The point of intersection of the ecliptic of the given time with the meridian of the place is the tenth house for that moment. If A is the sidereal time expressed in degrees and B is the tenth house, then tenth house can be computed as, tan B = tan A Sec w , where w is the inclination of earth's equatorial plane to the ecliptic.
Ascendant : The ascendant is the point of intersection of the ecliptic with the eastern horizon of the place, if A is the sidereal time in degrees + 90° then tan B = tan A cos w ....(1)
From A & B, we can evaluate D the declination & q =90 - angle between meridian & ecliptic, as: sin D = sin A sin w ....(2)
sin q = sin w cos b ....(3)
From D & q, we compute the ascendant as :
tan E = sin D tan(j + q) ...(4)
where j is the latitude of the place. Ascendant = B + E ....(5)
The value of the ascendant as calculated above is the sayan value. Subtracting ayanamsa we get nirayana ascendant. The above formulae gives accurate values of ascendant. In absence of scientific calculators, the ascendant & the tenth house can be computed using tables of ascendant by N.C. Lahiri. However, calculation of ascendant using tables gives rise to errors because of tables not available for the given place or for the given sidereal time. This error some times goes up to many minutes of arc.
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