Monday, 13 December 2021
Sunday, 12 December 2021
Evolution of Electrical energy
The fundamental principle of electricity generation was discovered during the 1820s and early 1830s by the British scientist Michael Faraday. His basic method is still used today: electric current is generated by the movement of a loop of wire or disc of copper between the poles of a magnet.
Electricity is most often generated at a power
station by electromechanical generators, primarily driven
by heat engines fueled by chemical combustion or nuclear
fission but also by other means such as the kinetic
energy of flowing water and wind. There are many other
technologies that can be and are used to generate electricity such as
solar photovoltaics and geothermal
power.
Mathematically, electric current is defined
as the rate of
flow of charge through the cross-section of a conductor.
Electricity is Electrical charges moving through a wire.
E = QV
Where, Q is charge
V is
the potential difference.
Units of Electrical Energy
The basic unit of electrical energy is the
joule or watt-second. Electrical energy is said to be one joule when one
ampere of current flows through the circuit for a second when the potential
difference of one volt is applied across it. The commercial unit of electrical
energy is the kilowatt-hour (kWh) which is also known as the Board of trade
unit (B.O.T).
1 kwh = 1000 × 60 × 60 watt-second
1 kwh = 36 × 105 Ws or Joules
Generally, one kwh is called one unit.
Electrical Energy into Mechanical Energy
Electrical energy can be converted into other
forms of energy like heat energy, light energy, motion etc. The best-known examples
are:
- Fan: The motor in Fan converts
electrical energy into mechanical energy
- Bulb: Here the electrical
energy is converted into light energy.
Electricity travels at the speed of light that is more than
186,000 miles per second.
Electric power Definition – It is the rate
at which work is done or energy is transformed in an electrical circuit.
Simply put, it is a measure of how much energy is used in a span of time.
In physics, the rate of transfer of electrical energy by an
electrical circuit per unit time is called electrical power.
P=VI watt or
Joule per second.
Where, V is the potential difference (volts),
I is
the electric current (ampere).
We talked about the energy that is dissipated due to the
heating up of the conductor.
But we know the formula for power is given by P = I V
according to Ohm’s law, V =
IR. Substituting we have,
P = I2R
It is this power that is responsible for
heating up the coil of a bulb, which gives out heat and light.
Alternating Current (AC) is
a type of electrical current, in which the direction of the flow of electrons
switches back and forth at regular intervals or cycles. Current flowing in
power lines and normal household electricity that comes from a wall outlet is
alternating current. The standard current used in the U.S. is 60 cycles per
second (i.e. a frequency of 60 Hz); in Europe and most other parts of the world
it is 50 cycles per second (i.e. a frequency of 50 Hz.).
Direct current (DC) is an electrical current that flows consistently in one direction. The current that
flows in a flashlight or another appliance running on batteries is a direct
current.
One advantage of alternating current is that it is
relatively cheap to change the voltage of the current. Furthermore, the
inevitable loss of energy that occurs when current is carried over long
distances is far smaller with the alternating current than with the direct current.
Examples
of alternating current
To illustrate these concepts, consider a 230 V AC mains supply
used in many
countries around the world. It is so-called because its root mean square value
is 230 V. This means that the time-averaged power delivered is equivalent to
the power delivered by a DC voltage of 230 V. To determine the peak voltage
(amplitude), we can rearrange the above equation to: For 230 V AC, the peak voltage
is, therefore,
, which is about 325 V. During the
course of one cycle the voltage rises from zero to 325 V, falls through zero to
−325 V, and returns to zero.
For
decades, alternating current (AC) had the distinct advantage over direct current (DC; a steady flow
of electric charge in one direction) of being able to transmit power over large
distances without great loss of energy to resistance. The power
transmitted is equal to the current times the voltage; however, the power lost
is equal to the resistance times the square of the current. Changing voltages
was very difficult with the first DC electric power grids in the late
19th century. Because of the power loss, these grids used low voltages to
maintain high current and thus could only transmit usable power over short
distances. DC power transmission was soon supplanted by AC systems that
transmit power at very high voltages (and correspondingly low current) and
easily use transformers to change the
voltage. Present AC systems transmit power from generators at hundreds of
thousands of volts and use transformers to lower the voltage to 220 volts (as
in much of the world) for individual customers.
Alternating current is used to transmit information, as in the cases of telephone and cable
television. Information signals are carried over a wide
range of AC frequencies. POTS telephone signals have a frequency of about
3 kHz, close to the baseband audio frequency. Cable television and other
cable-transmitted information currents may alternate at frequencies of tens to
thousands of megahertz. These frequencies are similar to the electromagnetic
wave frequencies often used to transmit the same types of information over the air.
Alternating current systems can use transformers to change the voltage from low to a high level and back,
allowing generation and consumption at low voltages but transmission, possibly
over great distances, at high voltage, with savings in the cost of conductors
and energy losses.
The three engineers ZBD transformers:
The Ganz factory in 1884 shipped the world's first five
high-efficiency AC transformers. This first unit had been
manufactured to the following specifications: 1,400 W, 40 Hz, 120:72 V,
11.6:19.4 A, ratio 1.67:1, one-phase, shell form.
In early
1885, the three engineers also eliminated the problem of eddy
current losses with the invention of the lamination
of electromagnetic cores.
The AC power system was developed and adopted rapidly after 1886 due to its ability to distribute electricity efficiently over long distances, overcoming the limitations of the direct current system. In 1886, the ZBD engineers designed the world's first power station that used AC generators to power a parallel-connected common electrical network, the steam-powered Rome-Cerchi power plant. The reliability of the AC technology received impetus after the Ganz Works electrified a large European metropolis: Rome in 1886.
In 1888, alternating current systems gained further viability
with the introduction of a functional AC
motor, something these systems had lacked up till then.
The design of, an induction
motor, was independently invented by Galileo
Ferraris and Nikola
Tesla (with Tesla's design being licensed by
Westinghouse in the US). This design was further developed into the modern
practical three-phase form.
The Ames Hydroelectric Generating Plant and the original Niagara Falls Adams Power plant were among the first hydroelectric alternating current power plants. The first long-distance transmission of single-phase electricity was from a hydroelectric generating plant in Oregon at Willamette Falls which in 1890 sent power fourteen miles downriver to downtown Portland for street lighting. In 1891, a second transmission system was installed in Telluride Colorado. The San Antonio Canyon Generator was the third commercial single-phase hydroelectric AC power plant in the United States to provide long-distance electricity. It was completed on December 31, 1892, by Almarian William Decker to provide power to the city of Pomona, California, which was 14 miles away. In 1893, he designed the first commercial three-phase power plant in the United States using alternating current—the hydroelectric Mill Creek No. 1 Hydroelectric Plant near California. Decker’s design incorporated a 10 kV three-phase transmission and established the standards for the complete system of generation, transmission, and motors used today.
Nikola
Tesla, Serbian American inventor, and engineer discovered and
patented the rotating magnetic
field, the basis of most alternating-current machinery.
He also developed the three-phase system of electric
power transmission. He immigrated to the United States in
1884 and sold the patent rights
to his system of alternating-current dynamos, transformers, and
motors to George
Westinghouse. In 1891 he invented the Tesla coil, an induction
coil widely used in radio
technology.
Serbian-American engineer and physicist
Nikola Tesla (1856-1943) made dozens of breakthroughs in the production,
transmission, and application of electric power. He invented the first
alternating current (AC) motor and developed AC generation and
transmission technology.
Tesla was
from a family of Serbian origin. His father was an Orthodox priest; his mother
was unschooled but highly intelligent. As he matured, he displayed remarkable
imagination and creativity as well as a poetic touch.
Training
for an engineering career,
he attended the Technical University at Graz, Austria, and
the University
of Prague. At Graz, he first saw the Gramme dynamo, which
operated as a generator and, when reversed, became an electric
motor, and he conceived a way to use alternating
current to advantage. Later, at Budapest, he
visualized the principle of the rotating magnetic
field and developed plans for an induction motor
that would become his first step toward the successful utilization of
alternating current. In 1882 Tesla went to work in Paris for the Continental
Edison Company, and, while on assignment to Strassburg in 1883, he constructed,
after work hours, his first induction motor. Tesla sailed for America in 1884,
arriving in New York with four cents in his pocket, a few of his own poems, and
calculations for a flying machine. He first found employment with Thomas
Edison, but the two inventors were far apart in background and
methods, and their separation was inevitable.
In May
1888 George
Westinghouse, head of the Westinghouse
Electric Company in Pittsburgh, bought
the patent rights to Tesla’s polyphase
system of alternating-current dynamos, transformers, and motors. The
transaction precipitated a titanic power struggle between Edison’s direct-current systems
and the Tesla-Westinghouse alternating-current approach, which eventually won
out.
Wednesday, 28 July 2021
เฒฐเฒธಾเฒฏเฒจ เฒถಾเฒธ್เฒค್เฒฐเฒฆ เฒเฒคಿเฒนಾเฒธ :
เฒ เฒเฒเฒค್เฒคು เฒชಂเฒเฒฎเฒนಾเฒญೂเฒคเฒเฒณಿಂเฒฆ เฒเฒಿเฒฆೆ เฒಂเฒฆเฒฐು เฒนಿಂเฒฆಿเฒจเฒตเฒฐು. เฒเฒಾเฒถ , เฒ เฒ್เฒจಿ , เฒตಾเฒฏು , เฒเฒฒ เฒฎเฒค್เฒคು เฒฎเฒฃ್เฒฃು ; เฒ เฒชಂเฒเฒฎเฒนಾเฒญೂเฒคเฒเฒณು .
เฒตเฒธ್เฒคು , เฒถเฒ್เฒคಿ , เฒเฒಾเฒถ เฒฎเฒค್เฒคು เฒಾเฒฒ เฒಂเฒฆು เฒಂเฒฆಿเฒจเฒตเฒฐು เฒตเฒฐ್เฒಿเฒเฒฐเฒฃ เฒฎಾเฒกಿเฒฆเฒฐು . เฒตಾเฒฏು, เฒเฒฒ, เฒฎเฒค್เฒคು เฒฎเฒฃ್เฒฃเฒจ್เฒจು เฒเฒ್เฒಿเฒೆ เฒฆ್เฒฐเฒต್เฒฏ เฒಂเฒฆเฒฐು . เฒฆ್เฒฐเฒต್เฒฏเฒตು เฒธ್เฒฅเฒณเฒตเฒจ್เฒจು เฒเฒ್เฒฐเฒฎಿเฒธುเฒค್เฒคเฒฆೆ . เฒ เฒฆเฒ್เฒೆ เฒฆ್เฒฐเฒต್เฒฏเฒฐಾเฒถಿ เฒเฒฆೆ .
เณงเณฌเณฌเณงเฒฐเฒฒ್เฒฒಿ เฒฐಾเฒฌเฒฐ್เฒ เฒฌಾเฒฏ್เฒฒ್ เฒงಾเฒคುเฒตಿเฒจ เฒชเฒฐಿเฒเฒฒ್เฒชเฒจೆ เฒจಿเฒฐೂเฒชಿเฒธಿเฒฆ . เฒเฒคเฒจು เฒเฒฎ್เฒฒ เฒฎเฒค್เฒคು เฒช್เฒฐเฒค್เฒฏಾเฒฎ್เฒฒเฒเฒณ เฒตಿเฒตเฒฐ เฒจೀเฒกಿเฒฆ.
เฒเฒคเฒจು เฒಾเฒณಿเฒฏ เฒುเฒฃเฒเฒณು เฒ เฒง್เฒฏเฒฏเฒจ เฒฎಾเฒกಿ, เฒಂเฒฆು เฒจಿเฒฐ್เฒฆಿเฒท್เฒ เฒฐಾเฒถಿเฒฏ เฒ เฒจಿเฒฒเฒฆ เฒಾเฒค್เฒฐ, เฒเฒค್เฒคเฒก, เฒนಾเฒೂ เฒเฒท್เฒฃเฒคೆเฒฏ เฒธಂเฒญಂเฒฆเฒฆ เฒจಿเฒฏเฒฎเฒตเฒจ್เฒจು เฒจಿเฒฐೂเฒชಿเฒธಿเฒฆเฒจು.
เฒಂเฒฆೇ เฒช್เฒฐเฒಾเฒฐเฒฆ เฒฎೂเฒฒ เฒเฒฃเฒเฒณಿಂเฒฆ เฒเฒฆ เฒฆ್เฒฐเฒต್เฒฏเฒตเฒจ್เฒจು เฒงಾเฒคು เฒ เฒฅเฒตಾ เฒฎೂเฒฒเฒตเฒธ್เฒคು เฒಂเฒฆเฒฐು. เฒಂเฒฆು เฒงಾเฒคುเฒตಿเฒจ เฒ เฒคಿเฒธเฒฃ್เฒฃ เฒเฒฃเฒ್เฒೆ เฒชเฒฐเฒฎಾเฒฃು เฒಂเฒฆเฒฐು. เฒಂเฒฆೇ เฒช್เฒฐเฒಾเฒฐเฒฆ เฒชเฒฐเฒฎಾเฒฃುเฒเฒณಿಂเฒฆ เฒเฒฆ เฒตเฒธ್เฒคುเฒตೇ เฒงಾเฒคು.
เณงเณฎเฒจೇเฒฏ เฒถเฒคเฒฎಾเฒจเฒฆเฒฒ್เฒฒಿ เฒเฒฒเฒเฒจเฒ , เฒเฒฎ್เฒฒเฒเฒจเฒ . เฒฎเฒค್เฒคು เฒಂเฒಾเฒฒเฒฆ เฒกೈ เฒ เฒ್เฒธเฒฏಿเฒก್ เฒเฒจ್เฒจುเฒต เฒ เฒจಿเฒฒเฒเฒณ เฒถೋเฒง เฒฎเฒค್เฒคು เฒ เฒตುเฒเฒณ เฒುเฒฃเฒเฒณ เฒ เฒง್เฒฏเฒฏเฒจ เฒจเฒกೆเฒฏಿเฒคು .
เณงเณญเณซเณชเฒฐเฒฒ್เฒฒಿ เฒೋเฒธೆเฒซ್ เฒฌ್เฒฒ್เฒฏಾเฒ್ เฒเฒจ್เฒจುเฒต เฒเฒชเฒจ್เฒฏಾเฒธเฒเฒจು เฒธುเฒฃ್เฒฃเฒฆ เฒเฒฒ್เฒฒเฒจ್เฒจು เฒಾเฒฏಿเฒธಿ เฒ เฒฆเฒฐಿಂเฒฆ เฒಂเฒಾเฒฒเฒฆ เฒกೈ เฒ เฒ್เฒธเฒฏಿเฒก್ เฒ เฒจಿเฒฒ เฒนೊเฒฐเฒธೂเฒธುเฒตುเฒฆเฒจ್เฒจು เฒเฒฎเฒจಿเฒธಿเฒฆเฒจು. เฒเฒคเฒจು เฒจೀเฒฐಿเฒจ เฒುเฒช್เฒคೋเฒท್เฒฃเฒตเฒจ್เฒจು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒจು.
เณงเณญเณฌเณฌเฒฐเฒฒ್เฒฒಿ เฒนೆเฒจ್เฒฐಿ เฒೆเฒตೆಂเฒกಿเฒท್ เฒคเฒจ್เฒจ เฒช್เฒฐเฒฏೋเฒเฒถಾเฒฒೆเฒฏเฒฒ್เฒฒಿ เฒเฒฒเฒเฒจเฒ เฒ เฒจಿเฒฒเฒตเฒจ್เฒจು เฒಂเฒกುเฒนಿเฒกಿเฒฆเฒจು.
เณงเณญเณญเณชเฒฐเฒฒ್เฒฒಿ เฒช್เฒฐೀเฒธ್เฒ್เฒฒೆ เฒชಾเฒฆเฒฐเฒธเฒฆ เฒเฒ್เฒธเฒฏಿเฒก್ เฒ เฒฆಿเฒฐು เฒಾเฒฏಿเฒธಿ เฒเฒฎ್เฒฒเฒเฒจเฒ เฒ เฒจಿเฒฒ เฒಂเฒกುเฒนಿเฒกಿเฒฆเฒจು .
เณงเณญเณญเณฎเฒฐเฒฒ್เฒฒಿ เฒซ್เฒฐಾเฒจ್เฒธ เฒฆೇเฒถเฒฆ เฒฒಾเฒตೋเฒทಿเฒฏೆเฒฐ್ เฒเฒจ್เฒจುเฒต เฒตಿเฒ್เฒಾเฒจಿ เฒฆเฒนเฒจ เฒ್เฒฐಿเฒฏೆเฒฏเฒจ್เฒจು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒจು . เฒเฒคเฒจು เฒเฒฎ್เฒฒเฒเฒจเฒ เฒಂเฒฆು เฒงಾเฒคು เฒಂเฒฆು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒจು . เฒจಿเฒธเฒฐ್เฒเฒฆเฒฒ್เฒฒಿ เฒธเฒนเฒเฒตಾเฒಿ เฒเฒฎ್เฒฒเฒเฒจเฒเฒตು เฒ เฒจಿเฒฒ เฒฐೂเฒชเฒฆเฒฒ್เฒฒಿ เฒเฒฐುเฒค್เฒคเฒฆೆ. เฒಾเฒณಿเฒฏเฒฒ್เฒฒಿ เณจเณง% เฒเฒฎ್เฒฒเฒเฒจเฒ เฒเฒฆೆ . เฒเฒฆು เฒ್เฒฐಿเฒฏಾเฒถೀเฒฒเฒตಾเฒಿเฒฆ್เฒฆು เฒ เฒจ್เฒฏ เฒงಾเฒคುเฒเฒณೊಂเฒฆಿเฒೆ เฒฐಾเฒธಾเฒฏเฒจಿเฒเฒตಾเฒಿ เฒตเฒฐ್เฒคಿเฒธಿ เฒเฒ್เฒธเฒฏಿเฒกเฒเฒณเฒจ್เฒจು เฒಂเฒುเฒฎಾเฒกುเฒค್เฒคเฒฆೆ เฒಂเฒฆು เฒคೋเฒฐಿเฒธಿเฒฆเฒจು. เฒಾเฒณಿเฒฏเฒฒ್เฒฒಿ เณญเณฎ% เฒธಾเฒฐเฒเฒจเฒ เฒ เฒจಿเฒฒ เฒเฒฆೆ. เฒเฒณಿเฒฆ เฒญಾเฒ เฒเฒก เฒ เฒจಿเฒฒเฒเฒณเฒฆ್เฒฆು. เฒจೀเฒฐಾเฒตಿเฒฏ เฒช್เฒฐเฒฎಾเฒฃ เฒธเฒฆಾ เฒฌเฒฆเฒฒಾเฒುเฒค್เฒคเฒเฒฐುเฒค್เฒคเฒฆೆ.
เณงเณญเณฎเณฏเฒฐเฒฒ್เฒฒಿ เฒฒಾเฒตೋเฒทಿเฒฏเฒฐเฒจು เฒฎೊเฒฆเฒฒเฒฌಾเฒฐಿเฒೆ เฒ ಂเฒฆಿเฒจเฒตเฒฐೆเฒೆ เฒคಿเฒณಿเฒฆಿเฒฐುเฒต เณจเณฉ เฒงಾเฒคುเฒเฒณ เฒชเฒ್เฒಿ เฒฎಾเฒกಿเฒฆเฒจು . เฒเฒคเฒจು เฒฐಾเฒธಾเฒฏเฒจಿเฒ เฒฌเฒฆเฒฒಾเฒตเฒฃೆเฒฏเฒฒ್เฒฒಿ เฒญಾเฒเฒตเฒนಿเฒธುเฒต เฒงಾเฒคುเฒเฒณ เฒฐಾเฒถಿ เฒธಂเฒฐเฒ್เฒೆเฒฃೆเฒฏ เฒจಿเฒฏเฒฎเฒตเฒจ್เฒจು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒจು. เฒเฒคเฒจเฒจ್เฒจು เฒฐเฒธಾเฒฏเฒจ เฒถಾเฒธ್เฒค್เฒฐเฒฆ เฒชಿเฒคಾเฒฎเฒน เฒಂเฒฆು เฒชเฒฐಿเฒเฒฃಿเฒธเฒฒಾเฒುเฒค್เฒคเฒฆೆ.
เณงเณญเณฏเณชเฒฐ เฒซ್เฒฐೆಂเฒ್ เฒ್เฒฐಾಂเฒคಿเฒฏเฒฒ್เฒฒಿ เฒตಿเฒ್เฒಾเฒจಿ เฒฒಾเฒตೊเฒธಿเฒฐเฒจು เฒೊเฒฒೆเฒฏಾเฒฆเฒจು.
เณงเณญเณฎเณฏ เฒฐเฒฒ್เฒฒಿ เฒช್เฒฐೌเฒธ್เฒ್ เฒเฒจ್เฒจುเฒต เฒตಿเฒ್เฒಾเฒจಿเฒฏು เฒเฒฐเฒกು เฒงಾเฒคುเฒเฒณು เฒฐಾเฒธಾเฒฏเฒจಿเฒเฒตಾเฒಿ เฒธಂเฒฏೋเฒ เฒนೊಂเฒฆುเฒตಾเฒ เฒ เฒตು เฒಂเฒฆು เฒจಿเฒฐ್เฒฆಿเฒท್เฒ เฒฐಾเฒถಿเฒฏ เฒ เฒจುเฒชಾเฒคเฒฆเฒฒ್เฒฒಿ เฒธೇเฒฐಿเฒೊเฒณ್เฒณುเฒค್เฒคเฒตೆ เฒಂเฒฆು เฒจಿเฒฐೂเฒชಿเฒธಿเฒฆเฒฐು.
เณงเณฎเณฆเณฆเฒฐเฒฒ್เฒฒಿ เฒจೀเฒฐಿเฒจเฒฒ್เฒฒಿ เฒตಿเฒฆ್เฒฏುเฒค್ เฒช್เฒฐเฒตಾเฒน เฒนเฒฐಿเฒธಿ , เฒจೀเฒฐเฒจ್เฒจು เฒตಿเฒญเฒಿเฒธಿ เฒเฒฎ್เฒฒเฒเฒจเฒ เฒฎเฒค್เฒคು เฒเฒฒเฒเฒจเฒ เฒ เฒจಿเฒฒเฒเฒณಾเฒಿ เฒตಿಂเฒเฒกಿเฒธಿเฒฆเฒฐು . เฒเฒฆ್เฒฆเฒฐಿಂเฒฆ เฒจೀเฒฐು เฒฎೂเฒฒเฒตเฒธ್เฒคು เฒ เฒฒ್เฒฒ เฒฌเฒฆเฒฒಿเฒೆ เฒเฒฆೊಂเฒฆು เฒธಂเฒฏುเฒ್เฒค เฒตเฒธ್เฒคು เฒಂเฒฆು เฒเฒಿเฒคเฒตಾเฒฏಿเฒคು .
เฒ เฒช್เฒฐเฒฏೋเฒเฒฆเฒฒ್เฒฒಿ เฒนೊเฒฐเฒธೂเฒธಿเฒฆ เฒเฒฒเฒเฒจเฒ เฒฎเฒค್เฒคು เฒเฒฎ್เฒฒเฒเฒจเฒ เฒ เฒจಿเฒฒเฒเฒณ เฒಾเฒค್เฒฐเฒฆ เฒ เฒจುเฒชಾเฒค เณจ:เณง เฒเฒฐುเฒค್เฒคเฒฆೆ. เฒ ಂเฒฆเฒฐೆ เฒเฒฐเฒกು เฒตಿเฒญಿเฒจ್เฒจ เฒ เฒจಿเฒฒเฒเฒณು เฒಂเฒฆು เฒจಿเฒฐ್เฒฆಿเฒท್เฒ เฒಾเฒค್เฒฐเฒฆ เฒ เฒจುเฒชಾเฒคเฒฆเฒฒ್เฒฒಿ เฒธೇเฒฐಿ เฒธಂเฒฏುเฒ್เฒค เฒตเฒธ್เฒคು เฒฐೂเฒชเฒೊเฒณ್เฒณುเฒค್เฒคเฒฆೆ เฒಂเฒฆು เฒธಿเฒฆ್เฒฆเฒตಾเฒฏಿเฒคು. เฒเฒฆเฒจ್เฒจು เฒೆ เฒฒುเฒธಾเฒಾเฒฐ เฒจಿเฒฏเฒฎ เฒเฒจ್เฒจುเฒตเฒฐು.
เฒจೀเฒฐು เฒตಿเฒญเฒಿเฒธುเฒต เฒฐಾเฒธಾเฒฏเฒจಿเฒ เฒ್เฒฐಿเฒฏೆเฒೆ เฒนೊเฒฐเฒಿเฒจಿಂเฒฆ เฒถเฒ್เฒคಿ เฒเฒฆเฒಿเฒธเฒฌೇเฒಾเฒฏಿเฒคು. เฒเฒฆเฒ್เฒೆ เฒตಿเฒฐುเฒฆ್เฒงเฒตಾเฒಿ เฒเฒฒเฒเฒจเฒ เฒฎเฒค್เฒคು เฒเฒฎ್เฒฒเฒเฒจเฒ เฒ เฒจಿเฒฒเฒเฒณು เฒฐಾเฒธಾเฒฏเฒจಿเฒเฒตಾเฒಿ เฒธೇเฒฐಿ, เฒจೀเฒฐು เฒಂเฒಾเฒುเฒต เฒฌเฒฆเฒฒಾเฒตเฒฃೆเฒฏเฒฒ್เฒฒಿ เฒถเฒ್เฒคಿ เฒนೊเฒฐเฒೆ เฒนಾเฒเฒฒಾเฒುเฒค್เฒคเฒฆೆ. เฒนೀเฒೆ เฒถเฒ್เฒคಿเฒฏเฒจ್เฒจು เฒชเฒกೆเฒฆುเฒೊเฒณ್เฒณುเฒต เฒ เฒฅเฒตಾ เฒถเฒ್เฒคಿเฒฏเฒจ್เฒจು เฒนೊเฒฐเฒೆเฒฒ್เฒฒುเฒต, เฒเฒฐเฒกು เฒช್เฒฐเฒಾเฒฐเฒฆ เฒฐಾเฒธಾเฒฏเฒจಿเฒ เฒ್เฒฐಿเฒฏೆเฒเฒณಿเฒฐುเฒค್เฒคเฒตೆ.
เณงเณฎเณฆเณฉเฒฐเฒฒ್เฒฒಿ เฒกಾเฒฒ್เฒเฒจ್ เฒเฒจ್เฒจುเฒต เฒตಿเฒ್เฒಾเฒจಿ เฒงಾเฒคುเฒตಿเฒจ เฒชเฒฐเฒฎಾเฒฃು เฒธಿเฒงಾಂเฒคเฒตเฒจ್เฒจು เฒฎಂเฒกಿเฒธಿเฒฆเฒจು. เฒงಾเฒคುเฒเฒณು เฒชเฒฐเฒฎಾเฒฃುเฒเฒณೆಂเฒฌ เฒเฒกೆเฒฏเฒฒಾเฒเฒฆ เฒ เฒคಿเฒธเฒฃ್เฒฃ เฒเฒฃเฒเฒณಿಂเฒฆ เฒเฒಿเฒตೆ เฒಂเฒฆು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒจು . เฒตಿเฒตಿเฒง เฒงಾเฒคುเฒเฒณ เฒชเฒฐเฒฎಾเฒฃುเฒเฒณು เฒญಿเฒจ್เฒจ เฒญಿเฒจ್เฒจ เฒฐಾเฒถಿเฒฏเฒจ್เฒจು เฒนೊಂเฒฆಿเฒฐುเฒตುเฒฆಾเฒಿ เฒคಿเฒณಿเฒธಿเฒฆเฒจು . เฒเฒคเฒจು เฒฎೊเฒฆเฒฒเฒฌಾเฒฐಿเฒೆ เฒงಾเฒคುเฒเฒณ เฒธಾเฒชೇเฒ್เฒท เฒชเฒฐเฒฎಾเฒฃು เฒฐಾเฒถಿเฒเฒณ เฒชเฒ್เฒಿ เฒฎಾเฒกಿเฒฆเฒจು .
เณงเณฎเณงเณงเฒฐเฒฒ್เฒฒಿ เฒ เฒตเฒಾเฒก್เฒฐೋ เฒเฒจ್เฒจುเฒต เฒตಿเฒ್เฒಾเฒจಿ เฒ เฒจಿเฒฒเฒเฒณ เฒ เฒฃು เฒฐೂเฒชเฒฆ เฒเฒฃเฒเฒณ เฒฎೇเฒฒೆ เฒช್เฒฐเฒฏೋเฒเฒเฒณเฒจ್เฒจು เฒฎಾเฒกಿ; เฒธเฒฎಾเฒจ เฒಾเฒค್เฒฐเฒฆ เฒฏಾเฒตುเฒฆೇ เฒ เฒจಿเฒฒเฒเฒณು เฒธเฒฎಾเฒจ เฒช್เฒฐเฒฎಾเฒฃเฒฆ เฒเฒฃเฒเฒณು เฒนೊಂเฒฆಿเฒฐುเฒค್เฒคเฒตೆಂเฒฆು เฒช್เฒฐเฒคಿเฒชಾเฒฆಿเฒธಿเฒฆเฒจು.
เฒธเฒฎಾเฒจ เฒಾเฒค್เฒฐเฒฆ เฒเฒฒเฒเฒจเฒ เฒนಾเฒು เฒ เฒฎ್เฒฒเฒเฒจเฒ เฒ เฒจಿเฒฒเฒเฒณ เฒฐಾเฒถಿเฒฏು เณง:เณงเณฌ เฒ เฒจುเฒชಾเฒคเฒฆเฒฒ್เฒฒಿ เฒเฒฐುเฒค್เฒคเฒฆೆ. เฒเฒฒเฒเฒจเฒเฒฆ เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒธಾเฒชೇเฒ್เฒทೆเฒฐಾเฒถಿ เณง เฒเฒฆเฒฐೆ เฒเฒฎ್เฒฒเฒเฒจเฒเฒฆ್เฒฆು เณงเณฌ เฒเฒುเฒค್เฒคเฒฆೆ. เฒจೀเฒฐಿเฒจ เฒ เฒฃು เฒฐಾเฒถಿ เณงเณฎ เฒเฒฐುเฒค್เฒคเฒฆೆ. เณงเณฎ เฒ್เฒฐಾಂ เฒจೀเฒฐเฒจ್เฒจು เฒಂเฒฆು เฒฎೋเฒฒ್ เฒจೀเฒฐು เฒเฒจ್เฒจುเฒตเฒฐು. เฒಂเฒฆು เฒฎೋเฒฒ್ เฒจೀเฒฐಿเฒจเฒฒ್เฒฒಿ เณฌ.เณฆเณจเณจ x เณงเณฆเฒฐ เฒಾเฒค เณจเณฉ เฒจೀเฒฐಿเฒจ เฒเฒฃเฒเฒณಿเฒตೆ. เฒเฒฆเฒจ್เฒจು เฒ เฒตเฒಾเฒก್เฒฐೋ เฒธಂเฒ್เฒฏೆ เฒಂเฒฆು เฒธೂเฒಿเฒธುเฒตเฒฐು.
เณงเณฎเณงเณจเฒฐเฒฒ್เฒฒಿ เฒนಂเฒซ್เฒฐಿ เฒกೇเฒตಿ เฒเฒจ್เฒจುเฒต เฒตಿเฒ್เฒಾเฒจಿเฒฏು เฒฒเฒตเฒฃเฒเฒณ เฒฎೇเฒฒೆ เฒช್เฒฐเฒฌเฒฒเฒตಾเฒฆ เฒตಿเฒฆ್เฒฏುเฒค್ เฒนเฒฐಿเฒธಿ, เฒฐಾเฒธಾเฒฏเฒจಿเฒ เฒฌเฒฆเฒฒಾเฒตเฒฃೆ เฒಂเฒುเฒฎಾเฒกಿ, เฒนೊเฒธ เฒงಾเฒคುเฒเฒณ เฒถೋเฒง เฒฎಾเฒกಿเฒฆเฒจು. เฒเฒคเฒจು เฒชೊเฒ್เฒฏಾเฒธಿเฒฏಂ เฒธೋเฒกಿเฒฏಂ, เฒ್เฒฏಾเฒฒ್เฒธಿเฒฏಂ เฒฎ್เฒฏಾเฒ್เฒจೇเฒธಿเฒฏಂ เฒฌೇเฒฐಿเฒฏಂ เฒฎเฒค್เฒคು เฒธ್เฒ್เฒฐಾเฒจเฒಿเฒฏಂ เฒงಾเฒคುเฒเฒณเฒจ್เฒจು เฒಂเฒกುเฒนಿเฒกಿเฒฆเฒจು. เฒ เฒฒ್เฒฒเฒฆೆ เฒ್เฒฒೋเฒฐಿเฒจ್ เฒ เฒจಿเฒฒเฒตೂ เฒೂเฒกಾ เฒಂเฒฆು เฒงಾเฒคು เฒಂเฒฆು เฒธಿเฒฆ್เฒงเฒฎಾเฒกಿเฒฆ.
เณงเณฎเณจเณฌ เฒฐเฒฒ್เฒฒಿ เฒกಾเฒฒ್เฒเฒจ್เฒจ เฒถಿเฒท್เฒฏเฒจಾเฒฆ เฒฌเฒฐ್เฒೆเฒฒಿเฒฏเฒธเฒจೂ, เฒงಾเฒคುเฒเฒณเฒจ್เฒจು เฒนೆเฒธเฒฐಿเฒธಿเฒฆ เฒฎเฒค್เฒคು เฒ เฒตುเฒเฒณ เฒนೆเฒธเฒฐಿเฒจ เฒฎೂเฒฒಾเฒ್เฒทเฒฐเฒฆಿಂเฒฆ เฒงಾเฒคುเฒเฒณเฒจ್เฒจು เฒธಾಂเฒೇเฒคಿเฒเฒตಾเฒಿ เฒฌเฒฐೆเฒฏುเฒต เฒเฒฒೆ เฒฐೂเฒขಿเฒธಿเฒฆเฒจು . เฒเฒฆเฒฐಿಂเฒฆ เฒธಂเฒฏುเฒ್เฒค เฒตเฒธ್เฒคುเฒเฒณเฒจ್เฒจು เฒธಾಂเฒೇเฒคಿเฒเฒตಾเฒಿ เฒ เฒฃು เฒธೂเฒค್เฒฐเฒฆ เฒฐೂเฒชเฒฆเฒฒ್เฒฒಿ เฒฌเฒฐೆเฒฏเฒฒು เฒ เฒจುเฒೂเฒฒเฒตಾเฒฏಿเฒคು.
เณงเณฎเณจเณฎเฒฐเฒฒ್เฒฒಿ เฒตೋเฒน್เฒฒเฒฐเฒจು เฒฎೊเฒฆเฒฒเฒฌಾเฒฐಿเฒೆ เฒจಿเฒฐเฒฏเฒต เฒฐಾเฒธಾเฒฏเฒจเฒเฒณเฒจ್เฒจು เฒฌเฒณเฒธಿ, เฒೀเฒตಿเฒเฒณเฒฒ್เฒฒಿ เฒಂเฒกುเฒฌเฒฐುเฒต เฒฏೂเฒฐಿเฒฏಾ เฒเฒจ್เฒจುเฒต เฒธಾเฒตเฒฏเฒต เฒชเฒฆಾเฒฐ್เฒฅเฒตเฒจ್เฒจು เฒคเฒฏ್เฒฏಾเฒฐಿเฒธಿเฒฆเฒจು.
เณงเณฎเณฉเณฆเฒฐ เฒตเฒฐೆเฒೆ เฒಂเฒกುเฒนಿเฒกಿเฒฆ เฒงಾเฒคುเฒเฒณ เฒธಂเฒ್เฒฏೆ เณซเณชเฒ್เฒೆ เฒเฒฐಿเฒคು.
เณงเณฎเณฉเณชเฒฐเฒฒ್เฒฒಿ เฒฎೈเฒเฒฒ್ เฒซ್เฒฏಾเฒฐเฒกೆเฒฏเฒตเฒฐ เฒจಿเฒฐೂเฒชเฒฃೆ ; "เฒ เฒฏಾเฒจಿเฒ್ เฒฆ್เฒฐಾเฒตเฒฃเฒเฒณเฒฒ್เฒฒಿ เฒตಿเฒฆ್เฒฏುเฒค್ เฒนเฒฐಿเฒธಿเฒฆಾเฒ เฒಂเฒಾเฒುเฒต เฒฐಾเฒธಾเฒฏเฒจಿเฒ เฒฌเฒฆเฒฒಾเฒตเฒฃೆเฒฏು, เฒฆ್เฒฐಾเฒตเฒฃเฒฆเฒฒ್เฒฒಿ เฒนเฒฐಿเฒธಿเฒฆ เฒเฒ್เฒು เฒตಿเฒฆ್เฒฏುเฒค್เฒคಿเฒจ เฒฎೊเฒค್เฒคเฒ್เฒೆ เฒ เฒจುเฒฐೂเฒชเฒตಾเฒಿ เฒเฒฐುเฒค್เฒคเฒฆೆ."
เณงเณฎเณชเณงเฒฐเฒฒ್เฒฒಿ เฒฒಂเฒกเฒจ್ เฒชเฒ್เฒเฒฃเฒฆเฒฒ್เฒฒಿ เฒฐಾเฒธಾเฒฏเฒจ เฒถಾเฒธ್เฒค್เฒฐเฒฆ เฒธಂเฒ เฒธ್เฒฅಾเฒชเฒจೆเฒೊಂเฒกಿเฒคು.
เณงเณฎเณซเณจเฒฐเฒฒ್เฒฒಿ เฒฐಾเฒธಾเฒฏเฒจಿเฒ เฒธಂเฒฏೋเฒ เฒธಾเฒฎเฒฐ್เฒค್เฒฏเฒฏ เฒจಿเฒฐೂเฒชเฒฃೆเฒฏಾเฒฏಿเฒคು.
เณงเณฎเณซเณฏเฒฐเฒฒ್เฒฒಿ เฒฌเฒจ್เฒธೆเฒจ್ เฒฐೂ, เฒช್เฒฐเฒคಿเฒฏೊಂเฒฆು เฒงಾเฒคುเฒตು เฒคเฒจ್เฒจเฒฆೇ เฒเฒฆ, เฒตಿเฒถಿเฒท್เฒ เฒฌೆเฒณเฒಿเฒจ เฒตเฒฐ್เฒฃเฒชเฒเฒฒเฒตเฒจ್เฒจು เฒಂเฒುเฒฎಾเฒกುเฒค್เฒคเฒฆೆ เฒಂเฒฆು เฒಂเฒกುเฒนಿเฒกಿเฒฆเฒฐು. เฒ เฒตಿเฒงಾเฒจเฒตು เฒนೊเฒธ เฒงಾเฒคುเฒเฒณเฒจ್เฒจು เฒಾเฒกುเฒนಿเฒกಿเฒฏเฒฒು เฒ เฒจುเฒೂเฒฒเฒตಾเฒฏಿเฒคು.
เณงเณฎเณฌเณฆเฒฐเฒฒ್เฒฒಿ เฒตಿเฒ್เฒಾเฒจಿ เฒೆเฒೂเฒฒೆเฒฏเฒตเฒฐ เฒจೇเฒค್เฒฐಿเฒค್เฒตเฒฆเฒฒ್เฒฒಿ , เฒเฒฐ್เฒฎเฒจಿ เฒฆೇเฒถเฒฆเฒฒ್เฒฒಿ เฒฎೊเฒฆเฒฒเฒฌಾเฒฐಿเฒೆ เฒಾเฒเฒคಿเฒ เฒฐเฒธಾเฒฏเฒจ เฒถಾเฒธ್เฒค್เฒฐเฒฆ เฒธเฒฎ್เฒฎೇเฒณเฒจ เฒเฒฐ್เฒชเฒ್เฒಿเฒค್เฒคು. เฒเฒฆเฒฐเฒฒ್เฒฒಿ เณงเณชเณฆ เฒเฒจ เฒตಿเฒ್เฒಾเฒจಿเฒเฒณು เฒชಾเฒฒ್เฒೊಂเฒกเฒฐು.
เณงเณฎเณฌเณฏเฒฐเฒฒ್เฒฒಿ เฒธೈเฒฌೀเฒฐಿเฒฏಾเฒฆ เฒตಿเฒ್เฒಾเฒจಿ เฒฎೆಂเฒกೆเฒฒಿเฒตเฒฐು เฒงಾเฒคುเฒเฒณ เฒเฒตเฒฐ್เฒคเฒ เฒೋเฒท್เฒเฒเฒตเฒจ್เฒจು เฒช್เฒฐเฒเฒಿเฒธಿเฒฆเฒฐು. เฒ เฒตเฒฐು เฒ เฒฒ್เฒฒಿเฒฏเฒตเฒฐೆเฒೆ เฒคಿเฒณಿเฒฆಿเฒฐುเฒต เณฌเณฌ เฒงಾเฒคುเฒเฒณเฒจ್เฒจು เฒೋเฒท್เฒเฒเฒฆเฒฒ್เฒฒಿ เฒ เฒก್เฒกเฒธಾเฒฒು เฒนಾเฒು เฒಂเฒฌเฒธಾเฒฒುเฒเฒณಾเฒಿ เฒตเฒฐ್เฒಿเฒเฒฐಿเฒธಿเฒฆเฒฐು. เฒงಾเฒคುเฒเฒณเฒจ್เฒจು เฒ เฒตುเฒเฒณ เฒชเฒฐเฒฎಾเฒฃು เฒฐಾเฒถಿเฒฏ เฒเฒฐಿเฒೆเฒฏ เฒ್เฒฐเฒฎเฒฆเฒฒ್เฒฒಿ เฒฌเฒฐೆเฒฆเฒฐು.
เณงเณฎเณฎเณญเฒฐเฒฒ್เฒฒಿ เฒเฒฎ್เฒฒ, เฒช್เฒฐเฒค್เฒฏಾเฒฎ್เฒฒ, เฒฎเฒค್เฒคು เฒฒเฒตเฒฃเฒเฒณು เฒจೀเฒฐಿเฒจเฒฒ್เฒฒಿ เฒเฒฐเฒಿ เฒ เฒฏಾเฒจ್เฒเฒณಾเฒಿ เฒฌೇเฒฐ್เฒชเฒกುเฒค್เฒคเฒตೆ เฒಂเฒฆು เฒಂเฒกುเฒೊಂเฒกเฒฐು.
เณงเณฎเณฏเณฎเฒฐเฒฒ್เฒฒಿ เฒตಿเฒฒಿเฒฏಂ เฒฐಾเฒฎเฒธೇ เฒเฒจ್เฒจುเฒต เฒตಿเฒ್เฒಾเฒจಿ, เฒเฒก เฒ เฒจಿเฒฒเฒเฒณเฒจ್เฒจು เฒಂเฒกುเฒนಿเฒกಿเฒฆเฒฐು.
เณงเณฏเณฆเณฆเฒฐ เฒนೊเฒค್เฒคಿเฒೆ เฒงಾเฒคುเฒเฒณ เฒธಂเฒ್เฒฏೆ เณฎเณฎเฒ್เฒೆ เฒคเฒฒುเฒชಿเฒคು.
เณงเณฎเณฏเณญเฒฐเฒฒ್เฒฒಿ เฒೆ เฒೆ เฒฅಾเฒฎ್เฒธเฒจ್เฒจเฒฐು เฒ್เฒฏಾเฒฅೋเฒก್ เฒಿเฒฐเฒฃเฒเฒณ เฒช್เฒฐเฒฏೋเฒ เฒฎಾเฒกಿ, เฒเฒฒ್เฒฒಾเฒงಾเฒคುเฒเฒณ เฒชเฒฐเฒฎಾเฒฃುเฒเฒณು เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจ್ เฒเฒณೆಂเฒฌ เฒเฒชเฒเฒฃเฒเฒณು เฒนೊಂเฒฆಿเฒตೆ เฒಂเฒฆು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒฐು. เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจ್ เฒเฒณು เฒเฒฃ เฒตಿเฒฆ್เฒฏುเฒค್ เฒเฒตೇเฒถ เฒนೊಂเฒฆಿเฒฐುเฒค್เฒคเฒตೆ.
เณงเณฏเณงเณงเฒฐ เฒนೊเฒค್เฒคಿเฒೆ เฒชเฒฐเฒฎಾเฒฃುเฒตೂ เฒเฒฃ เฒตಿเฒฆ್เฒฏುเฒค್ เฒเฒตೇเฒถเฒฏುเฒณ್เฒณ เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจ್ เฒฎเฒค್เฒคು เฒงเฒจ เฒเฒตೇเฒถเฒฏುเฒณ್เฒณ เฒฌೀเฒเฒೇಂเฒฆ್เฒฐ เฒนೊಂเฒฆಿเฒฆೆ เฒಂเฒฆು เฒฐเฒฆเฒฐเฒซೋเฒฐ್เฒกเฒฐ เฒช್เฒฐเฒฏೋเฒเฒเฒณಿಂเฒฆ เฒเฒಿเฒคเฒตಾเฒฏಿเฒคು. เฒฎೂเฒฒเฒคಃ เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒฐಾเฒถಿเฒฏು เฒฌೀเฒเฒೇಂเฒฆ್เฒฐเฒฆ್เฒฆೇ เฒเฒಿเฒฆೆ. เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจಿเฒจ เฒฐಾเฒถಿเฒฏು เฒจเฒเฒฃ್เฒฏ .
เณงเณฏเณงเณฉเฒฐเฒฒ್เฒฒಿ เฒกೆเฒจ್เฒฎಾเฒฐ್เฒಿเฒจ เฒตಿเฒ್เฒಾเฒจಿ เฒจೀเฒฒ್เฒธ เฒฌೊเฒนเฒฐเฒฐು, เฒนೈเฒก್เฒฐೋเฒเฒจ್ เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒฐเฒเฒจಾ เฒธಿเฒงಾಂเฒคเฒตเฒจ್เฒจು เฒเฒธೆเฒธ್เฒตಿเฒฏಾเฒಿ เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒฐು. เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒฌೀเฒเฒೇಂเฒฆ್เฒฐเฒฆ เฒธುเฒค್เฒค เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจ್ เฒจಿเฒฐ್เฒงಾเฒฐಿเฒค เฒถเฒ್เฒคಿ เฒเฒตเฒเฒฆเฒฒ್เฒฒಿ เฒฎಾเฒค್เฒฐ เฒธುเฒค್เฒคುเฒค್เฒคಿเฒฐುเฒค್เฒคเฒฆೆ. เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒนೆเฒ್เฒಿเฒจ เฒಾเฒค್เฒฐ เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจುเฒเฒณೇ เฒเฒ್เฒฐเฒฎಿเฒธಿเฒೊಂเฒกಿเฒฐುเฒค್เฒคเฒตೆ.
เณงเณฏเณงเณชเฒฐเฒฒ್เฒฒಿ เฒಂเฒ್เฒฒ เฒตಿเฒ್เฒಾเฒจಿ เฒนೆเฒจ್เฒฐಿ เฒฎೊเฒธೆเฒฒಿเฒฏเฒตเฒฐಿಂเฒฆ เฒชเฒฐเฒฎಾเฒฃು เฒธಂเฒ್เฒฏೆเฒฏ เฒต್เฒฏಾเฒ್เฒฏಾเฒจ เฒจೀเฒกเฒฒಾเฒฏಿเฒคು. เฒชเฒฐเฒฎಾเฒฃು เฒธಂเฒ್เฒฏೆเฒฏು เฒชเฒฐเฒฎಾเฒฃು เฒฌೀเฒ เฒนೊಂเฒฆಿเฒฐುเฒต เฒเฒ್เฒು เฒช್เฒฐೋเฒಾเฒจ್ เฒเฒณ เฒธಂเฒ್เฒฏೆเฒೆ เฒธเฒฎ เฒเฒฐುเฒค್เฒคเฒฆೆ. เฒเฒฆಾเฒฆเฒจಂเฒคเฒฐ เฒงಾเฒคುเฒเฒณ เฒเฒตเฒฐ್เฒคเฒ เฒೋเฒท್เฒเฒเฒตเฒจ್เฒจು เฒงಾเฒคುเฒเฒณ เฒชเฒฐเฒฎಾเฒฃು เฒธಂเฒ್เฒฏೆ เฒฌเฒณเฒธಿ เฒೋเฒท್เฒ เฒเฒฆ เฒจ್เฒฏೂเฒจเฒคೆเฒเฒณเฒจ್เฒจು เฒคಿเฒฆ್เฒฆเฒฒಾเฒฏಿเฒคು. เฒเฒงುเฒจಿเฒ เฒเฒตเฒฐ್เฒคเฒ เฒೋเฒท್เฒเฒเฒฆเฒฒ್เฒฒಿ เณงเณฎ เฒಂเฒญ เฒธಾเฒฒುเฒเฒณಿเฒตೆ.
เณงเณฏเณงเณฌเฒฐเฒฒ್เฒฒಿ เฒ್เฒฏೂเฒฒಿเฒฏเฒธเฒฐಿಂเฒฆ, เฒ เฒฏಾเฒจಿเฒ್ เฒธಂเฒฏುเฒ್เฒคเฒเฒณ เฒฐเฒเฒจೆเฒฏเฒฒ್เฒฒಿ, เฒชเฒฐเฒฎಾเฒฃುเฒเฒณ เฒ เฒท್เฒเฒ เฒจಿเฒฏเฒฎ เฒจಿเฒฐೂเฒชเฒฃೆ.
เณงเณฏเณงเณฌเฒฐเฒฒ್เฒฒಿ เฒ เฒฎೆเฒฐಿเฒೆเฒฏ เฒตಿเฒ್เฒಾเฒจಿ เฒಿ. เฒเฒจ್. เฒฒೆเฒตಿเฒธเฒฐು, เฒฐಾเฒธಾเฒฏเฒจಿเฒ เฒธเฒนเฒตೇเฒฒೆเฒจ್เฒธಿ เฒฌಂเฒงเฒฆ เฒจಿเฒฐೂเฒชเฒฃೆ เฒೊเฒ್เฒเฒฐು. เฒฒೆเฒตಿเฒธเฒฐು เฒธเฒนเฒตಾเฒฒೆเฒจ್เฒธಿ เฒฌಂเฒง เฒฌเฒณเฒธಿ, เฒธಂเฒฏುเฒ್เฒค เฒเฒฃเฒเฒณ เฒ เฒฃುเฒฐเฒเฒจೆเฒฏเฒจ್เฒจು เฒเฒธೆเฒธ್เฒตಿเฒฏಾเฒಿ เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒฐು.
เฒ เฒตเฒฐು, เณงเณฏเณจเณฉเฒฐเฒฒ್เฒฒಿ เฒฒೆเฒตಿเฒธ್ เฒเฒฎ್เฒฒ เฒฎเฒค್เฒคು เฒช್เฒฐเฒค್เฒฏಾเฒฎ್เฒฒเฒเฒณ เฒชเฒฐಿเฒเฒฒ್เฒชเฒจೆ เฒೊเฒ್เฒเฒฐು. เฒฐಾเฒธಾเฒฏเฒจಿเฒ เฒฌเฒฆเฒฒಾเฒตเฒฃೆเฒฏเฒฒ್เฒฒಿ, เฒฒೆเฒตಿเฒธ್ เฒเฒฎ್เฒฒเฒเฒณು, เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจ್ เฒೋเฒกಿเฒฏเฒจ್เฒจು [เฒช್เฒฐเฒค್เฒฏಾเฒฎ್เฒฒเฒเฒณಿಂเฒฆ] เฒธ್เฒตೀเฒเฒฐಿเฒธುเฒค್เฒคเฒตೆ.
เณงเณฏเณงเณฏเฒฐเฒฒ್เฒฒಿ เฒฐเฒฆเฒฐ್เฒซೋเฒฐ್เฒกเฒฐು, เฒชเฒฐเฒฎಾเฒฃು เฒฌೀเฒเฒೇಂเฒฆ್เฒฐเฒฆเฒฒ್เฒฒಿเฒฐುเฒต เฒงเฒจಾเฒตೇเฒถเฒฏುเฒณ್เฒณ เฒช್เฒฐೋเฒಾเฒจ್ เฒเฒฃเฒตเฒจ್เฒจು เฒಂเฒกುเฒนಿเฒกಿเฒฆเฒฐು.
เณงเณฏเณจเณชเฒฐเฒฒ್เฒฒಿ เฒฌ್เฒฐೊเฒ್เฒฒೆเฒฏเฒตเฒฐಿಂเฒฆ เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจಿเฒจ เฒฐเฒเฒจಾ เฒฐೂเฒช, เฒ เฒฒೆ เฒนಾเฒೂ เฒเฒฃ เฒเฒจ್เฒจುเฒต เฒฆ್เฒตಿเฒುเฒฃ เฒช್เฒฐเฒೃเฒคಿเฒฏ เฒจಿเฒฐೂเฒชเฒฃೆ.
เณงเณฏเณจเณฌเฒฐเฒฒ್เฒฒಿ เฒถ್เฒฐೋเฒกಿಂเฒเฒฐเฒฐಿಂเฒฆ เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒฐเฒเฒจೆเฒฏ เฒถเฒเฒฒเฒธಿเฒงಾಂเฒคเฒฆ เฒจಿเฒฐೂเฒชเฒฃೆ.
เณงเณฏเณฉเณจเฒฐเฒฒ್เฒฒಿ เฒೇเฒฎ್เฒธ್ เฒಾเฒก್เฒตಿเฒ್ เฒฐเฒตเฒฐು, เฒชเฒฐเฒฎಾเฒฃು เฒฌೀเฒเฒೇಂเฒฆ್เฒฐ เฒนೊಂเฒฆಿเฒฐುเฒต เฒจ್เฒฏೂเฒ್เฒฐಾเฒจ್ เฒเฒจ್เฒจುเฒต เฒเฒชเฒเฒฃเฒตเฒจ್เฒจು เฒಂเฒกುเฒนಿเฒกಿเฒฆเฒฐು. เฒ เฒเฒฃเฒ್เฒೆ เฒฏಾเฒตುเฒฆೇ เฒตಿเฒฆ್เฒฏುเฒค್ เฒเฒตೇเฒท เฒเฒฒ್เฒฒ. เฒนೀเฒೆ เฒಂเฒฆು เฒชเฒฐเฒฎಾเฒฃುเฒตೂ เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจ್, เฒช್เฒฐೋเฒಾเฒจ್, เฒฎเฒค್เฒคು เฒจ್เฒฏೂเฒ್เฒฐಾเฒจ್ เฒเฒจ್เฒจುเฒต เฒธೂเฒ್เฒท್เฒฎ เฒเฒฃเฒเฒณಿಂเฒฆ เฒเฒಿเฒฆೆ. เฒช್เฒฐೋเฒಾเฒจ್ เฒ เฒฅเฒตಾ เฒจ್เฒฏೂเฒ್เฒฐಾเฒจ್ เฒเฒฃเฒฆ เฒฐಾเฒถಿเฒೆ เฒนೋเฒฒಿเฒธಿเฒฆเฒฐೆ เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจ್ เฒฐಾเฒถಿเฒฏು เฒจเฒเฒฃ್เฒฏ เฒเฒจಿเฒธುเฒค್เฒคเฒฆೆ. เฒเฒฆเฒฐೆ เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจ್ เฒฎเฒค್เฒคು เฒช್เฒฐೋเฒಾเฒจ್ เฒเฒณ เฒตಿเฒฆ್เฒฏುเฒค್ เฒเฒตೇเฒถเฒตು เฒธเฒฎ เฒเฒฐುเฒค್เฒคเฒฆೆ. เฒಂเฒฆು เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒเฒฒೆเฒ್เฒ್เฒฐಾเฒจ್ เฒฎเฒค್เฒคು เฒช್เฒฐೋเฒಾเฒจ್ เฒเฒณ เฒธಂเฒ್เฒฏೆ เฒธเฒฎಾเฒจเฒตಾเฒಿเฒฐುเฒค್เฒคเฒฆೆ.
Sunday, 23 May 2021
Hindu Calendar
Throughout most of history, most calendars were based on the moon and each waxing and waning of the moon would count as one month. One example of this is the Muslim Hijri calendar, which takes 12 lunar months. However, 12 lunar months are only 354 days, which is 11 days shorter than a solar year. This creates a problem because if people use a purely lunar calendar, the months in which spring, summer or winter occur will change from year to year (as the seasons depend on the earth’s movement around the sun). In fact, every few years, summer would occur in December!
The Hindu calendar is known as a lunisolar calendar. The 12 months move according to the moon and the year is 354 days long. However, every third year, 33 days (11 extra days * 3) are added by creating one extra lunar month of 29 days. The remaining four days are adjusted here and there.
The 12 Indian months are: Chaitra, Vaisakha, Jyeshtha, Ashadha, Shravana, Bhadra, Ashvin, Kartik, Agahana, Pausha, Magha, Phalguna. So every three years, one of these months occurs twice in the same year…it’s like having two Marches or two Julys in a year!
There are two main calendars in common use in India today, the Vikram Samvat with a zero point of 57 BC and the Shaka Samvat with a zero point of 78 AD. They are used for calculating the dates of all Hindu festivals like Diwali and Holi.
Hindu calendar, dating system used in India from about 1000 BCE and still used to establish dates of the Hindu religious year. It is based on a year of 12 lunar months; i.e., 12 full cycles of phases of the Moon. The discrepancy between the lunar year of about 354 days and the solar year of about 365 days is partially resolved by intercalation of an extra month every 30 months.
The Saka Calender is based on luni-solar reckoning of time. The calendar consists of 365 days and 12 months like the normal Gregorian calendar. Chaitra is the first month of the year beginning on March 22 which is the day after the Spring Equinox. During leap years, the starting day of Chaitra corresponds with March 21. To convert years in AD to Saka years, 78 must be subtracted for a date.
The names of the months in Saka Calendar are:
• Chhaitra (March 21 – April 20)
• Vaishakha (April 21-May 21)
• Jyeshtha (May 22-June 21)
• Ashadha (June 22- July 22)
• Shravana (July 23-August 22)
• Bhaadra (August 22-September 22)
• Ashwin (September 23-October 22)
• Kartika (October 23-November 21)
• Agrahayana (November 22-December 21)
• Pausha (December 22-January 20)
• Magha (January 21- February 19) and
• Phalguna (February 20-March 20/21)
The month of Chaitra has generally 30 days but there are 31 days during leap years. The months of Vaish?kha, Jy?shtha, ?sh?dha, Shr?vana, Bhaadra, have 31 days while the rest have 30 days. This is done by taking into account the ellipticity of earth’s orbit around the sun.
Computation and calculation of time was a hallmark of all ancient civilizations. Egyptian and Mesopotamian civilization had their abiding interest in chronology and astronomy. The oldest and the largest civilization, the Indus valley civilization, was by far the most advanced and sophisticated in terms of chronological and astronomical acumen. They even had professional astronomers, called ‘nakshatra darshaks’ or ‘star gazers’, who meticulously observed and recorded the phases of the moon in reference to fixed constellations of stars. This method of calculation and its precision, sharply distinguishes Indian astronomy from the astronomy of all other countries.
The Indian calendar is ingeniously based on both the sun as well as the moon. It uses a solar year, but divides it into 12 lunar months. A lunar month, is the time required for the moon to orbit once around the earth and pass through its complete cycle of phases. Furthermore, these months are formulated in accordance with the successive entrances of the sun into the 12 rashis or the signs of the zodiac derived from the 12 constellations marking the path of the sun.
Vedic literature show that the knowledge of chronology (science of Time) and chronometry (scientific measurement of Time) existed even during Vedic times, thousands of years before the Christian era. Knowledge of planetary motions, constellations, eclipses, solstices, seasons, etc. has existed since the beginning of the Vedic age. A method of distributing time into various periods such as days, fortnights, months and years was adopted for the purposes of civic life, these divisions being intimately connected with the affairs of the people. And because of the very fact that the Indian calendar was devised to serve the affairs of day-to-day living, it was allowed the freedom of being both lunar and solar. The Rig Veda, cites months being lunar, but years luni-solar.
This means that there was a constant correlation between the solar year and its monthly lunar divisions. A lunar month is precisely 29 days 12 hours 44 minutes and 3 seconds long. Twelve such months constitute a lunar year of 354 days 8 hours 48 minutes and 36 seconds. To help the lunar months coincide with the solar year, the practice arose of inserting intercalary (extra) months. In general, 60 solar months = 62 lunar months. And so an extra month, called the Adhik Maas (extra month), is inserted every 30 months, approximately every 2½ years. Such a practice was prevalent even in Vedic times. An intercalary month mentioned in the Rig Veda {Vedamรฃso dhrutavrato dvรฃdasha prajรฃvatah; vedรฃ ya upajรฃyate. (I/25:8)} proves that the month was added to preserve the correspondence between a whole solar year and the 12 lunations.
Seasons within the Hindu calendar
It is even more interesting, how the solar year was classified on the basis of seasons. The 12 lunar months of a solar year are divided into six ritus (seasons), each comprising of approximately two months. Since the seasons are solar based, each of the six seasons — Sharad (late monsoon), Hemant (early winter), Shishir (winter), Vasant (spring), Grishma (summer) and Varsha (monsoon)- commence around the 21st date (±2) of each even month of the Western calendar.
The Hindu calendar recognizes the importance of the summer solstice and winter solstice in a solar year, determining the six seasons. The Dakshinayana or the sun’s southern course starts from June 21 till December 21, during which the day-length is successively getting shorter until it is the shortest in december. The Uttarayana or the sun’s northern course progresses from December 21 until June 21, during which the day-length gets successively longer until it is the longest in June. Sun reaches the equinox twice in a year, during which the length of day and night are equal. The first point is Vernal Equinox in March 20(Vasant Sampaat). The other point is called Autumnal Equinox in September 22(Sharad Sampaat).Monday, 19 April 2021
Ancient India
About three lakh years ago, homosepians appeared in African plains.
200000 BCE- Probable birth of Humans evolved on the planet Earth. Monkey to man.
80,000 BCE- Humans appeared in this part of the earth, Jumbo Dveepa [Indin sub-continent].
74000 years ago, a volcanic eruption in Indonesia, destroyed life in the central and southern regions of India. Very few survived this carbon smoke eruption.
14,500 BCE- Brahma lived in India, Birth of Manu.
14500-11500 BCE Proto Indic language developed.
13500 BCE- The sage Viswamitra’s period.
11500- 3000 BCE Early Brahmi script evolved.
11200 BCE- Enormous earthquake in Kashmir Lake and flooding in the western part of India.
10000 BCE- The star, Agastya was visible at the south pole from Kanyakumari, the southern tip of India.
11200 BCE -10200 BCE- Rigveda was written during this time span.
9000 BCE- Atharvana Veda was written during this period.
7000- 3000 BCE Indus script was developed.
6778 BCE- Surya Siddhanta was written by Mayasura.
6777-5577 - Tretayuga period [1200 years].
5677-5577 BCE- The period of Ramayana.
5674 BCE- Birth of Shri Rama.[3rd February 5674 BCE]
5635 BCE- Ravana was killed by Rama.[in a war].
5577- 3177 BCE- Dwapara yuga. [2400 years].
3162 BCE- The period of Mahabharatha.
3102 BCE- Start of Kaliyuga time.
18th February 3192 BCE- Start of Kaliyuga.
2982 BCE- SaamaVeda and Yajurveda were written.
2000-1900 BCE- River Saraswathi dried up. There was a widespread drought all over the Indian subcontinent. And migration started to the outside world from India.
3000-2500 BCE- Indus Script refinement.
2500-1300 BCE- Ashokan or Mauryan Brahmi scipt.
2000- 0 BCE-Dialects of local languages were developed.
1864 BCE- Budha attained Nirvana.
1662 BCE-Mahapadma Nanda’s period.
1596- 1459- Mauryas period.
1500 BCE-Brahmi script evolved.
1400 BCE- six Vedangas were written.
1250BCE - 600 CE-Kushana Brahmi.
1200 BCE- Vedanga Jotisha
0719 BCE- Karttikadi Vikrama Era.
0057 CE- Chitradi Vikram Era.
0700BCE- Surya Siddhantha was re-written.
583 BCE- Saka Era
78 CE -Sakanta Era
0509 BCE- Adi Shankaracharya’s period.
[Indian textbook errors-1380 years].
540 BCE-Tamil Brahmi script evolved in Palani.
0600 BCE- Kanaadha’s theory of matter[Atom].
0570-495 BCE- Pythagoras time. His Indian connection.
0300-400CE Devanagari Script evolved.
499 ACE- Aryabhata-I. A great mathematician and scientist.
598 ACE- Brahmagupta.
600 ACE- Bhaskara-I
950 ACE-Aryabhata-II
Indian time scale:
8000 years- Satya yuga [from 14500 to 6777 BCE] Vedic period.
1200 years -Treta yuga [6777 to 5577 BCE]
2400 years- Dwapara yuga [5577 to 3102 BCE]
Astronomy
Precession duration: 25700 years cycle.