Our civil day is divided into 24 hours (primary division), each hour is divided into 60 minutes (secondary division), and each minute is divided into 60 seconds (tertiary division). Accordingly the time of day is represented as a triple

hour : minute : second

- where hour is an integer in the range of 0 to 23, minute is an integer in the range 0 to 59 , and second is a non-negative real number less than 60. Minimum value: 0 : 0 : 0 , Maximum value: 23 : 59 : 59.999.
The primary division of the civil day is the most important. It controls the duration of not only the hour but also the minutes and seconds. The division by 24 is responsible for 86,400 seconds in a day. The duration or time period of each of the three time parameters is longer than desirable.

• Isn't 24 hours an odd random number?

• Why should the day be divided into 24 hours while the hours and minutes are divided by 60?

• Why can't the number of hours be some other random number 16 or 80?

• Should we not decide the primary division of day on a scientific basis?

• Should not the convenience of usage be a criteria while selecting such an important 'primary' division?

• Should not the counting of hours be done from the time we wake up in the morning (sunrise) rather than midnight?

• In the modern age is it not time to remove the irregularities that were introduced due to limitation of the available technologies (sundial) in the medieval times.

• Why can't we, in India, restore our ancient 60 hours in a day (sexagesimal), system instead of 24 to make it regular?

If you are asked 'How was your day?", you would recall the different activities that you performed during your day but probably not calculate the number of hours that you put amongst them since you woke up. Two reasons why time calculations are difficult are: (1) the day is divided by an irregular 24 hour clock, and (2) the body clock and the mechanical clock do not reset at the same time. While the body clock resets when you wake up in the morning (typically 6:00 a.m.), the mechanical clock resets at mid-night.

Origins of the 24-hour

The origins of the 24-hour clock can be traced back to 127 B.C. when Hipparchus proposed dividing the day into 24 equinoctial hours. When Hipparchus and other Greek astronomers needed to divide the hour further for astronomical calculations, they followed the Babylonian's sexagesimal system for convenience, to divide further, an hour into 60 minutes and each minute into 60 seconds. Thus there are 86,400 seconds in a day.

Today, interestingly, regardless of the system being used, CGS (Centimeter Gram Second), MKS (Meter Kilogram Second), FPS (Foot Pound Second) systems, or the International System of Units (SI), the 'second' is defined universally in the same manner, i.e. there are 86,400 seconds in a day. This is because all have understood the importance of a stable almanac and have accepted UTC as the Worlds' Time Standard.

Coordinated Universal Time (UTC)

Today, the basis for the civil time is the Coordinated Universal Time (UTC), the World's Time Standard. In 1960, the International Radio Consultative Committee formalised the concept of UTC, and it was put into practice the year after. This is a 24-hour time standard that is kept using highly precise atomic clocks combined with the Earth's rotation. Unlike Greenwich Mean Time (GMT), UTC is not a Time Zone, but a standard. The world's timing centers keep their time scales closely synchronized - or coordinated - therefore the name Coordinated Universal Time.

Two components are used to determine Coordinated Universal Time (UTC):

1. International Atomic Time (TAI) is a time scale that uses the combined output of some 400 highly precise atomic clocks in in 69 national laboratories worldwide. It provides the exact speed at which our clocks tick. Atomic clocks deviate only 1 second in up to 100 million years. The secret to this impeccable precision is the correct measurement of the second as the base unit of modern time-keeping. The International System of Units (SI) defines one second as the time it takes a Cesium-133 atom at the ground state to oscillate exactly 9,192,631,770 times.

2. Universal Time (UT1), also known as astronomical time, refers to the Earth's rotation. It is used to compare the pace provided by TAI with the actual length of a day on Earth.

The Earth's rotation is not constant, so in terms of solar time, most days are a little longer or shorter than that. For example, the shortest day in 2021 is 24 hours -1.61 ms, on Sat, 11 Sep 2021, while the longest one in 2021 is 24 hours +1.00 ms, on Mon, 26 Apr 2021. TAI does not take into account the variations in Earth's rotation speed, which determines the true length of a day. For this reason, UTC is constantly compared to UT1. Before the difference between the two scales reaches 0.9 seconds, a leap second is added to UTC. On average, Earth has been slowing down a bit over the past decades, so UTC is currently running 37 seconds behind TAI. The system of leap seconds was introduced in 1972. So far, there have been 27 leap seconds, and they have all been positive.

Thus it can be said that the Earth is a good timekeeper: the length of a day is consistently within a few milliseconds of 86,400 seconds, which is equivalent to 24 hours. And by comparing the UTC constantly with UT1, it is possible to correct the difference using leap seconds.

The 24-hour clock is popularly referred to in the United States as the military time. It is the most commonly used time notation and is used by international standard ISO 8601. Why is it, then, that we call the 24-hour clock as an irregular one?

The answer is simple. The International Radio Consultative Committee formalised the concept of UTC in 1960 considering the length of the day to be 86,400 seconds based on a 24-hour time standard. They never questioned the appropriateness of the 24-hour time standard. Just like the French who tried to introduce a decimal system, this committee should have questioned the inappropriate duodecimal system and should have tried to change it.

The 12-Hour Clock

The 12-hour clock is a time convention in which the 24 hours of the day are divided into two periods: a.m. (from Latin ante meridiem, translating to "before midday") and p.m. (from Latin post meridiem, translating to "after midday"). The 12-hour clock was first used from the middle of the second millennium BC and reached its modern form in the 16th century AD.

The 12-hour time convention is common in several English-speaking nations and former British colonies, as well as a few other countries. It is an example of a duodecimal system. Many nations use a combination of the 12-hour and the 24-hour systems; the 12-hour system is preferred in colloquial speech but the 24-hour system is used in written form and formal contexts.

The combination of the 12-hour and the 24-hour time conventions, and its interchangeable usage has resulted in a lot of confusion. When the suffix a.m. or p.m. is omitted it becomes difficult to identify if the said time belongs to the 12-hour or 24-hour system. Major mistakes in reading the time has been observed as a consequence.

DayLight Saving Time for the 24-hour Clock.

Every March, the clocks in several (approx. 70) countries around the world change by one hour and don't change back until October. The adoption of Daylight Saving Time is almost always rife with controversy. It means one fewer hour of sleep for those involved. It results in people reporting late for work. A study has shown an increase in fatal car accidents on the day of the shift into daylight savings.
All European Union countries and many European non-members continue to make the switch twice a year. Outside of Europe and North America, changing the clocks is also practised in Iran, most of Mexico, Argentina, Paraguay, Cuba, Haiti, the Levant, New Zealand and parts of Australia.

So far only two U.S. states – Arizona and Hawaii – have abandoned changing the clocks, both adopting permanent winter/standard time. Canadian provinces Saskatchewan and Yukon have adopted permanent daylight savings. China, too, do not observe DST now.

The 24-hour clock is not a sunrise clock; it does not reset in the morning at sunrise. If it had, then the contentious practise of adhering to the DST would have been abandoned.

Different Division Systems for 24-hour Clock

Civil time is not anyone's personal property to meddle with in any manner whatsoever. Only his own time is!

Time is probably the only parameter where different systems have been put in use for division. Though there are irregularities in the division of time at the 'Macro' level: months, years, centuries, etc., here, we restrict our study to the division of time at the 'micro' level going down from a 'day' to hours, minutes and seconds. At the micro level we see three different systems - namely, duodecimal (base 12), sexagesimal (base 60), and decimal ( base 10) is use. The arbitrary combination of these different systems has not only led to complexity in analysis, but in poor usage of the different divisions. Few are able to appreciate that there are 1,440 minutes or 86,400 seconds in a day. Compare this with 3,600 palas and 216,000 vipalas in a day, respectively under a purely sexagesimal Indian 60-ghati clock

Disadvantages of having fewer hours

The primary division of the day plays an extremely important role in the effective and efficient utilisation of time. While 'hour' is the primary division in the Egyptian clocks, 'ghati' is the primary division in the Indian clocks.

The coarse primary division of day, namely 24 hours in the case of the Egyptian clocks, is responsible for an inefficient utilisation of time. Let us consider a day in the life of a typical Indian worker. Let us say he sleeps 8 hours a day. So he is left with (24-8) =16 hours. Let us deduct another 6 hours for bath, lunch, and such other daily activities that are non-productive. He ends up with just 10 hours which he needs to plan - say 8 hours for work and 2 hours for leisure, friends and family. With the large number of tasks that need to be executed during work it becomes necessary to split each hour amongst various tasks. In short, he needs to split the hour using the secondary division - minutes. Say 15 minutes for one task, 10 for the next and 30 minutes for the third. It becomes a herculean task to do this for each of the 8 hours.

Now consider the same day that is primarily divided by 60 instead of 24. We have 60 ghatis in a day. The same 8 hours work duration would now be presented as 20 ghatis. Without resorting to the use of the secondary division of time - palas, the primary division itself can be very effectively used to schedule upto 20 tasks. Since each ghati is just 24 minutes in duration, there would be more pressure to complete the task within the said 24 minutes leading to more productivity at work.

As we grow up, our brain gets programmed is give more importance to the primary unit of time compared to the secondary and tertiary units. We, generally set our calendar by the hour - say Lecture at 4:00 pm rather than 4:10 pm. When we work in the office for 8 hours, the primary division number '8' is a small one and while setting the calendar appointments, tasks or events, we attribute the inefficiency to this small number '8'. Would it not be a simpler job to set the calendar if we work for the same time duration, but if this duration is represented as '20-ghati' instead. In fact, Ghati which represents '24 minutes' was the primary measurement unit of time, and 60-ghatis instead of 24 hours have been in use since ancient times in India to indicate the time of the day.

In India, particularly, the problem due to a course 'number of hours', gets compounded, when the scheduled events rarely start on time. People in general are observed to show no respect to the appointment time if it includes the secondary division of time - say a non-zero value for 'minutes'.

Students often complain that the 1-hour lectures are boring. They are often seen to fall asleep during the one hour lecture period. It is well known that the attention span of the students is max 10 to 15 minutes. So why set lectures of 1 hour duration?

The combination of the three different division systems has also resulted in an inappropriate time division for seconds. If we ask a kindergarten child to count seconds in real time, s/he would hardly be able to match the count with the number of seconds elapsed (i.e. at the rate of 1 count per second). Even after many years of experience, grownups still have difficulty in acquiring the supposedly simple skill to count seconds. On the other hand, if we ask any child or adult to count as per the Indian unit of time 'vipala' which is 0.4 seconds, it is likely that the counting would match the number of elapsed vipalas. Try it - you can count upto 5 in 2 seconds and upto 10 in 4 seconds. What you are naturally counting are vipalas and not seconds!

Normal breathing takes 10 to 20 vipala. Or the breathing rate is 3 to 6 breaths/pala.

Disadvantages of a Midnight Reset

The body clock starts from the time you wake up in the morning. Ideally the mechanical clock should help us with our body rhythm by starting from the time you wake up. Would it not be so much better if the clock starts from zero at sunrise, or 6:00 in the morning (an approximation for sunrise).

Does the Ghati clock represent a transition from new innovations back to the past era?

Definitely not. The modern technology savy man may note that just as the second was redefined as the duration of 9,192,631,770 (or x) energy transitions of the cesium atom, so also, the vipala can be similarly redefined as the duration of 3,677,052,708 (or x/2.5) energy transitions of the cesium atom.

Even this may not be required. While the 'seconds' may continue to be used for all scientific purposes - ranging from acceleration, velocity (m/sec), to energy (Watt Second, Ws); we could shift to the more appropriate units of time - ghati : pala : vipala, for day to day common usage- such as tracking our daily activities, or activities that relate to the body clock - counting, breathing, yoga, etc.

Clock should meet Common Man's Expectations

The clock should be made to suit the needs of a common man. It was alright for the ancient Egyptians in 1500 BC to design a sundial with 12 hours with the available technologies then. But, today, those technological limitations do not hold any longer. We need to correct the deficiencies introduced over the period of time and ensure that clock is redesigned to suit the needs of today's common man. The Bharat Clock is one such attempt.

Under the proposed Ghati system, our civil day would be divided into 60 ghatis, each ghati divided into 60 palas, and each pal divided into 60 vipalas. Accordingly the time of day is represented as a triple

ghati : pala : vipala

- where ghati is an integer in the range of 0 to 59, pala is an integer in the range 0 to 59 , and vipala is an integer in the range of 0 to 59. Minimum value: 0 : 0 : 0, Maximum value: 59 : 59 : 59.

1 day & night or 24 hours = 60 ghatis (also called dand)
1 ghati = 60 palas (also called vighati or kala)
1 pala = 60 vipalas (also called lipta or vikala)

The following conversions may be remembered:
2 hours = 5 ghatis or 4 hours = 10 ghatis
2 minutes = 5 palas or 4 minutes = 10 palas
2 seconds = 5 vipalas or 4 seconds = 10 vipalas.

Thus we have a total of 60 x 60 x 60 = 216,000 vipalas in a day, rather than 86,400 seconds in a day.

Let us try to design the “Clockwork Mechanism” for the Bharat Clock.

The Bharat Clock is a sunrise clock. The span of a solar day is from the start of one sunrise to the next. A “sunrise” is determined by when the upper edge of solar disc becomes visible over the horizon. Calculations are to be performed to nullify the effect of refraction caused by atmosphere. Depending on the latitute and longitude or the location on the map, the sunrise time would vary. This means the clock would be reset to zero at different times in Mumbai, Delhi, Chennai, or Kolkatta.

Thanks to the internet, the design of such a clock is not only possible but is already available as a mobile app or as a Desktop widget - see Alok Mandavgane's App on Google Play Store : 'Hindu Calendar' and click / select from the pull down menu, the page on the Hindu Time. There are already over 1 crore downloads of this app and hence the app is widely used, but when it comes to the day to day usage of the 'Hindu Time' it has been observed that very few use it. The Hindu Time is used generally by astrologers and astronomers to know the time of any auspicious period of time during any festival.

For the modern technology savy man, just as the second was redefined as the duration of 9,192,631,770 energy transitions of the cesium atom, so also, the Ghati can be similarly redefined as the duration of 3,677,052,708 energy transitions of the cesium atom.

The objective here is to make this Bharat Clock more popular so that everyone in India use it once again as the primary clock just as it was in use centuries earlier. In order to achieve this, it is important to design the Bharat clock as an analog clock with a Ghati hand, a Pal hand and a Vipal hand.

In Phase 1 of the implementation, we would suggest freezing the Sunrise at 6:00 AM. This would enable us to match the Ghati clock with the 24 hour clock easily and allow easy conversion from one system to the other. Particularly for events that are international in nature (say a webinar set in another country). With this assumption, the following will hold:
6:00 AM would match with ghati : pala = 00:00 ,
10:00 AM would match with ghati : pala = 10:00,
02:00 PM would match with ghati : pala = 20:00,
6:00 PM would match with ghati : pala = 30:00,
12:00 Noon would match with ghati : pala = 15:00,
12:00 Midnight would match with ghati : pala = 45:00,

For accuracy, it needs to be a Quartz crystal driven clock. To make the stepper motor step every 0.4 seconds (1 vipala) instead of 1 second all that is required is to change the crystal from 32.768 kHz to 81.92 kHz. Since the Bharat clock is a new development, the 81.92 kHz crystal is not available in the market at the moment. Till then, it may be good idea to divide a 8.192 MHz clock (which is easily available in any electronic component shop) by 100.

The only other change that is required in the quartz movement for a Bharat clock is the change of the gear ratio that drives the 'ghati' hand. The gear ratio needs to be increased by 5 (12 x 5 = 60). But then this would result in another problem. If we have 60 division on a circular dial, it is quite easy to make a mistake while reading the ghati (since 1 ghati is only 6 degrees - too small to distinguish clearly). It may be considered alright to make a mistake while reading the smaller unit (vipala) or even pala); but to make a mistake while reading the ghati could be a disaster (as this would mean an error of +/- 24 minutes).

A better solution would be to split up the ghatis on two dials so that it would be easy to read 60 ghatis without making a mistake. One advantage of the sexagesimal (base 60) system is that 60 is divisible by all numbers upto 6 and also by 10, 12, 15, 20 and 30. We have conceptualised the split in wo ways : (a) in terms of two concentric dials (Model 3) and (b) with two smaller dials for the units place of ghati and pala (Models 4, 5 and 6). We have shown the dial face of both these ghati concepts in the figures below. In both these dial faces, we have split the 60 ghatis as 10 x 6. The Units position of ghati is brought out clearly with a separate dial with 10 divisions. We have shown this separate dial as a larger concentric circle or as a baby dial inside the main dial. The main dial displays all the three time divisions : ghati, pala and vipala with 60 divisions!

In Model 4, we have two baby dials, left and right, for the units place of ghati and pala respectively for their easy readability. In Model 5, we have rotated the clock anticlockwise by 90 degrees, so that the clock would represent a Sunrise clock. The digit 0 is on the left hand side and denotes 'Sunrise'. Similarly 30 ghati is on the right hand side representing 'Sunset". The top half of the ghati (main) dial represents day while the bottom half represents night. The baby dials are also rotated so that the position of zero ('0') matches that of the main dial.

Lastly, in Model 6, we have divided the main dial into 8 parts / sectors each of 45 degrees and shaded differently so as to denote the 8 different pahars - 4 pahars in the day and 4 pahars in the night, or more precisely: 1. Purvaanha, 2. Madhyaanha, 3. Aparaanha, 4. Saayankala, 5. Pradosha, 6. Nishita, 7. Triyaamaa, 8. Ushaa. We consider Model 6 dial face to be a likely candidate for the Ghati Clock.

The Babylonians made astronomical calculations in the sexagesimal (base 60) system they inherited from the Sumerians, who developed it around 2000 B.C. But so far has been unknown to the West why they did so (Science ABC). When Hipparchus and other Greek astronomers needed to divide the hour further for astronomical calculations, they followed the Babylonian's sexagesimal system for convenience, to divide further, an hour into 60 minutes and each minute into 60 seconds.

Why did the Babylonians choose the sexagesimal system? It would not be incorrect to say, that they might have been influenced by the Vedic Time System and its widespread use in India by the astrologers, astronomers, scholars and even the commoner in India.

Guided by the Vedic Time System http://veda.wikidot.com/vedic-time-system, Indians divide the civil day into 60 ghatikas of 24-minute duration, each of which is divided into 60 palas of 24 second duration, and each pala is divided into 60 vipalas of 0.4 seconds duration. In parallel, Indian astrologers also also divide the sidereal day into 60 nadis, each nadi into 60 vinadis, and each of the latter into 6 asus / pranas.

Why Sexagesimal?

Sexagesimal system has a number of advantages in mathematics. It is the smallest number divisible by the first 6 counting numbers, and also by 10,12,15, 20 and 30. It was well understood by the astrologers that 60 is a special number for fraction calculations.

The sexagesimal system is still used to measure angles, geographic coordinates and time. The Western world attributes the usage of sexagesimal to the Greek astronomer Eratosthenes (who lived circa 276 to 194 B.C.). He divided a circle into 60 parts in order to devise an early geographic system of latitude, with the horizontal lines running through well-known places on the earth at the time. A century later, Hipparchus normalised the lines of latitude, making them parallel and obedient to the earth's geometry. He also devised a system of longitude lines that encompassed 360 degrees and that ran north to south, from pole to pole. In his treatise Almagest (circa A.D. 150), Claudius Ptolemy explained and expanded on Hipparchus' work by subdividing each of the 360 degrees of latitude and longitude into smaller segments. Each degree was divided into 60 parts, each of which was again subdivided into 60 smaller parts. The first division, partes minutae primae, or first minute, became known simply as the "minute." The second segmentation, partes minutae secundae, or "second minute," became known as the second.

It is likely that the further division of time from hours to minutes and seconds was influenced by the primary and secondary partition of the angle since both time and angle division bear the same names - minutes and seconds. But, the vice-versa is also likely, - that the division of angle was influenced by the division of time and not the other way around. Whichever way the influence went, it escaped their mind that in the case of time, 'hours' is the primary or first division and not 'minutes'.

The Redefined Odd 'Second'

As technologies matured from sun-dials to mechanical clocks, a mix of duodecimal and sexagesimal systems made time measurement more complex and irregular. As if this was not enough, in the modern digital age, the concept of milliseconds where yet another system - the base 10 (decimal) system was introduced where each second is divided into 1000 milliseconds.

Before 1967, the International System of Units (SI) defined the 'second' as a fraction of a solar day and later related it to the tropical year. However, the modern man was not content and armed with the advances in the science of timekeeping, made a radical change in the way the 'second' was defined. In the year 1967, the second was redefined as the duration of 9,192,631,770 energy transitions of the cesium atom. This recharacterization ushered in the era of atomic timekeeping and Coordinated Universal Time (UTC).

The modern scientist then understood his folly and observed that the atomic time is no longer in agreement with the astronomical time, and that in order to match them, leap seconds had to be added to UTC. Thus, not all minutes contain 60 seconds! A few rare minutes, occurring at a rate of about eight per decade, actually contain 61 and in the year 2021, a debate is on whether to add a leap second or not this year!

Ghaṭikā (घटिका) as a measure of time has been mentioned in the Purana (Sanskrit literature) and Itihasa (epic history). Sixty vināḍikās make one Ghaṭikā. The Purana (पुराण, purāṇas) refers to Sanskrit literature preserving ancient India’s vast cultural history, including historical legends, religious ceremonies, various arts and sciences. The eighteen mahapuranas total over 400,000 shlokas (metrical couplets) and date to atleast several centuries BCE. Ghatikas is used as a measure of time in Jyotisha (astronomy and astrology). It mentions 60 ghatikas in a single lunar day (tithi). Ghatika is also used in ancient Indian sciences - mathematics and geometry.

Various regional languages such as Marathi mention ghatika to be a metal vessel, by the sinking of which in water, the ghatika is measured. In Sanskrit dictionary, Ghatika is referred to a a small earthern vessel. ghaṭikā is defined in the 'Indian epigraphical glossary' as it can be found on ancient inscriptions commonly written in Sanskrit, Prakrit or Dravidian languages (Ghatika : 20 definitions) . Earthern vessel implies that Ghatika dates several century BCE.

The sun-dial of the world-renowned Umayyad mosque in Damascus, capital of Syria, whose original form goes back to the time of the rule of Caliph al-Walid bin 'Abdalmalik who ruled in the 8th century AD, represents the climax of this type in the Arabic-Islamic world. This sundial measured time in terms of Ghatika. Hence, it is clear that the Ghatikas (earthern vessels) were in use much before the Sundials.

The sun-dial of Mecca Masjid, Hyderabad, also displays a simplified version of dials using hyperbolic curves, similar to that of the Umayyad Mosque. The hour lines are marked on either side of meridian as a series of 10 straight lines, denoting 'ghati' of 24 minutes each (instead of 60 minutes). Thus 10 lines cover a time span of 240 minutes or 4 hours each on either side of the meridian, i.e. from 8 am to 12 noon on the left and from 12 noon to 4 pm on the right.

The sundial in the Khanqah of the 18th century Sufi saint Hazrat Maulana Ziauddin in Jaipur, who was also remembered as the builder of Hawa Mahal in the city ruled by Sawai Pratap Singh (1778-1803) also belongs to this category. This dial is also marked with the traditional Indian Ghatis of 24 minutes and is preserved in good condition with its gnomon intact.

The Nadi Valaya / Narivalaya Yantra - sundial in Jantar Mantar built in 1728, having two sundials on different faces of the instrument each representing north and south hemispheres, and measuring the time to an accuracy of less than a minute also has its divisions in terms of Ghatis.

Ghati was also refered to as 'Ghari'. In all important towns of India, a group of men called 'ghariyalis' were appointed to measure time. When the bowl / vessel with a hole in the bottom (Ghatika Yantra) would sink, they would strike a thick brass disc called ghariyal hung at at high place with a mallet. This indicated the completion of the next primary division of time - 'Ghari' or 'Ghati'.

Thus it can be observed that all religions in India used Ghati as a measure to perform their religious rituals at particular times of the day. On a cloudy day or night when the sundial could not be used, the Ghatika Yantra, or the water clock was used. It is important to note that regardless of the measurement instrument - sundial or water clock, the primary division of a day was a Ghati or (24 minutes) and that Indians had divided day and night into 60 Ghatis.

Below we offer further information that is directly or indirectly related to the use of ghatika, pala and vipala.

Civilizations in the classic period and earlier created divisions of the calendar as well as arcs using a sexagesimal system of counting, so at that time the vipala (classic second) was a sexagesimal subdivision of the day (ancient second = day/(60x60x60), and not of the hour like the modern second (= hour/(60x60)). Sundials and water clocks were among the earliest timekeeping devices, and units of time were measured in degrees of arc. Conceptual units of time smaller than realisable on sundials were also used.

According to Western science, there are 86,400 seconds in a day and night, whereas in Indian science, a day and night consists of 46,65,60,000,00 Tatparas.

According to Indian system, the division of time is

60 ghati = 1 Day & Night or 24 hours
60 pal = 1 ghati (or ghatika or danda or nadi)
60 vipala = 1 pala (or kala or vighati)
60 vilipta = 1 vipala (or vikala or lipta)
60 paras = 1 vilipta (or liksaka)
60 tatparas = 1 paras (or lava)
60 truti = 1 tatparas (or renu)
Therefore, it is also clear that there are 2,799,360,000,000 trutis in a day and night. This means that 1 truti equals 0.309 microseconds.

As a lot of charts made in the olden days mention the birth time in ghatis and vighatis. The following is the conversion to remember:
5 ghatis = 2 hours, and
5 palas or vighatis = 2 minutes

For division of time, some other Indian systems have also been in use such as

30 Muhurta = 1 Day & Night or 24 hours
30 Kala = 1 Muhurta
30 Kastha = 1 Kala
15 Nimesha = 1 Kastha.

But, in our design of Bharat clock we will restrict ourselves to the more widely used sexagesimal subdivision of the day and the usage of the ancient classic second = vipala = day/(60x60x60).

There are 108,000 vipalas in a day and another 108,000 vipalas in the night. Thus the total number of vipalas over a day and night is 216,000.

The number 108 has a special meaning in the Universe, the Divine, the Body, the Tradition and the Practice:

108 and the universe

Consider the mathematics of the universe. The diameter of the Sun is 108 times the diameter of the Earth. The average distance of the Sun and the Moon to Earth is 108 times their respective diameters. Mathematicians from the Vedic tradition came to view 108 as the number representing the wholeness of existence. This number reminds us of our place in the cosmic order of things.

108 and the divine

In the Hindu tradition, there are 108 attendants of Shiva. In Gaudiya Vaishnavism, Lord Krishna in Brindavan had 108 followers. The words of the Buddha are recorded in the Tibetan Kangyur in 108 volumes. A bell is chimed 108 times in Buddhist temples in Japan to finish the old year and welcome the new one.

108 and the human body

As we focus in on the human body, the number 108 holds special significance. There are 108 marma points, considered to be sacred places in the body. In Ayurveda, these pressure points are seen as vital for giving life to living beings for it is at these points that consciousness and flesh intersect. Additionally, there are 108 nadis, or energy lines, which converge to form the heart chakra. Placing significance on the number 108 embraces the life-giving energy so vital for human existence.

108 and the tradition of yoga

The number 108 has emerged as a truly significant number within the tradition of yoga. According to yogic tradition, there are 108 sacred sites known as pithas, throughout India. There are 108 Upanishads (a collection of Indian religious and philosophical texts from as early as 800 BCE) and 108 Puranas (Sanskrit sacred writings on Hindu mythology from as early as 400 BCE). There are 54 letters in Sanskrit, where each can be seen as either masculine (Shiva) or feminine (Shakti), and therefore totalling 108.

108 and the practice of yoga and meditation

In yoga, the number 108 has significance as the number representing spiritual completion. Sun salutations are often performed in nine rounds of the 12 postures which totals 108 poses. A yoga mala consists of 108 sun salutations. Pranayama is also often completed in cycles of 108. A mala is traditionally a string of 108 prayer beads with a guru bead. As you pray, you move along the beads, reciting your chosen mantra 108 times.

As we practise chanting, breath work, or asana in rounds of this sacred number, we become aligned with the rhythm of the universe and the energy of the divine source. Placing significance on the number 108 connects the essence of each individual yoga practice to the whole.

Just like months, the Indian calendar has two measures of a day, one based on the lunar movement and the other on solar [2]. The solar day or civil day, called divasa ( दिवस), has been what most Indians traditionally use, is easy and empirical to observe, by poor and rich, with or without a clock, and it is defined as the period from one sunrise to another. The lunar day is called tithi (तिथि), and this is based on complicated measures of lunar movement. A lunar day or tithi may, for example, begin in the middle of an afternoon and end next afternoon. Both these days do not directly correspond to a mathematical measure for a day such as equal 24 hours of a solar year, a fact that the Hindu calendar scholars knew, but the system of divasa was convenient for the general population. The tithi have been the basis for timing rituals and festivals, while divasa for everyday use. The Hindu calendars adjust the mismatch in divasa and tithi, using a methodology similar to the solar and lunar months.

A Tithi is technically defined in Vedic texts, states John E. Cort, as "the time required by the combined motions of the sun and moon to increase (in a bright fortnight) or decrease (in a dark fortnight) their relative distance by 12 degrees of the zodiac. These motions are measured using a fixed map of celestial zodiac as reference, and given the elliptical orbits, a duration of a tithi varies between 21.5 and 26 hours, states Cort. However, in the Indian tradition, the general population's practice has been to treat a tithi as a solar day between one sunrise to next.

A lunar month has 30 tithi. The technical standard makes each tithi contain different number of hours, but helps the overall integrity of the calendar. Given the variation in the length of a solar day with seasons, and moon's relative movements, the start and end time for tithi varies over the seasons and over the years, and the tithi adjusted to sync with divasa periodically with intercalation.

Days of the Week/Vāsara

Vāsara refers to the days of the week in Sanskrit. Also referred to as Vara and used as a suffix. The correspondence between the names of the days in a week in Hindu and other Indo-European calendars are exact. This alignment of names probably took place sometime during the 3rd century CE. The weekday of a Hindu calendar has been symmetrically divided into 60 ghatika, each ghatika (24 minutes) is divided into 60 pala, each pala (24 seconds) is subdivided into 60 vipala, and so on.

Just as a day was divided into 60 Ghatikas, it was also divided into larger units - namely Muhurtas and Praharas.
2 Ghatikas = 1 Muhurta, and 7.5 Ghatikas = 1 Prahara
Hence, in a day, we have 30 Muhurtas or 8 Praharas.
The measure Muhurta was generally used to time auspicious ceremonies such as marriage.

Similarly, a sidereal day is also divided into eight Praharas. The counting of the Ghatikas, Muhurtas as well as the Praharas commences with sunrise. The timing of the Muhurtas and the Praharas coincides only at sunrise and sunset.

The concept of prahar originated where the lengths of the day and night were based on actual, observable sunrise and sunset. The four praharas of the day start at sunrise, and the four praharas of the night at sunset.

Thus, near the equator, when days are equal to nights, each Prahara would be of of equal duration, namely 7 Ghati and 30 Pal ( 7.5 Ghati). Starting with Sunrise, the four Praharas are Purvaanha, Madhyaanha, Aparaanha, and Saayankala. Similarly, in the night time, starting with sunset, the four Praharas are Pradosha, Nishitha, Triyaamaa, and Ushaa.

During the summer, when the days are longer than the nights, the praharas of the day will be longer than the praharas of the night, and vice versa during the winter.

In Indian classical music, some Ragas are prescribed to be performed at a particular prahara to maximize their aesthetic effects. Sangita-Makaranda is an ancient Indian text that warns musicians against playing ragas at the incorrect time of day. Traditionally, disastrous consequences are to be expected.

Coming to Raga Darbari Kanada. It can cure insomnia and induce sleep. It belongs to the Asavari Thaat.

Though most of the ragas in Asavari thaat are performed in the late morning hours. Darbari is sung in the Night prahars as it is a grave raga.

One of the valuable assets of any advanced nation is the chronology it maintains. All the technological and scientific breakthroughs, cultural wonders can be summarised there. A chronology carries the legacy of a nation. Our modern history starts from roughly 20000 years earlier. Aztecs could not go beyond a mere 4000 – 5000 years. The Sumerian empire recorded up to 250000 years. Babylon was a little further, maintaining a journal of 400000 years. Legendary Egyptians reached their limit at 100000 years. Ancient Mayans stands apart from this list, who had the concept of cyclic time and a mechanism to measure a billion year long cycle. But all of them combined, is dwarfed by enormity and complexity of the ancient Bharat almanac.

The Bharat almanac model deals with huge iterations of time ranging as far as hundreds of quadrillions (10²⁶ ) of years, with every major unit being exclusively defined and related with specific cosmic event. On the other hand, the same model crafted the idea of an “absolute base unit” of time. Even with all the latest discoveries, modern science is far from implementing another fully functional cosmic model. The cosmologist, Carl Sagan expressed his amazement – “The Hindu religion is the only one of the world’s great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths. It is the only religion in which time scales correspond to those of modern scientific cosmology.”

According to the cosmic model of ancient Bharat, “Time” is something that is beyond the universe itself. The ancient wisdom tells us that there always is and will be a cause and an effect of every action; that is what keeps this universe together. That is where time comes in. “Time” is used to maintain the continuity of all the events that takes place.

Unlike today’s Gregorian system, Bharat months are not decided by Earth’s revolution around Sun. In fact, both Sun and Moon get equal importance in doing so. The number of days in a month is not decided arbitrarily either. Though exactly 30 lunar days forms each month, the count of solar days varies. The procedure of synchronization between lunar and solar days is systematic as described below.

While deciding a month, all three factors are taken into account – “Rashi” (position of Sun in the astronomical chart), “Nakshatra” (position of Moon in the astronomical chart) and “Tithi” (relative position of Moon with respect to Sun in the astronomical chart). All of the months consist of 30 lunar days. The name of a month is derived from the name of the constellation (“Nakshatra” ) where Moon resides during the full moon phase of that 30-day lunar cycle. End of current month is decided when the immediately following new moon completes and Sun enters into a new “Rashi” (a new sector in the astronomical chart).

Calculation of one year is quite straight-forward. As we can recall, the solar ecliptic is divided into 12 equal sectors, each measuring 30^o . The time span is roughly equals to time needed for Sun to complete 360^o coverage of all these sectors. The fine-tuned calculation takes into account additional period for completion of then-ongoing lunar month. Usually, one year consists of 12 months. We know that the axis Earth is tilted by 23.5^o . Because of this tilt, there are only two days in a year where Sun rises exactly in the East direction. For the rest of the year, it either moves a little north or a little south. When Sun passes through the “Rashi” Capricorn to Cancer, we experience Sun’s northward drift; similarly, when Sun passes through Cancer to Capricorn, we see a southward drift. The first phase is called “Uttarayan” (Summer Solstice), while the other is called “Dakshinayan” (Winter Solstice). The two days, when Sun rises exactly in East direction are known as “Sankranti“-s. One solar year indicates that the Earth has completed one revolution around the Sun.

So, by now, the significance of “Rashi“, “Tithi” and “Nakshatra” has been established. Any time in one solar year can be pinpointed using these astronomical units. The beauty of these reference frame is, it is something that can break the language or cultural barrier. Till now, in modern India, important religious and social activities solely relies upon this computation, which started from time unknown.

Here, we simply focus on the most common time period we experience in our life – a solar day. To keep track of our daily activities we use a “Clockwork Mechanism” or a Clock that . Actually, we are not keeping track of time here. We have set up a relative point to indicate the start of a day (12:00 PM of previous day), and then we are counting how many rotations the clockwork gears are completing. The only way one can decide whether one specific clock is working correctly or not, is by comparing it with another clock. Needless to say that, not only it is entirely influenced by cultural dominance instead of a strong scientific base, but this procedure is also highly sensitive to mechanical imperfections.

Contrasting to this, each and every time measurement unit of ancient Bharat used to be directly derived from astronomical phenomena. From day-to-day calculations to massive cosmic predictions, everything is perfectly synchronized with the universe – that clarifies why they are able to manage a logbook of zillions of years; which easily predates our very existence.

Long before the introduction of a 24-hour system starting from midnight, in ancient Bharat, the span of a solar day was decided starting from one sunrise until the next sunrise. A “Sunrise” is determined by when the upper edge of solar disc becomes visible from surface. Calculations used to be performed to nullify the effect of refraction caused by atmosphere. The said system still exists to a large extent in modern India; during the time of any Hindu festival, the priests used to determine the timing based on such calculations (the same system is followed even today which was present billions of years ago – Amazing, isn’t it?). One solar day is further divided into eight “Prahara” -s: Purvanhaa, Madhyanhaa, Aparanhaa, Sayanhaa, Prodasha, Nisheetha, Triyamaa, Usha. The first quadruplet are unfolded in between sunrise to the successive sunset; the rest of them are considered from the sunset to the next sunrise. Just like sunrise, a “Sunset” is determined by when the upper edge of solar disc becomes invisible from surface, after the effect of refraction being neutralized. Depending on the time of the year and position of the observer on the globe, the length of Day and Night varies, so does the length of the “Prahara” -s.

To fine tune the timing further, one solar day is divided into 30 “Muhurta” -s. Unlike “Prahara” -s, the “Muhurta” -s are of equal duration. In case the length of day and night are of equal length, 15 “Muhurta” -s are considered for each. According to Vishnu Purana, customization is a common practice to cope up with varying proportion of day and night; formulating up to 18 “Muhurta” -s for day and 12 “Muhurta” -s for night, when days are longer than night; or vice-versa otherwise. Each of the “Muhurta” -s is divided into 30 “Kala” -s, each “Kala” into 30 “Kastha” -s and each “Kastha” is divided into 15 “Nimesha” -s. If we assume the difference between two consecutive “Sunrise” -s as exactly 24 hours as of modern day then the units would become as: one “Muhurta” = 48 Minutes, one “Kala” = 1.6 Minutes, one “Kastha” = 3.2 Seconds, one “Nimesha” = 0.2 Seconds. These fine-tuned measurements were calculated based on polar co-ordinates of the Sun relative to the ground (amount of angular traversal of the sun in the sky starting from the point of sunrise, as observed from ground). The process involves an application of Trigonometry. Some examples of actual machines which were used to carry out the calculation in the past, can be found in ancient astronomical observatories throughout modern India, like the “Jantan-Mantar” at the city of Jaipur.

The Saptarishi from Sanskrit: सप्तर्षि (saptarṣī), meaning "seven sages" or rishis in ancient India are regarded in the Vedas as the patriarchs of the Vedic religion.

A manvantara (age of Manu) is a unit of time within a kalpa (day of Brahma). There are fourteen manvantaras in a kalpa, each separated by sandhyas (connecting periods). Each manvantara is ruled by a different Manu, with the current seventh one ruled by Vaivasvata Manu. Rishis and their sons are born anew in each manvantara.

1 Manvantara = 30,6720,000 Years

The Vedic Units of Time – Macro level

SATYUG 4,32,000 YEARS X 4 = 17,28,000 YEARS

TRETA 4,32,000 YEARS X 3 = 12,96,000 YEARS

DWAPAR 4,32,000 YEARS X 2 = 8,64,000 YEARS

KALIYUG 4,32,000 YEARS X 1 = 4,32,000 YEARS

1 MAHAYUG (GRAND TOTAL OF ALL THE YUGAS) = 4,320,000 YEARS

71 MAHAYUG = 43,20,000X71 = 1 MANVANTAR

1 MANVANTAR = 30,6720,000 YEARS

14 MANVANTAR = 4,294,080,000 YEARS

(There are 14 Manvantars)

In order to understand the importance of a stable almanac, let us take at look at the calendar used in most of the world today - the Gregorian calendar that was introduced by Pope Gregory XIII in October 1582 as a modification of the Julian calendar.

The Julian calendar by Julius Caesar, used from 46 B.C to 1582, did not reflect the actual time it takes the Earth to circle once around the Sun, known as a tropical year, had only one rule of a leap year every 4th year when an extra leap day was added, which is too frequent. An average year in Julian calendar is 365.25 days, while actually the Earth rotates about 365.242375 times a year.

In 1582, Pope Gregory XIII felt that he understood the incorrect assumption of the Julian calendar and tried to correct it with the Gregorian calendar that advanced the date by 10 whole days. The reform also altered the lunar cycle used by the Church to calculate the date for Easter. An average year in Gregorian calendar is 365.2425 days which is closer to the actual Earth's rotation of 365.242375 days than the Julian calendar; but still not too accurate. Gregorian calendar is the normal calendar we currently use to determine the date.

Leap year Rules for the currently used Gregorian calendar: How to know if it is a Leap Year:

Leap Years are any year that can be exactly divided by 4 (such as 2016, 2020, 2024, etc)

except if it can be exactly divided by 100, then it isn't (such as 2100, 2200, etc)

except if it can be exactly divided by 400, then it is (such as 2000, 2400)

There were two reasons to establish the Gregorian calendar. First, the Julian calendar assumed incorrectly that the average solar year is exactly 365.25 days long, an overestimate of a little under one day per century. The Gregorian reform shortened the average (calendar) year by 0.0075 days to stop the drift of the calendar with respect to the equinoxes. Second, in the years since AD 325, the excess leap days introduced by the Julian algorithm had caused the calendar to drift such that the (Northern) spring equinox was occurring well before its nominal 21 March date. This date was important to the Christian churches because it is fundamental to the calculation of the date of Easter. To reinstate the association, the reform advanced the date by 10 whole days : Thursday 4 October 1582 was followed by Friday 15 October 1582! In addition, the reform also altered the lunar cycle used by the Church to calculate the date for Easter, because astronomical new moons were occurring four days before the calculated dates. Different countries switched to Gregorian calendars in different years creating more chaos.

Moreover, it is a solar calendar based on a 365-day common year divided into 12 months of 'irregular' lengths - January has 31 days while February has 28 days!

In sharp contrast, it may be noted that neither the Bharat almanac nor its base unit of time, have ever been arbitrarily modified.