Timekeeping Instruments
Time measurement is an important aspect of astronomical observations. In the 14th century, with the invention of the first mechanical clock, instruments such as sundials, and water clocks gradually faded away from the category of essential astronomical instruments. Unfortunately, we often forget that inventions are not one-day efforts but the gradual development of ideas leads to inventions. Numerous developments have been made in the past to find the accurate measure of time. Initially, people were dependent on nature, they observed periodicity in the movement of the Sun and the moon and took it as the primary basis to set their daily activities, Later on, People started to take an interest in numeration methods, and also observed such unusual activities in the nature, resulting them to take interest in astronomy and mathematics. Their initial efforts included finding the set the systemic units of measurement for the fundamental quantities, length, time, etc, Various units have been adopted, the smallest unit used is nimesha (time spent in the blinking of the eye)- found its mention in Rigveda, Satapatha Brahmana.
दश च वै सहस्राण्यष्टौ च शतानि संवत्सरस्य मुहूर्ताः। यावन्तो मुहूर्तास्तावन्ति पञ्चदशकृत्वः क्षिप्राणि । यावन्ति क्षिप्राणि तावन्ति पञ्चचदशकृत्व एतर्हीणि । यावन्त्येतर्हीणि तावन्ति पञ्चदशकृत्व इदानीनि। यावन्तीदानीनि तावन्तः पञ्चदशकृत्वः प्राणाः । यावन्तः प्राणास्तावन्तोऽक्तनाः । यावन्तोऽक्तनास्तावन्तो निमेषाः। यावन्तो निमेषास्तावन्तो लोमगर्ताः । यावन्तो लोमगर्तास्तावन्ति स्वेदायनानि। यावन्ति स्वेदायनानि तावन्त एते स्तोका वर्षन्ति ॥ ŚB (12.3.2.5).
Now the question arises as to how and why people got interested in measuring time. There could be many reasons, for example, to measure the exact time for conducting Vedic practices, and other, agricultural practices. The primary source of living was agriculture, and agricultural practices were rain-dependent, which in turn encouraged people to speculate the beginning of the rainy season. Moreover, Celestial navigation is an important part of observational astronomy, Marine navigation was equally important for trade, and many instruments have been developed to precisely measure the time for the same. The earliest known instruments include water clocks which were used for time measurement from the earliest times up to the nineteenth century. Gnomons, mentioned in the Shulbasutra, were initially used to measure the directions, Later on, it was included as a major component of sundials.
Water Clock
A water clock is an instrument that uses the flow of water through a small aperture as a measure of the interval of time. It can be of three types, a water clock of outflow type was mentioned in the Vedanga Jyotisha, However, the specification of the apparatus has not been defined, those texts in which outflow type water clock is mentioned, incorporate the units of measurement “nali, nalika, nadika, nadi” the instrument is called a Nadika Yantra. As the name suggests nali means reed, tube, of cylindrical shape. The outflow-type water clock consists of a vessel with a hole through which water flows at a constant rate. In addition to Vedāṅga-jyotiṣa, Kauṭilya’s Arthaśāstra, the Śārdūlakarṇāvadāna of the Divyāvadāna and Jyotiṣkaraṇḍaka also describes outflow type instrument, some of them includes their specifications as well.
Later at the beginning of Siddhanta astronomy, Aryabhata describes another type of water clock (sinking bowl), which is called Ghatika Yantra in which time is measured in ghatis, one ghati, one nadi, which is similar to modern 24 minutes, further smaller unit palas – 24 seconds. A vessel of hemispherical shape made of copper and a hole is so formed at the center that a bowl sinks into the larger vessel filled with water exactly 60 times a day, and once every 24 minutes.
वृत्तं ताम्रमयं पात्रं कारयेद् दशभिः पलैः |
षडङ्गुलं तदुत्सेधो विस्तारो द्वादशानने ||
तस्याधः कारयेच् छिद्रं पलेनाष्टाङ्गुलेन तु |
इत्य् एतद् घटिकासंज्ञं पलषष्ट्याम्बुपूरणात् ||
स्वेष्टं वान्यद् अहोरात्रे षष्ट्याम्भसि निमज्जति |
ताम्रपात्रम् अधश्छिद्रम् अम्बुयन्त्रं कपालकम् || आर्यभटीय सिद्धान्त||
‘Get a round (i.e. hemispherical) bowl made with ten palas of copper. Let its height be six aṅgulas and the diameter at the mouth twelve aṅgulas. Get a hole bored at its bottom [so that a gold wire] one pala [in weight] and eight aṅgulas [in length can pass through it]. This is designated as Ghaṭikā -Yantra because it is filled with sixty palas of water”. After Aryabhata, the sinking bowl-type water is described in several astronomical texts. Lallacharya (8th or 9th century) in Sishyadhivriddhitantra modified the size of the perforation as,
दशभिः शुल्बस्य पलैः पात्रं कलशार्धसन्निभं घटितम् |
हस्तार्धमुखव्यासं समघटवृत्तं दलोच्छ्रायम् ||
सत्र्यंशमाषकत्रयकृतनलया समवृत्तया हेम्नः |
चतुरङ्गुलया विद्धं मज्जति विमले जले नाड्या ||
“The bowl, which resembles half a pot (i.e. hemispherical), which is made of ten palas of copper, which is half a cubit (i.e. twelve aṅgulas) in diameter at the mouth and half (i.e. six aṅgulas) as high, which is evenly circular, and which is bored by a uniformly circular needle, made of three and one-third māṣas of gold and of four aṅgulas in length, sinks into clear water in one ghaṭikā (nāḍī)”.
This description was more accurate than the earlier texts but possibly some trial and error methods have always been involved in measuring the size of the perforation.
Gnomons and Sundials
Although the use of gnomon was prevalent since the period of Sulbasutra but to find direction. directions. Kautilya in his Arthashastra mentioned the measurement of time by means of the length of the shadow (Chaya- Pramana) as
“He should divide the day into eight parts as also the night by means of nālikās, or by the measure of the shadow (of the gnomon). (A shadow measuring three pauruṣas, one pauruṣa, (and) four aṅgulas, and the midday when the shadow disappears are the four eighth parts of the day. By them are explained the later (four)”.
Further, Siddhanta texts AryabhatiyaShiddhanta, BrahmaShutaSiddhanta, Siddhantatatvaviveka, Siddhanta Shekhara describes different varieties of sundials for measuring time using sunlight. Different varieties of sundials include the horizontal dial with a triangular gnomon (Palabhā-yantra), the column dial with a horizontal gnomon (Kaśā-yantra), and the graduated ring in which sunlight enters through an aperture (Cūḍā-yantra). Palabha denotes the length of the shadow thrown at noon by a gnomon of 12 units (aṅgulas) on the days of the equinox. In Jai Singh’s Observatories, two masonry instruments, viz. the Nadivalaya-yantra and the Samrat-yantra are constructed on the principle of Palabha Yantra.
Perpetual machines: A perpetual motion machine (Ajasra Yantra) is a device that is supposed to perform useful work without any external source of useful energy, along with various astronomical instruments Brahmagupta in his Brahmasphuta Siddhanta (628CE) describes perpetual motion wheel thus,
“Make a wheel of light timber with uniformly hollow spokes at equal intervals. Fill each spoke up to half with mercury and seal its opening situated in the rim. Set up the wheel so that its axle rests horizontally on two upright supports. Then the mercury runs in some hollow spaces and downwards in some others, as a result of which the wheel rotates automatically forever”.
In his opinion, if mercury overcomes the inertia, it can be used as the time measuring device ( Akhanda kala- immeasurable cyclic time). Further, in the twelfth century, Bhaskara added that the hollow spokes of the wheel mercury wheel should be kinchid vakrah like Nandyavarta Flower.
ताश्च नद्यावर्तवदेकत एव सर्वाःकिञ्चिद्वक्रा योज्याः|.... अत्र युक्तिः|यन्त्रैकभागे रसो ह्यारामूलं प्रविशति| अन्यभागेत्वाराग्रं धावति| तेनाऽऽकृष्टं तत् स्वयं भ्रमतीति|| (सिद्धान्तशिरोमणि-५०)
“Spokes should be slightly curved, all towards the same direction like the petal of the Nandyavarta (Tabernaemontana coronaria) flower”.
Yasti Yantra (The staff): It is basically a representation of the radius of the celestial sphere. To measure time, Brahmagupta describes the use of Yasti Yantra as,
यष्टिव्यासार्धे ऽग्रायष्ट्यग्रान्तरसमज्यया धनुषि ।
घटिका द्वितीयवृत्ते याताः प्रागपरतः शेषाः । । 21 । ।
"On the sphere whose Radius is equal to the length of the yaşți, the distance between the rising (or setting) point and the tip of the yaşți is represented by an arc (dhanus). On the second circle (i.e. the diurnal circle drawn inside the level circle), the ghatikās elapsed or remaining, in the forenoon or afternoon respectively, are measured."
Chakra Yantra: Chakra Yantra is an instrument resembling a circular hoop, Aryabhata, in his commentary on Surya Siddhanta describes chakra Instruments, similarly, Varahamihira, Brahmagupta, Lalla, Sripati, and Bhaskara also give some information on chakra Yantra.
Lalla explanation of chakra Yantra can be represented as,
वृत्तं कृत्वा फलकं षड्वर्गाकं तथा च षष्ट्यङ्कम् ।
मध्यस्थितावलम्बं मध्यस्थित्या प्रविष्टोष्णम् ।|20||
तदधोलम्बविमुक्तं गृहादि यत्तदुदितं दिनकरांशात् ।
नाड्यः पूर्वकपाले द्युगतास्ताः पश्चिमे द्युदलात् ।। 21 ।।
"Construct a circular board, graduate it with the 360 divisions (of degrees) as well as the 60 divisions (of ghaṭīs), fix a vertical needle at its center, and set it up in such a way that the Sun may lie centrally in its plane. Moreover, according to K. S. Shukla, Lalla must have used the following formula in order to deduce the time elapsed since sunrise using the solar altitude.
Time elapsed = (semi-duration of day x Sun's altitude)/ (Sun's meridian altitude)
The other instruments are generally variations of Chakra Yantra, Kapala, and Kartari Yantra, Kapala is the horizontally placed semicircular plate, axis pointing upwards, diameter in the north-south directions, and arc to the east or to the west where the shadow happens to fall. These instruments are used to measure time from sunrise to sunset.
Phalaka Yantra (type of Quadrant):Phalaka Yantra was invented by Bhaskaracharya, a simple instrument used to measure time after sunrise. It consists of a vertical gnomon and a rectangular board. The shadow of the gnomon is used to determine the time, and markings on the board help interpret the position of the sun or other celestial bodies. Yantraprakasha (1428CE), a text by Ramachandra Vajpeyin mentions the Kachayantra “glass instrument” to measure time, It description is neither based on European source, nor on an Islamic prototype, (Sarma 2014)
काचस्य पात्र्यौ वदने युते सृजेत्|
ऊर्ध्वं भृतां वालुकयावधारयेत्||
घट्यां तुतत्पातत एव वालुका-
धरोर्ध्वगा स्वेततरा पुणस् तथा||
“Make two glass ampoules joined mouth to mouth. The upper one should be filled with sand. Owing to its trickling down, after one ghati all the sand will be below, and the upper [ ampoule becomes] white Do the same again.”
Astrolabes
Another important instrument of the medieval period is the Astrolabe, it is a multifunctional instrument, that contains two- a dimensional projection of the heavens. The rete is the perforated open plate containing the ecliptic and a star map with pointers indicating the positions of some bright stars. Beneath the rete are to be found a series of plates or discs which are specific to a particular terrestrial latitude and display stereographic projections of local horizon, equal altitude circles. Mahendra Suri called it ‘Yantraraja’ the king of astronomical instruments. It is not known precisely when the astrolabe was invented or by whom, but astrolabes were introduced in India in the eleventh century most probably by al-Biruni. Mahendra suri, a Jaina monk wrote a Sanskrit manual on astrolabe entitled Yantra Raja under the reign of Sultan Firuz Shah in 1370. Along with these instruments, various instruments have been constructed even after the invention of the first mechanical clock, In some places traditional methods are still in use, particularly for ritual purposes.
References
Ohashi, Y., 1994. Astronomical instruments in classical Siddhantas. Indian journal of history of science, 29(2), pp.155-313.
Plofker, K., 2011. The mathematics of measuring time: astronomical timekeeping and the sinking-bowl water-clock in India. Mathematical Time Capsules: Historical Modules for the Mathematics Classroom, 77, pp.55-62.
Raju, C.K., 2007. Cultural foundations of mathematics: The nature of mathematical proof and the transmission of the calculus from India to Europe in the 16th c. CE. Pearson Education India
Sarma, S.R. and Knudsen, T.L., 2011. The Archaic and the Exotic: Studies in the History of Indian Astronomical Instruments. Aestimatio: Sources and Studies in the History of Science, 8, pp.121-127.