पृष्ठम्:लघुभास्करीयम्.djvu/१२०

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vs. 7-10, ] The ghatऽ clapsed since sumrise in the foremoon or to clapse before sunset in the aftermoon, being multiplied by 60 and again by 6, give the minutes of arc in the arc of the celestial'euator 1ying between the hour circles passing through the Sun at that time and through the Sun's positioth on the horizon t sumrise or sunset. When these asus are diminished or increased by the arsus of the Sun's ascensional difference (according as the.Sum is in the north ern or southern themisphere), the usus of the difference or sum give the minutes of arc in the arc : of the celestial cपृuator lying between the or sum multiplied by the day-radius and. divided by the radius gives the distance of the Sun from the line joining the points of intersection of the six o'clock circle and the Sun's diurrnal circle. This increased or diminished by the earthsine (according as . the Sun is in the northeri or southern hemis phere) gives the distance of the Sun from the Sun's rising - setting line (i.e., the line joining the points of the horizon where the Sun rises and sets) S3 In Fig.5 let S denote the position of the Sun on the celestial sphere, SA the perpendicular from S on the plane of the celestial horizon, and SB the perpendicular from S on the rising-setting line. Then in the plane triangle SAB, we have 47 ८ SBA=90० Rऽांn (given time in 05us - + asc. diff.) x day radius


+ earthsilue,

and Z८ SAB=90, where a is the Sun's altitude, and # the latitude of the place Therefore, we have Fig. 5 Als०since the Sun's 2ernith distance ८ is the complement of ८, therefore Rsin 2 = Rcos ८ = */फलकम्:R* - (Rsin ८)*