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the sun rose 1 gh. later than at Poona the tithi would have ended when 7 gh. 11 pa. had elapsed since the sunrise at that place, or at about 8.52 a.m.

35. For this reason the expunction and repetition of tithis often differs in different localities. Thus the nakshatra Pûrvâshâḍhâ (see pañchâṅg extract Art. 30) was 58 gh. 11 pa.^[1] at Poona on Sunday, śukla 10th. At a place which is on the same parallel of latitude, but 12 degrees eastward, the sun rises 2 gh. earlier than at Poona, and there this nakshatra ended (58 gh. 11 pa. + 2 gh =) 60 gh. 11 pa. after sunrise on Sunday, that is at 11 pa. after sunrise on Monday. It therefore touches three natural days, and therefore it (Pûrvâshâḍhâ) is repeated, whereas at Poona it is Uttarâshâḍhâ which is repeated. On the other hand, the nakshatra Maghâ on Kṛishṇa 13th was 3 gh. 4 pa., and Pûrva-phalgunî was (3 gh. 4 pa. + 56 gh.^[2] 51 pa. =) 59 gh. 55 pa. at Poona. At a place which has the same latitude as Poona, but is situated even at so short a distance as 1 degree to the east, the nakshatra Pûrva-phalgunî ended 60 gh. 5 pa after sunrise on Thursday, that is 5 pa. after sunrise on Friday; and therefore there will be no kshaya of that nakshatra at that place, but the following nakshatra Uttara phalgunî will be expunged there.

36. True or apparent, and mean, time. The sun, or more strictly the earth in its orbit, travels, not in the plane of the equator, but in that of the ecliptic, and with a motion which varies every day; the length of the day, therefore, is not always the same even on the equator. But for calculating the motions of the heavenly bodies it is evidently convenient to have a day of uniform length, and for this reason astronomers, with a view of obtaining a convenient and uniform measure of time, have had recourse to a mean solar day, the length of which is equal to the mean or average of all the apparent solar days in the year. An imaginary sun, called the mean sun, is conceived to move uniformly in the equator with the mean angular velocity of the true sun. The days marked by this mean sun will all be equal, and the interval between two successive risings of the mean sun on the equator is the duration of the mean solar day, viz., 24 hours or 60 ghaṭikâs. The time shown by the true sun is called true or apparent time, and the time shown by the mean sun is known as mean time. Clocks and watches, whose hands move, at least in theory, with uniform velocity, evidently give us mean time. With European astronomers "mean noon" is the moment when the mean sun is on the meridian; and the "mean time" at any instant is the hour angle of the mean sun reckoned westward from 0 h. to 24 h., mean noon being 0 h. for astronomical purposes.

Indian astronomers count the day from sunrise, to sunrise, and give, at least in theory, the ending moments of tithis in time reckoned from actual or true sunrise. The true or apparent time of a place, therefore, in regard to the Indian pañchâṅg, is the time counted from true (i.e., actual) sunrise at that place. For several reasons it is convenient to take mean sunrise on the equator under any given meridian to be the mean sunrise at all places under the same meridian. The mean sunrise at any place is calculated as taking place at 0 gh. or 0 h.—roughly 6 a.m. in European civil reckoning; and the mean time of a place is the time counted from 0 gh. or 0 h.

The moment of true sunrise is of course not always the same at all places, but varies with the latitude and longitude. Even at the same place it varies with the declination of the sun, which