Sunday, 12 December 2021

Electric motor เคตाเค‡ंเคกिंเค—्เคธ เค•ो เคธเคฎเคเคจा

 

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 GrazAustria, 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 เฒ‡เฒคಿเฒนಾเฒธ :

เฒˆ เฒœเฒ—เฒค್เฒคು เฒชಂเฒšเฒฎเฒนಾเฒญೂเฒคเฒ—เฒณಿಂเฒฆ เฒ†เฒ—ಿเฒฆೆ เฒŽಂเฒฆเฒฐು เฒนಿಂเฒฆಿเฒจเฒตเฒฐು. เฒ†เฒ•ಾเฒถ , เฒ…เฒ—್เฒจಿ , เฒตಾเฒฏು , เฒœเฒฒ เฒฎเฒค್เฒคು เฒฎเฒฃ್เฒฃು ; เฒˆ เฒชಂเฒšเฒฎเฒนಾเฒญೂเฒคเฒ—เฒณು .

เฒตเฒธ್เฒคು , เฒถเฒ•್เฒคಿ , เฒ†เฒ•ಾเฒถ เฒฎเฒค್เฒคು เฒ•ಾเฒฒ เฒŽಂเฒฆು เฒ‡ಂเฒฆಿเฒจเฒตเฒฐು เฒตเฒฐ್เฒ—ಿเฒ•เฒฐเฒฃ เฒฎಾเฒกಿเฒฆเฒฐು . เฒตಾเฒฏು, เฒœเฒฒ, เฒฎเฒค್เฒคು เฒฎเฒฃ್เฒฃเฒจ್เฒจು เฒ’เฒŸ್เฒŸಿเฒ—ೆ เฒฆ್เฒฐเฒต್เฒฏ เฒŽಂเฒฆเฒฐು . เฒฆ್เฒฐเฒต್เฒฏเฒตು เฒธ್เฒฅเฒณเฒตเฒจ್เฒจು เฒ†เฒ•್เฒฐเฒฎಿเฒธುเฒค್เฒคเฒฆೆ . เฒ…เฒฆเฒ•್เฒ•ೆ เฒฆ್เฒฐเฒต್เฒฏเฒฐಾเฒถಿ เฒ‡เฒฆೆ .

เณงเณฌเณฌเณงเฒฐเฒฒ್เฒฒಿ เฒฐಾเฒฌเฒฐ್เฒŸ เฒฌಾเฒฏ್เฒฒ್  เฒงಾเฒคುเฒตಿเฒจ เฒชเฒฐಿเฒ•เฒฒ್เฒชเฒจೆ เฒจಿเฒฐೂเฒชಿเฒธಿเฒฆ . เฒ†เฒคเฒจು เฒ†เฒฎ್เฒฒ เฒฎเฒค್เฒคು เฒช್เฒฐเฒค್เฒฏಾเฒฎ್เฒฒเฒ—เฒณ เฒตಿเฒตเฒฐ เฒจೀเฒกಿเฒฆ.

เฒˆเฒคเฒจು เฒ—ಾเฒณಿเฒฏ เฒ—ುเฒฃเฒ—เฒณು เฒ…เฒง್เฒฏเฒฏเฒจ เฒฎಾเฒกಿ, เฒ’ಂเฒฆು เฒจಿเฒฐ್เฒฆಿเฒท್เฒŸ เฒฐಾเฒถಿเฒฏ เฒ…เฒจಿเฒฒเฒฆ เฒ—ಾเฒค್เฒฐ, เฒ’เฒค್เฒคเฒก, เฒนಾเฒ—ೂ เฒ‰เฒท್เฒฃเฒคೆเฒฏ เฒธಂเฒญಂเฒฆเฒฆ เฒจಿเฒฏเฒฎเฒตเฒจ್เฒจು เฒจಿเฒฐೂเฒชಿเฒธಿเฒฆเฒจು. 

เฒ’ಂเฒฆೇ เฒช್เฒฐเฒ•ಾเฒฐเฒฆ เฒฎೂเฒฒ เฒ•เฒฃเฒ—เฒณಿಂเฒฆ เฒ†เฒฆ เฒฆ್เฒฐเฒต್เฒฏเฒตเฒจ್เฒจು เฒงಾเฒคು เฒ…เฒฅเฒตಾ เฒฎೂเฒฒเฒตเฒธ್เฒคು เฒŽಂเฒฆเฒฐು. เฒ’ಂเฒฆು เฒงಾเฒคುเฒตಿเฒจ เฒ…เฒคಿเฒธเฒฃ್เฒฃ เฒ•เฒฃเฒ•್เฒ•ೆ เฒชเฒฐเฒฎಾเฒฃು เฒŽಂเฒฆเฒฐು. เฒ’ಂเฒฆೇ เฒช್เฒฐเฒ•ಾเฒฐเฒฆ เฒชเฒฐเฒฎಾเฒฃುเฒ—เฒณಿಂเฒฆ เฒ†เฒฆ เฒตเฒธ್เฒคುเฒตೇ เฒงಾเฒคು.

เณงเณฎเฒจೇเฒฏ เฒถเฒคเฒฎಾเฒจเฒฆเฒฒ್เฒฒಿ เฒœเฒฒเฒœเฒจเฒ• , เฒ†เฒฎ್เฒฒเฒœเฒจเฒ• . เฒฎเฒค್เฒคು เฒ‡ಂเฒ—ಾเฒฒเฒฆ เฒกೈ เฒ…เฒ•್เฒธเฒฏಿเฒก್ เฒŽเฒจ್เฒจುเฒต เฒ…เฒจಿเฒฒเฒ—เฒณ เฒถೋเฒง เฒฎเฒค್เฒคು เฒ…เฒตುเฒ—เฒณ เฒ—ುเฒฃเฒ—เฒณ เฒ…เฒง್เฒฏเฒฏเฒจ เฒจเฒกೆเฒฏಿเฒคು .

เณงเณญเณซเณชเฒฐเฒฒ್เฒฒಿ เฒœೋเฒธೆเฒซ್ เฒฌ್เฒฒ್เฒฏಾเฒ•್ เฒŽเฒจ್เฒจುเฒต เฒ‰เฒชเฒจ್เฒฏಾเฒธเฒ•เฒจು เฒธುเฒฃ್เฒฃเฒฆ เฒ•เฒฒ್เฒฒเฒจ್เฒจು เฒ•ಾเฒฏಿเฒธಿ เฒ…เฒฆเฒฐಿಂเฒฆ เฒ‡ಂเฒ—ಾเฒฒเฒฆ เฒกೈ เฒ…เฒ•್เฒธเฒฏಿเฒก್ เฒ…เฒจಿเฒฒ เฒนೊเฒฐเฒธೂเฒธುเฒตುเฒฆเฒจ್เฒจು เฒ—เฒฎเฒจಿเฒธಿเฒฆเฒจು. เฒˆเฒคเฒจು เฒจೀเฒฐಿเฒจ เฒ—ುเฒช್เฒคೋเฒท್เฒฃเฒตเฒจ್เฒจು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒจು.

เณงเณญเณฌเณฌเฒฐเฒฒ್เฒฒಿ เฒนೆเฒจ್เฒฐಿ เฒ•ೆเฒตೆಂเฒกಿเฒท್ เฒคเฒจ್เฒจ เฒช್เฒฐเฒฏೋเฒ—เฒถಾเฒฒೆเฒฏเฒฒ್เฒฒಿ เฒœเฒฒเฒœเฒจเฒ• เฒ…เฒจಿเฒฒเฒตเฒจ್เฒจು เฒ•ಂเฒกುเฒนಿเฒกಿเฒฆเฒจು. 

เณงเณญเณญเณชเฒฐเฒฒ್เฒฒಿ เฒช್เฒฐೀเฒธ್เฒŸ್เฒฒೆ เฒชಾเฒฆเฒฐเฒธเฒฆ เฒ†เฒ•್เฒธเฒฏಿเฒก್  เฒ…เฒฆಿเฒฐು เฒ•ಾเฒฏಿเฒธಿ เฒ†เฒฎ್เฒฒเฒœเฒจเฒ• เฒ…เฒจಿเฒฒ เฒ•ಂเฒกುเฒนಿเฒกಿเฒฆเฒจು .

เณงเณญเณญเณฎเฒฐเฒฒ್เฒฒಿ เฒซ್เฒฐಾเฒจ್เฒธ เฒฆೇเฒถเฒฆ เฒฒಾเฒตೋเฒทಿเฒฏೆเฒฐ್ เฒŽเฒจ್เฒจುเฒต เฒตಿเฒœ್เฒžಾเฒจಿ เฒฆเฒนเฒจ เฒ•್เฒฐಿเฒฏೆเฒฏเฒจ್เฒจು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒจು . เฒˆเฒคเฒจು เฒ†เฒฎ್เฒฒเฒœเฒจเฒ• เฒ’ಂเฒฆು เฒงಾเฒคು เฒŽಂเฒฆು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒจು . เฒจಿเฒธเฒฐ್เฒ—เฒฆเฒฒ್เฒฒಿ เฒธเฒนเฒœเฒตಾเฒ—ಿ เฒ†เฒฎ್เฒฒเฒœเฒจเฒ•เฒตು เฒ…เฒจಿเฒฒ เฒฐೂเฒชเฒฆเฒฒ್เฒฒಿ เฒ‡เฒฐುเฒค್เฒคเฒฆೆ. เฒ—ಾเฒณಿเฒฏเฒฒ್เฒฒಿ เณจเณง% เฒ†เฒฎ್เฒฒเฒœเฒจเฒ• เฒ‡เฒฆೆ . เฒ‡เฒฆು เฒ•್เฒฐಿเฒฏಾเฒถೀเฒฒเฒตಾเฒ—ಿเฒฆ್เฒฆು เฒ…เฒจ್เฒฏ เฒงಾเฒคುเฒ—เฒณೊಂเฒฆಿเฒ—ೆ เฒฐಾเฒธಾเฒฏเฒจಿเฒ•เฒตಾเฒ—ಿ เฒตเฒฐ್เฒคಿเฒธಿ เฒ†เฒ•್เฒธเฒฏಿเฒกเฒ—เฒณเฒจ್เฒจು เฒ‰ಂเฒŸುเฒฎಾเฒกುเฒค್เฒคเฒฆೆ เฒŽಂเฒฆು เฒคೋเฒฐಿเฒธಿเฒฆเฒจು. เฒ—ಾเฒณಿเฒฏเฒฒ್เฒฒಿ เณญเณฎ% เฒธಾเฒฐเฒœเฒจเฒ• เฒ…เฒจಿเฒฒ เฒ‡เฒฆೆ. เฒ‰เฒณಿเฒฆ เฒญಾเฒ— เฒœเฒก เฒ…เฒจಿเฒฒเฒ—เฒณเฒฆ್เฒฆು. เฒจೀเฒฐಾเฒตಿเฒฏ เฒช್เฒฐเฒฎಾเฒฃ เฒธเฒฆಾ เฒฌเฒฆเฒฒಾเฒ—ುเฒค್เฒคเฒ‡เฒฐುเฒค್เฒคเฒฆೆ.

เณงเณญเณฎเณฏเฒฐเฒฒ್เฒฒಿ เฒฒಾเฒตೋเฒทಿเฒฏเฒฐเฒจು เฒฎೊเฒฆเฒฒเฒฌಾเฒฐಿเฒ—ೆ เฒ…ಂเฒฆಿเฒจเฒตเฒฐೆเฒ—ೆ เฒคಿเฒณಿเฒฆಿเฒฐುเฒต เณจเณฉ เฒงಾเฒคುเฒ—เฒณ เฒชเฒŸ್เฒŸಿ เฒฎಾเฒกಿเฒฆเฒจು . เฒˆเฒคเฒจು เฒฐಾเฒธಾเฒฏเฒจಿเฒ• เฒฌเฒฆเฒฒಾเฒตเฒฃೆเฒฏเฒฒ್เฒฒಿ เฒญಾเฒ—เฒตเฒนಿเฒธುเฒต เฒงಾเฒคುเฒ—เฒณ เฒฐಾเฒถಿ เฒธಂเฒฐเฒ•್เฒšೆเฒฃೆเฒฏ เฒจಿเฒฏเฒฎเฒตเฒจ್เฒจು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒจು. เฒˆเฒคเฒจเฒจ್เฒจು เฒฐเฒธಾเฒฏเฒจ เฒถಾเฒธ್เฒค್เฒฐเฒฆ เฒชಿเฒคಾเฒฎเฒน เฒŽಂเฒฆು เฒชเฒฐಿเฒ—เฒฃಿเฒธเฒฒಾเฒ—ುเฒค್เฒคเฒฆೆ.

เณงเณญเณฏเณชเฒฐ เฒซ್เฒฐೆಂเฒš್ เฒ•್เฒฐಾಂเฒคಿเฒฏเฒฒ್เฒฒಿ เฒตಿเฒœ್เฒžಾเฒจಿ เฒฒಾเฒตೊเฒธಿเฒฐเฒจು เฒ•ೊเฒฒೆเฒฏಾเฒฆเฒจು. 

เณงเณญเณฎเณฏ เฒฐเฒฒ್เฒฒಿ  เฒช್เฒฐೌเฒธ್เฒŸ್  เฒŽเฒจ್เฒจುเฒต  เฒตಿเฒœ್เฒžಾเฒจಿเฒฏು  เฒŽเฒฐเฒกು เฒงಾเฒคುเฒ—เฒณು เฒฐಾเฒธಾเฒฏเฒจಿเฒ•เฒตಾเฒ—ಿ เฒธಂเฒฏೋเฒ— เฒนೊಂเฒฆುเฒตಾเฒ— เฒ…เฒตು เฒ’ಂเฒฆು เฒจಿเฒฐ್เฒฆಿเฒท್เฒŸ เฒฐಾเฒถಿเฒฏ เฒ…เฒจುเฒชಾเฒคเฒฆเฒฒ್เฒฒಿ เฒธೇเฒฐಿเฒ•ೊเฒณ್เฒณುเฒค್เฒคเฒตೆ  เฒŽಂเฒฆು เฒจಿเฒฐೂเฒชಿเฒธಿเฒฆเฒฐು.

เณงเณฎเณฆเณฆเฒฐเฒฒ್เฒฒಿ เฒจೀเฒฐಿเฒจเฒฒ್เฒฒಿ เฒตಿเฒฆ್เฒฏುเฒค್ เฒช್เฒฐเฒตಾเฒน เฒนเฒฐಿเฒธಿ , เฒจೀเฒฐเฒจ್เฒจು เฒตಿเฒญเฒœಿเฒธಿ เฒ†เฒฎ್เฒฒเฒœเฒจเฒ• เฒฎเฒค್เฒคು เฒœเฒฒเฒœเฒจเฒ• เฒ…เฒจಿเฒฒเฒ—เฒณಾเฒ—ಿ เฒตಿಂเฒ—เฒกಿเฒธಿเฒฆเฒฐು . เฒ†เฒฆ್เฒฆเฒฐಿಂเฒฆ เฒจೀเฒฐು เฒฎೂเฒฒเฒตเฒธ್เฒคು เฒ…เฒฒ್เฒฒ เฒฌเฒฆเฒฒಿเฒ—ೆ เฒ‡เฒฆೊಂเฒฆು เฒธಂเฒฏುเฒ•್เฒค เฒตเฒธ್เฒคು เฒŽಂเฒฆು เฒ–เฒšಿเฒคเฒตಾเฒฏಿเฒคು .

เฒˆ เฒช್เฒฐเฒฏೋเฒ—เฒฆเฒฒ್เฒฒಿ เฒนೊเฒฐเฒธೂเฒธಿเฒฆ เฒœเฒฒเฒœเฒจเฒ• เฒฎเฒค್เฒคು เฒ†เฒฎ್เฒฒเฒœเฒจเฒ• เฒ…เฒจಿเฒฒเฒ—เฒณ เฒ—ಾเฒค್เฒฐเฒฆ เฒ…เฒจುเฒชಾเฒค เณจ:เณง เฒ‡เฒฐುเฒค್เฒคเฒฆೆ. เฒ…ಂเฒฆเฒฐೆ เฒŽเฒฐเฒกು เฒตಿเฒญಿเฒจ್เฒจ เฒ…เฒจಿเฒฒเฒ—เฒณು เฒ’ಂเฒฆು เฒจಿเฒฐ್เฒฆಿเฒท್เฒŸ เฒ—ಾเฒค್เฒฐเฒฆ เฒ…เฒจುเฒชಾเฒคเฒฆเฒฒ್เฒฒಿ เฒธೇเฒฐಿ เฒธಂเฒฏುเฒ•್เฒค เฒตเฒธ್เฒคು เฒฐೂเฒชเฒ—ೊเฒณ್เฒณುเฒค್เฒคเฒฆೆ เฒŽಂเฒฆು เฒธಿเฒฆ್เฒฆเฒตಾเฒฏಿเฒคು. เฒ‡เฒฆเฒจ್เฒจು เฒ—ೆ เฒฒುเฒธಾเฒ•ಾเฒฐ เฒจಿเฒฏเฒฎ เฒŽเฒจ್เฒจುเฒตเฒฐು.

เฒจೀเฒฐು เฒตಿเฒญเฒœಿเฒธುเฒต เฒฐಾเฒธಾเฒฏเฒจಿเฒ• เฒ•್เฒฐಿเฒฏೆเฒ—ೆ เฒนೊเฒฐเฒ—ಿเฒจಿಂเฒฆ เฒถเฒ•್เฒคಿ เฒ’เฒฆเฒ—ಿเฒธเฒฌೇเฒ•ಾเฒฏಿเฒคು. เฒ‡เฒฆเฒ•್เฒ•ೆ เฒตಿเฒฐುเฒฆ್เฒงเฒตಾเฒ—ಿ เฒœเฒฒเฒœเฒจเฒ• เฒฎเฒค್เฒคು เฒ†เฒฎ್เฒฒเฒœเฒจเฒ• เฒ…เฒจಿเฒฒเฒ—เฒณು เฒฐಾเฒธಾเฒฏเฒจಿเฒ•เฒตಾเฒ—ಿ เฒธೇเฒฐಿ, เฒจೀเฒฐು เฒ‰ಂเฒŸಾเฒ—ುเฒต เฒฌเฒฆเฒฒಾเฒตเฒฃೆเฒฏเฒฒ್เฒฒಿ เฒถเฒ•್เฒคಿ เฒนೊเฒฐเฒ—ೆ เฒนಾเฒ•เฒฒಾเฒ—ುเฒค್เฒคเฒฆೆ. เฒนೀเฒ—ೆ เฒถเฒ•್เฒคಿเฒฏเฒจ್เฒจು เฒชเฒกೆเฒฆುเฒ•ೊเฒณ್เฒณುเฒต เฒ…เฒฅเฒตಾ เฒถเฒ•್เฒคಿเฒฏเฒจ್เฒจು เฒนೊเฒฐเฒšೆเฒฒ್เฒฒುเฒต, เฒŽเฒฐเฒกು เฒช್เฒฐเฒ•ಾเฒฐเฒฆ เฒฐಾเฒธಾเฒฏเฒจಿเฒ• เฒ•್เฒฐಿเฒฏೆเฒ—เฒณಿเฒฐುเฒค್เฒคเฒตೆ.

เณงเณฎเณฆเณฉเฒฐเฒฒ್เฒฒಿ เฒกಾเฒฒ್เฒŸเฒจ್ เฒŽเฒจ್เฒจುเฒต เฒตಿเฒœ್เฒžಾเฒจಿ เฒงಾเฒคುเฒตಿเฒจ เฒชเฒฐเฒฎಾเฒฃು เฒธಿเฒงಾಂเฒคเฒตเฒจ್เฒจು เฒฎಂเฒกಿเฒธಿเฒฆเฒจು. เฒงಾเฒคುเฒ—เฒณು เฒชเฒฐเฒฎಾเฒฃುเฒ—เฒณೆಂเฒฌ เฒ’เฒกೆเฒฏเฒฒಾเฒ—เฒฆ เฒ…เฒคಿเฒธเฒฃ್เฒฃ เฒ•เฒฃเฒ—เฒณಿಂเฒฆ เฒ†เฒ—ಿเฒตೆ เฒŽಂเฒฆು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒจು . เฒตಿเฒตಿเฒง เฒงಾเฒคುเฒ—เฒณ เฒชเฒฐเฒฎಾเฒฃುเฒ—เฒณು เฒญಿเฒจ್เฒจ เฒญಿเฒจ್เฒจ เฒฐಾเฒถಿเฒฏเฒจ್เฒจು เฒนೊಂเฒฆಿเฒฐುเฒตುเฒฆಾเฒ—ಿ เฒคಿเฒณಿเฒธಿเฒฆเฒจು . เฒˆเฒคเฒจು เฒฎೊเฒฆเฒฒเฒฌಾเฒฐಿเฒ—ೆ เฒงಾเฒคುเฒ—เฒณ เฒธಾเฒชೇเฒ•್เฒท เฒชเฒฐเฒฎಾเฒฃು เฒฐಾเฒถಿเฒ—เฒณ เฒชเฒŸ್เฒŸಿ เฒฎಾเฒกಿเฒฆเฒจು .

เณงเณฎเณงเณงเฒฐเฒฒ್เฒฒಿ เฒ…เฒตเฒ—ಾเฒก್เฒฐೋ เฒŽเฒจ್เฒจುเฒต เฒตಿเฒœ್เฒžಾเฒจಿ เฒ…เฒจಿเฒฒเฒ—เฒณ เฒ…เฒฃು เฒฐೂเฒชเฒฆ เฒ•เฒฃเฒ—เฒณ เฒฎೇเฒฒೆ เฒช್เฒฐเฒฏೋเฒ—เฒ—เฒณเฒจ್เฒจು เฒฎಾเฒกಿ; เฒธเฒฎಾเฒจ เฒ—ಾเฒค್เฒฐเฒฆ เฒฏಾเฒตುเฒฆೇ เฒ…เฒจಿเฒฒเฒ—เฒณು เฒธเฒฎಾเฒจ เฒช್เฒฐเฒฎಾเฒฃเฒฆ เฒ•เฒฃเฒ—เฒณು เฒนೊಂเฒฆಿเฒฐುเฒค್เฒคเฒตೆಂเฒฆು เฒช್เฒฐเฒคಿเฒชಾเฒฆಿเฒธಿเฒฆเฒจು.

เฒธเฒฎಾเฒจ เฒ—ಾเฒค್เฒฐเฒฆ เฒœเฒฒเฒœเฒจเฒ• เฒนಾเฒ—ು เฒ…เฒฎ್เฒฒเฒœเฒจเฒ• เฒ…เฒจಿเฒฒเฒ—เฒณ เฒฐಾเฒถಿเฒฏು เณง:เณงเณฌ  เฒ…เฒจುเฒชಾเฒคเฒฆเฒฒ್เฒฒಿ เฒ‡เฒฐುเฒค್เฒคเฒฆೆ. เฒœเฒฒเฒœเฒจเฒ•เฒฆ เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒธಾเฒชೇเฒ•್เฒทೆเฒฐಾเฒถಿ เณง เฒ†เฒฆเฒฐೆ เฒ†เฒฎ್เฒฒเฒœเฒจเฒ•เฒฆ್เฒฆು เณงเณฌ เฒ†เฒ—ುเฒค್เฒคเฒฆೆ. เฒจೀเฒฐಿเฒจ เฒ…เฒฃು เฒฐಾเฒถಿ เณงเณฎ เฒ‡เฒฐುเฒค್เฒคเฒฆೆ.  เณงเณฎ เฒ—್เฒฐಾಂ เฒจೀเฒฐเฒจ್เฒจು เฒ’ಂเฒฆು เฒฎೋเฒฒ್ เฒจೀเฒฐು เฒŽเฒจ್เฒจುเฒตเฒฐು. เฒ’ಂเฒฆು เฒฎೋเฒฒ್ เฒจೀเฒฐಿเฒจเฒฒ್เฒฒಿ เณฌ.เณฆเณจเณจ x เณงเณฆเฒฐ เฒ˜ಾเฒค เณจเณฉ เฒจೀเฒฐಿเฒจ เฒ•เฒฃเฒ—เฒณಿเฒตೆ. เฒ‡เฒฆเฒจ್เฒจು เฒ…เฒตเฒ—ಾเฒก್เฒฐೋ เฒธಂเฒ–್เฒฏೆ เฒŽಂเฒฆು เฒธೂเฒšಿเฒธುเฒตเฒฐು. 

เณงเณฎเณงเณจเฒฐเฒฒ್เฒฒಿ เฒนಂเฒซ್เฒฐಿ เฒกೇเฒตಿ เฒŽเฒจ್เฒจುเฒต เฒตಿเฒœ್เฒžಾเฒจಿเฒฏು เฒฒเฒตเฒฃเฒ—เฒณ เฒฎೇเฒฒೆ เฒช್เฒฐเฒฌเฒฒเฒตಾเฒฆ เฒตಿเฒฆ್เฒฏುเฒค್ เฒนเฒฐಿเฒธಿ, เฒฐಾเฒธಾเฒฏเฒจಿเฒ• เฒฌเฒฆเฒฒಾเฒตเฒฃೆ เฒ‰ಂเฒŸುเฒฎಾเฒกಿ, เฒนೊเฒธ เฒงಾเฒคುเฒ—เฒณ เฒถೋเฒง เฒฎಾเฒกಿเฒฆเฒจು. เฒˆเฒคเฒจು เฒชೊเฒŸ್เฒฏಾเฒธಿเฒฏಂ เฒธೋเฒกಿเฒฏಂ, เฒ•್เฒฏಾเฒฒ್เฒธಿเฒฏಂ เฒฎ್เฒฏಾเฒ—್เฒจೇเฒธಿเฒฏಂ เฒฌೇเฒฐಿเฒฏಂ เฒฎเฒค್เฒคು เฒธ್เฒŸ್เฒฐಾเฒจเฒŸಿเฒฏಂ เฒงಾเฒคುเฒ—เฒณเฒจ್เฒจು เฒ•ಂเฒกುเฒนಿเฒกಿเฒฆเฒจು. เฒ…เฒฒ್เฒฒเฒฆೆ เฒ•್เฒฒೋเฒฐಿเฒจ್ เฒ…เฒจಿเฒฒเฒตೂ เฒ•ೂเฒกಾ เฒ’ಂเฒฆು เฒงಾเฒคು เฒŽಂเฒฆು เฒธಿเฒฆ್เฒงเฒฎಾเฒกಿเฒฆ.

เณงเณฎเณจเณฌ เฒฐเฒฒ್เฒฒಿ เฒกಾเฒฒ್เฒŸเฒจ್เฒจ เฒถಿเฒท್เฒฏเฒจಾเฒฆ เฒฌเฒฐ್เฒœೆเฒฒಿเฒฏเฒธเฒจೂ, เฒงಾเฒคುเฒ—เฒณเฒจ್เฒจು เฒนೆเฒธเฒฐಿเฒธಿเฒฆ  เฒฎเฒค್เฒคು เฒ…เฒตುเฒ—เฒณ เฒนೆเฒธเฒฐಿเฒจ เฒฎೂเฒฒಾเฒ•್เฒทเฒฐเฒฆಿಂเฒฆ เฒงಾเฒคುเฒ—เฒณเฒจ್เฒจು เฒธಾಂเฒ•ೇเฒคಿเฒ•เฒตಾเฒ—ಿ เฒฌเฒฐೆเฒฏುเฒต เฒ•เฒฒೆ เฒฐೂเฒขಿเฒธಿเฒฆเฒจು . เฒ‡เฒฆเฒฐಿಂเฒฆ เฒธಂเฒฏುเฒ•್เฒค เฒตเฒธ್เฒคುเฒ—เฒณเฒจ್เฒจು เฒธಾಂเฒ•ೇเฒคಿเฒ•เฒตಾเฒ—ಿ เฒ…เฒฃು เฒธೂเฒค್เฒฐเฒฆ เฒฐೂเฒชเฒฆเฒฒ್เฒฒಿ เฒฌเฒฐೆเฒฏเฒฒು เฒ…เฒจುเฒ•ೂเฒฒเฒตಾเฒฏಿเฒคು.

เณงเณฎเณจเณฎเฒฐเฒฒ್เฒฒಿ เฒตೋเฒน್เฒฒเฒฐเฒจು  เฒฎೊเฒฆเฒฒเฒฌಾเฒฐಿเฒ—ೆ เฒจಿเฒฐเฒฏเฒต เฒฐಾเฒธಾเฒฏเฒจเฒ—เฒณเฒจ್เฒจು เฒฌเฒณเฒธಿ, เฒœೀเฒตಿเฒ—เฒณเฒฒ್เฒฒಿ เฒ•ಂเฒกುเฒฌเฒฐುเฒต เฒฏೂเฒฐಿเฒฏಾ เฒŽเฒจ್เฒจುเฒต เฒธಾเฒตเฒฏเฒต เฒชเฒฆಾเฒฐ್เฒฅเฒตเฒจ್เฒจು เฒคเฒฏ್เฒฏಾเฒฐಿเฒธಿเฒฆเฒจು.

เณงเณฎเณฉเณฆเฒฐ เฒตเฒฐೆเฒ—ೆ เฒ•ಂเฒกುเฒนಿเฒกಿเฒฆ เฒงಾเฒคುเฒ—เฒณ เฒธಂเฒ–್เฒฏೆ เณซเณชเฒ•್เฒ•ೆ เฒเฒฐಿเฒคು.

เณงเณฎเณฉเณชเฒฐเฒฒ್เฒฒಿ เฒฎೈเฒ•เฒฒ್ เฒซ್เฒฏಾเฒฐเฒกೆเฒฏเฒตเฒฐ เฒจಿเฒฐೂเฒชเฒฃೆ ; "เฒ…เฒฏಾเฒจಿเฒ•್ เฒฆ್เฒฐಾเฒตเฒฃเฒ—เฒณเฒฒ್เฒฒಿ เฒตಿเฒฆ್เฒฏುเฒค್ เฒนเฒฐಿเฒธಿเฒฆಾเฒ— เฒ‰ಂเฒŸಾเฒ—ುเฒต เฒฐಾเฒธಾเฒฏเฒจಿเฒ• เฒฌเฒฆเฒฒಾเฒตเฒฃೆเฒฏು, เฒฆ್เฒฐಾเฒตเฒฃเฒฆเฒฒ್เฒฒಿ เฒนเฒฐಿเฒธಿเฒฆ เฒ’เฒŸ್เฒŸು เฒตಿเฒฆ್เฒฏುเฒค್เฒคಿเฒจ เฒฎೊเฒค್เฒคเฒ•್เฒ•ೆ เฒ…เฒจುเฒฐೂเฒชเฒตಾเฒ—ಿ เฒ‡เฒฐುเฒค್เฒคเฒฆೆ."

เณงเณฎเณชเณงเฒฐเฒฒ್เฒฒಿ เฒฒಂเฒกเฒจ್ เฒชเฒŸ್เฒŸเฒฃเฒฆเฒฒ್เฒฒಿ เฒฐಾเฒธಾเฒฏเฒจ  เฒถಾเฒธ್เฒค್เฒฐเฒฆ เฒธಂเฒ˜  เฒธ್เฒฅಾเฒชเฒจೆเฒ—ೊಂเฒกಿเฒคು. 

เณงเณฎเณซเณจเฒฐเฒฒ್เฒฒಿ เฒฐಾเฒธಾเฒฏเฒจಿเฒ• เฒธಂเฒฏೋเฒ— เฒธಾเฒฎเฒฐ್เฒค್เฒฏเฒฏ เฒจಿเฒฐೂเฒชเฒฃೆเฒฏಾเฒฏಿเฒคು.

เณงเณฎเณซเณฏเฒฐเฒฒ್เฒฒಿ เฒฌเฒจ್เฒธೆเฒจ್ เฒฐೂ, เฒช್เฒฐเฒคಿเฒฏೊಂเฒฆು เฒงಾเฒคುเฒตು เฒคเฒจ್เฒจเฒฆೇ เฒ†เฒฆ,  เฒตಿเฒถಿเฒท್เฒŸ เฒฌೆเฒณเฒ•ಿเฒจ เฒตเฒฐ್เฒฃเฒชเฒŸเฒฒเฒตเฒจ್เฒจು เฒ‰ಂเฒŸುเฒฎಾเฒกುเฒค್เฒคเฒฆೆ เฒŽಂเฒฆು เฒ•ಂเฒกುเฒนಿเฒกಿเฒฆเฒฐು. เฒˆ เฒตಿเฒงಾเฒจเฒตು เฒนೊเฒธ เฒงಾเฒคುเฒ—เฒณเฒจ್เฒจು เฒ•ಾเฒกುเฒนಿเฒกಿเฒฏเฒฒು เฒ…เฒจುเฒ•ೂเฒฒเฒตಾเฒฏಿเฒคು. 

เณงเณฎเณฌเณฆเฒฐเฒฒ್เฒฒಿ เฒตಿเฒœ್เฒžಾเฒจಿ เฒ•ೆเฒ•ೂเฒฒೆเฒฏเฒตเฒฐ เฒจೇเฒค್เฒฐಿเฒค್เฒตเฒฆเฒฒ್เฒฒಿ , เฒœเฒฐ್เฒฎเฒจಿ เฒฆೇเฒถเฒฆเฒฒ್เฒฒಿ เฒฎೊเฒฆเฒฒเฒฌಾเฒฐಿเฒ—ೆ เฒœಾเฒ—เฒคಿเฒ• เฒฐเฒธಾเฒฏเฒจ เฒถಾเฒธ್เฒค್เฒฐเฒฆ เฒธเฒฎ್เฒฎೇเฒณเฒจ เฒเฒฐ್เฒชเฒŸ್เฒŸಿเฒค್เฒคು. เฒ‡เฒฆเฒฐเฒฒ್เฒฒಿ เณงเณชเณฆ เฒœเฒจ เฒตಿเฒœ್เฒžಾเฒจಿเฒ—เฒณು เฒชಾเฒฒ್เฒ—ೊಂเฒกเฒฐು.

เณงเณฎเณฌเณฏเฒฐเฒฒ್เฒฒಿ เฒธೈเฒฌೀเฒฐಿเฒฏಾเฒฆ เฒตಿเฒœ್เฒžಾเฒจಿ เฒฎೆಂเฒกೆเฒฒಿเฒตเฒฐು เฒงಾเฒคುเฒ—เฒณ เฒ†เฒตเฒฐ್เฒคเฒ• เฒ•ೋเฒท್เฒŸเฒ•เฒตเฒจ್เฒจು เฒช್เฒฐเฒ•เฒŸಿเฒธಿเฒฆเฒฐು. เฒ…เฒตเฒฐು เฒ…เฒฒ್เฒฒಿเฒฏเฒตเฒฐೆเฒ—ೆ เฒคಿเฒณಿเฒฆಿเฒฐುเฒต เณฌเณฌ เฒงಾเฒคುเฒ—เฒณเฒจ್เฒจು เฒ•ೋเฒท್เฒŸเฒ•เฒฆเฒฒ್เฒฒಿ เฒ…เฒก್เฒกเฒธಾเฒฒು เฒนಾเฒ—ು เฒ•ಂเฒฌเฒธಾเฒฒುเฒ—เฒณಾเฒ—ಿ เฒตเฒฐ್เฒ—ಿเฒ•เฒฐಿเฒธಿเฒฆเฒฐು. เฒงಾเฒคುเฒ—เฒณเฒจ್เฒจು เฒ…เฒตುเฒ—เฒณ เฒชเฒฐเฒฎಾเฒฃು เฒฐಾเฒถಿเฒฏ เฒเฒฐಿเฒ•ೆเฒฏ เฒ•್เฒฐเฒฎเฒฆเฒฒ್เฒฒಿ เฒฌเฒฐೆเฒฆเฒฐು. 

เณงเณฎเณฎเณญเฒฐเฒฒ್เฒฒಿ เฒ†เฒฎ್เฒฒ, เฒช್เฒฐเฒค್เฒฏಾเฒฎ್เฒฒ, เฒฎเฒค್เฒคು เฒฒเฒตเฒฃเฒ—เฒณು เฒจೀเฒฐಿเฒจเฒฒ್เฒฒಿ เฒ•เฒฐเฒ—ಿ เฒ…เฒฏಾเฒจ್เฒ—เฒณಾเฒ—ಿ เฒฌೇเฒฐ್เฒชเฒกುเฒค್เฒคเฒตೆ เฒŽಂเฒฆು เฒ•ಂเฒกುเฒ•ೊಂเฒกเฒฐು.

เณงเณฎเณฏเณฎเฒฐเฒฒ್เฒฒಿ เฒตಿเฒฒಿเฒฏಂ เฒฐಾเฒฎเฒธೇ  เฒŽเฒจ್เฒจುเฒต เฒตಿเฒœ್เฒžಾเฒจಿ, เฒœเฒก เฒ…เฒจಿเฒฒเฒ—เฒณเฒจ್เฒจು เฒ•ಂเฒกುเฒนಿเฒกಿเฒฆเฒฐು.

เณงเณฏเณฆเณฆเฒฐ เฒนೊเฒค್เฒคಿเฒ—ೆ เฒงಾเฒคುเฒ—เฒณ เฒธಂเฒ–್เฒฏೆ เณฎเณฎเฒ•್เฒ•ೆ เฒคเฒฒುเฒชಿเฒคು.

เณงเณฎเณฏเณญเฒฐเฒฒ್เฒฒಿ เฒœೆ เฒœೆ เฒฅಾเฒฎ್เฒธเฒจ್เฒจเฒฐು เฒ•್เฒฏಾเฒฅೋเฒก್ เฒ•ಿเฒฐเฒฃเฒ—เฒณ เฒช್เฒฐเฒฏೋเฒ— เฒฎಾเฒกಿ, เฒŽเฒฒ್เฒฒಾเฒงಾเฒคುเฒ—เฒณ เฒชเฒฐเฒฎಾเฒฃುเฒ—เฒณು  เฒŽเฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจ್ เฒ—เฒณೆಂเฒฌ เฒ‰เฒชเฒ•เฒฃเฒ—เฒณು เฒนೊಂเฒฆಿเฒตೆ เฒŽಂเฒฆು เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒฐು. เฒŽเฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจ್ เฒ—เฒณು เฒ‹เฒฃ เฒตಿเฒฆ್เฒฏುเฒค್ เฒ†เฒตೇเฒถ เฒนೊಂเฒฆಿเฒฐುเฒค್เฒคเฒตೆ.

เณงเณฏเณงเณงเฒฐ เฒนೊเฒค್เฒคಿเฒ—ೆ เฒชเฒฐเฒฎಾเฒฃುเฒตೂ เฒ‹เฒฃ เฒตಿเฒฆ್เฒฏುเฒค್ เฒ†เฒตೇเฒถเฒฏುเฒณ್เฒณ เฒŽเฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจ್ เฒฎเฒค್เฒคು เฒงเฒจ เฒ†เฒตೇเฒถเฒฏುเฒณ್เฒณ เฒฌೀเฒœเฒ•ೇಂเฒฆ್เฒฐ เฒนೊಂเฒฆಿเฒฆೆ เฒŽಂเฒฆು เฒฐเฒฆเฒฐเฒซೋเฒฐ್เฒกเฒฐ เฒช್เฒฐเฒฏೋเฒ—เฒ—เฒณಿಂเฒฆ เฒ–เฒšಿเฒคเฒตಾเฒฏಿเฒคು. เฒฎೂเฒฒเฒคಃ เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒฐಾเฒถಿเฒฏು เฒฌೀเฒœเฒ•ೇಂเฒฆ್เฒฐเฒฆ್เฒฆೇ เฒ†เฒ—ಿเฒฆೆ. เฒŽเฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจಿเฒจ เฒฐಾเฒถಿเฒฏು เฒจเฒ—เฒฃ್เฒฏ .

เณงเณฏเณงเณฉเฒฐเฒฒ್เฒฒಿ เฒกೆเฒจ್เฒฎಾเฒฐ್เฒ•ಿเฒจ เฒตಿเฒœ್เฒžಾเฒจಿ เฒจೀเฒฒ್เฒธ เฒฌೊเฒนเฒฐเฒฐು, เฒนೈเฒก್เฒฐೋเฒœเฒจ್ เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒฐเฒšเฒจಾ เฒธಿเฒงಾಂเฒคเฒตเฒจ್เฒจು เฒŽเฒธೆเฒธ್เฒตಿเฒฏಾเฒ—ಿ เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒฐು. เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒฌೀเฒœเฒ•ೇಂเฒฆ್เฒฐเฒฆ เฒธುเฒค್เฒค เฒŽเฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจ್ เฒจಿเฒฐ್เฒงಾเฒฐಿเฒค เฒถเฒ•್เฒคಿ เฒ•เฒตเฒšเฒฆเฒฒ್เฒฒಿ เฒฎಾเฒค್เฒฐ เฒธುเฒค್เฒคುเฒค್เฒคಿเฒฐುเฒค್เฒคเฒฆೆ. เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒนೆเฒš್เฒšಿเฒจ เฒ—ಾเฒค್เฒฐ เฒŽเฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจುเฒ—เฒณೇ เฒ†เฒ•್เฒฐเฒฎಿเฒธಿเฒ•ೊಂเฒกಿเฒฐುเฒค್เฒคเฒตೆ.

เณงเณฏเณงเณชเฒฐเฒฒ್เฒฒಿ เฒ†ಂเฒ—್เฒฒ เฒตಿเฒœ್เฒžಾเฒจಿ เฒนೆเฒจ್เฒฐಿ เฒฎೊเฒธೆเฒฒಿเฒฏเฒตเฒฐಿಂเฒฆ เฒชเฒฐเฒฎಾเฒฃು เฒธಂเฒ–್เฒฏೆเฒฏ เฒต್เฒฏಾเฒ–್เฒฏಾเฒจ เฒจೀเฒกเฒฒಾเฒฏಿเฒคು. เฒชเฒฐเฒฎಾเฒฃು เฒธಂเฒ–್เฒฏೆเฒฏು เฒชเฒฐเฒฎಾเฒฃು เฒฌೀเฒœ เฒนೊಂเฒฆಿเฒฐುเฒต เฒ’เฒŸ್เฒŸು เฒช್เฒฐೋเฒŸಾเฒจ್ เฒ—เฒณ  เฒธಂเฒ–್เฒฏೆเฒ—ೆ เฒธเฒฎ เฒ‡เฒฐುเฒค್เฒคเฒฆೆ. เฒ‡เฒฆಾเฒฆเฒจಂเฒคเฒฐ เฒงಾเฒคುเฒ—เฒณ เฒ†เฒตเฒฐ್เฒคเฒ• เฒ•ೋเฒท್เฒŸเฒ•เฒตเฒจ್เฒจು เฒงಾเฒคುเฒ—เฒณ เฒชเฒฐเฒฎಾเฒฃು เฒธಂเฒ–್เฒฏೆ เฒฌเฒณเฒธಿ เฒ•ೋเฒท್เฒ เฒ•เฒฆ เฒจ್เฒฏೂเฒจเฒคೆเฒ—เฒณเฒจ್เฒจು เฒคಿเฒฆ್เฒฆเฒฒಾเฒฏಿเฒคು. เฒ†เฒงುเฒจಿเฒ• เฒ†เฒตเฒฐ್เฒคเฒ• เฒ•ೋเฒท್เฒŸเฒ•เฒฆเฒฒ್เฒฒಿ เณงเณฎ เฒ•ಂเฒญ เฒธಾเฒฒುเฒ—เฒณಿเฒตೆ.

เณงเณฏเณงเณฌเฒฐเฒฒ್เฒฒಿ เฒœ್เฒฏೂเฒฒಿเฒฏเฒธเฒฐಿಂเฒฆ, เฒ…เฒฏಾเฒจಿเฒ•್ เฒธಂเฒฏುเฒ•್เฒคเฒ—เฒณ เฒฐเฒšเฒจೆเฒฏเฒฒ್เฒฒಿ, เฒชเฒฐเฒฎಾเฒฃುเฒ—เฒณ  เฒ…เฒท್เฒŸเฒ• เฒจಿเฒฏเฒฎ เฒจಿเฒฐೂเฒชเฒฃೆ.

เณงเณฏเณงเณฌเฒฐเฒฒ್เฒฒಿ เฒ…เฒฎೆเฒฐಿเฒ•ೆเฒฏ เฒตಿเฒœ್เฒžಾเฒจಿ เฒœಿ. เฒŽเฒจ್. เฒฒೆเฒตಿเฒธเฒฐು, เฒฐಾเฒธಾเฒฏเฒจಿเฒ• เฒธเฒนเฒตೇเฒฒೆเฒจ್เฒธಿ เฒฌಂเฒงเฒฆ เฒจಿเฒฐೂเฒชเฒฃೆ เฒ•ೊเฒŸ್เฒŸเฒฐು. เฒฒೆเฒตಿเฒธเฒฐು เฒธเฒนเฒตಾเฒฒೆเฒจ್เฒธಿ เฒฌಂเฒง เฒฌเฒณเฒธಿ, เฒธಂเฒฏುเฒ•್เฒค เฒ•เฒฃเฒ—เฒณ เฒ…เฒฃುเฒฐเฒšเฒจೆเฒฏเฒจ್เฒจು เฒŽเฒธೆเฒธ್เฒตಿเฒฏಾเฒ—ಿ เฒตಿเฒตเฒฐಿเฒธಿเฒฆเฒฐು. 

เฒ…เฒตเฒฐು, เณงเณฏเณจเณฉเฒฐเฒฒ್เฒฒಿ เฒฒೆเฒตಿเฒธ್ เฒ†เฒฎ್เฒฒ เฒฎเฒค್เฒคು เฒช್เฒฐเฒค್เฒฏಾเฒฎ್เฒฒเฒ—เฒณ เฒชเฒฐಿเฒ•เฒฒ್เฒชเฒจೆ เฒ•ೊเฒŸ್เฒŸเฒฐು. เฒฐಾเฒธಾเฒฏเฒจಿเฒ• เฒฌเฒฆเฒฒಾเฒตเฒฃೆเฒฏเฒฒ್เฒฒಿ, เฒฒೆเฒตಿเฒธ್ เฒ†เฒฎ್เฒฒเฒ—เฒณು, เฒ‡เฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจ್ เฒœೋเฒกಿเฒฏเฒจ್เฒจು [เฒช್เฒฐเฒค್เฒฏಾเฒฎ್เฒฒเฒ—เฒณಿಂเฒฆ] เฒธ್เฒตೀเฒ•เฒฐಿเฒธುเฒค್เฒคเฒตೆ.

เณงเณฏเณงเณฏเฒฐเฒฒ್เฒฒಿ เฒฐเฒฆเฒฐ್เฒซೋเฒฐ್เฒกเฒฐು, เฒชเฒฐเฒฎಾเฒฃು เฒฌೀเฒœเฒ•ೇಂเฒฆ್เฒฐเฒฆเฒฒ್เฒฒಿเฒฐುเฒต  เฒงเฒจಾเฒตೇเฒถเฒฏುเฒณ್เฒณ เฒช್เฒฐೋเฒŸಾเฒจ್ เฒ•เฒฃเฒตเฒจ್เฒจು เฒ•ಂเฒกುเฒนಿเฒกಿเฒฆเฒฐು.

เณงเณฏเณจเณชเฒฐเฒฒ್เฒฒಿ เฒฌ್เฒฐೊเฒ—್เฒฒೆเฒฏเฒตเฒฐಿಂเฒฆ เฒŽเฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจಿเฒจ เฒฐเฒšเฒจಾ เฒฐೂเฒช, เฒ…เฒฒೆ เฒนಾเฒ—ೂ เฒ•เฒฃ เฒŽเฒจ್เฒจುเฒต เฒฆ್เฒตಿเฒ—ುเฒฃ เฒช್เฒฐเฒ•ೃเฒคಿเฒฏ เฒจಿเฒฐೂเฒชเฒฃೆ.

เณงเณฏเณจเณฌเฒฐเฒฒ್เฒฒಿ เฒถ್เฒฐೋเฒกಿಂเฒ—เฒฐเฒฐಿಂเฒฆ เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒฐเฒšเฒจೆเฒฏ เฒถเฒ•เฒฒเฒธಿเฒงಾಂเฒคเฒฆ เฒจಿเฒฐೂเฒชเฒฃೆ.

เณงเณฏเณฉเณจเฒฐเฒฒ್เฒฒಿ เฒœೇเฒฎ್เฒธ್ เฒšಾเฒก್เฒตಿเฒ•್ เฒฐเฒตเฒฐು, เฒชเฒฐเฒฎಾเฒฃು เฒฌೀเฒœเฒ•ೇಂเฒฆ್เฒฐ เฒนೊಂเฒฆಿเฒฐುเฒต เฒจ್เฒฏೂเฒŸ್เฒฐಾเฒจ್ เฒŽเฒจ್เฒจುเฒต เฒ‰เฒชเฒ•เฒฃเฒตเฒจ್เฒจು เฒ•ಂเฒกುเฒนಿเฒกಿเฒฆเฒฐು. เฒˆ เฒ•เฒฃเฒ•್เฒ•ೆ เฒฏಾเฒตುเฒฆೇ เฒตಿเฒฆ್เฒฏುเฒค್ เฒ†เฒตೇเฒท เฒ‡เฒฒ್เฒฒ. เฒนೀเฒ—ೆ เฒ’ಂเฒฆು เฒชเฒฐเฒฎಾเฒฃುเฒตೂ เฒŽเฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจ್, เฒช್เฒฐೋเฒŸಾเฒจ್, เฒฎเฒค್เฒคು เฒจ್เฒฏೂเฒŸ್เฒฐಾเฒจ್ เฒŽเฒจ್เฒจುเฒต เฒธೂเฒ•್เฒท್เฒฎ เฒ•เฒฃเฒ—เฒณಿಂเฒฆ เฒ†เฒ—ಿเฒฆೆ. เฒช್เฒฐೋเฒŸಾเฒจ್ เฒ…เฒฅเฒตಾ เฒจ್เฒฏೂเฒŸ್เฒฐಾเฒจ್ เฒ•เฒฃเฒฆ เฒฐಾเฒถಿเฒ—ೆ เฒนೋเฒฒಿเฒธಿเฒฆเฒฐೆ เฒŽเฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจ್ เฒฐಾเฒถಿเฒฏು เฒจเฒ—เฒฃ್เฒฏ เฒŽเฒจಿเฒธುเฒค್เฒคเฒฆೆ. เฒ†เฒฆเฒฐೆ เฒŽเฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจ್ เฒฎเฒค್เฒคು เฒช್เฒฐೋเฒŸಾเฒจ್ เฒ—เฒณ เฒตಿเฒฆ್เฒฏುเฒค್ เฒ†เฒตೇเฒถเฒตು เฒธเฒฎ เฒ‡เฒฐುเฒค್เฒคเฒฆೆ.  เฒ’ಂเฒฆು เฒชเฒฐเฒฎಾเฒฃುเฒตಿเฒจ เฒŽเฒฒೆเฒ•್เฒŸ್เฒฐಾเฒจ್ เฒฎเฒค್เฒคು เฒช್เฒฐೋเฒŸಾเฒจ್ เฒ—เฒณ เฒธಂเฒ–್เฒฏೆ เฒธเฒฎಾเฒจเฒตಾเฒ—ಿเฒฐುเฒค್เฒคเฒฆೆ.

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.