time: 20 seva = 1 sookam (zho gang?). 1 sookam = 12 cal , which corresponds to 5.06 g. See Khachikian, Levon: "The Ledger of the Merchant Hovhannes Joughayetsi". Journal of the Asiatic Society , vol 8, no 3, 1966, p. 153-186.