The Radius increased by the Sine of ascensional difference in the north, and diminished by it in the south, is the 'antya'. This, diminished by the Sine of the hour-angle, and multiplied by the radius of the diurnal circle and divided by the Radius, is the 'cheda' (divisor).
Modern Technical Commentary:
Calculates the Ascensional Difference (Cara). This is a critical correction in Indian astronomy that accounts for the difference between the local celestial horizon and the prime meridian (Lanka), determining the length of day and night for a given latitude.
Siddhantic Proof: Tri-prasna (Direction, Place and Time) v.34
The Radius increased by the Sine of ascensional difference in the north, and diminished by it in the south, is the 'antya'. This, diminished by the Sine of the hour-angle, and multiplied by the radius of the diurnal circle and divided by the Radius, is the 'cheda' (divisor).
Modern Technical Commentary:
Calculates the Ascensional Difference (Cara). This is a critical correction in Indian astronomy that accounts for the difference between the local celestial horizon and the prime meridian (Lanka), determining the length of day and night for a given latitude.
'Cara' is the time difference between the semi-diurnal
arc and a quadrant due to latitude. It is derived from 'Kujya'
(earth-correction) and 'Carajya'.
Calculate the Ascensional Difference (Cara).
[Ch. III, v.34-36]
Siddhantic Proof: Tri-prasna (Direction, Place and Time) v.34
Sanskrit (Devanagari):
त्रिज्योदक्चरजायुक्ता याम्यायां तद्विवर्जिता। अन्त्या नतोत्क्रमज्योना स्वाहोरात्रार्दसङ्गुणा।। त्रिज्या भक्ता भवेच्छेदो लम्बज्याघ्नोऽथ भाजितः।।
Translation (Burgess):
The Radius increased by the Sine of ascensional difference in the north, and diminished by it in the south, is the 'antya'. This, diminished by the Sine of the hour-angle, and multiplied by the radius of the diurnal circle and divided by the Radius, is the 'cheda' (divisor).
Modern Technical Commentary:
Calculates the Ascensional Difference (Cara). This is a critical correction in Indian astronomy that accounts for the difference between the local celestial horizon and the prime meridian (Lanka), determining the length of day and night for a given latitude.
Siddhantic Proof: Tri-prasna (Direction, Place and Time) v.34
Sanskrit (Devanagari):
त्रिज्योदक्चरजायुक्ता याम्यायां तद्विवर्जिता। अन्त्या नतोत्क्रमज्योना स्वाहोरात्रार्दसङ्गुणा।। त्रिज्या भक्ता भवेच्छेदो लम्बज्याघ्नोऽथ भाजितः।।
Translation (Burgess):
The Radius increased by the Sine of ascensional difference in the north, and diminished by it in the south, is the 'antya'. This, diminished by the Sine of the hour-angle, and multiplied by the radius of the diurnal circle and divided by the Radius, is the 'cheda' (divisor).
Modern Technical Commentary:
Calculates the Ascensional Difference (Cara). This is a critical correction in Indian astronomy that accounts for the difference between the local celestial horizon and the prime meridian (Lanka), determining the length of day and night for a given latitude.