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way. The work shows that there was no suppression of a lunar month during the period 1901 to 1950 A.D., and since (Indian Calendar, foot of p. 29) it had been already determined that in all probability there would not be a suppression till 1944, the discovery that there will be none in that year renders it practically certain that there will be none till A.D. 1963, viz., after 141 years have elapsed since the last suppression.
193. Owing to the diurnal revolution of the earth on its axis a meridian on the earth's surface passes once in every 24 hours completely round the circle of the 12 solar signs and 27 or 28 nakshatras (§ 113 &c.); and therefore, roughly, the meridian is within one of the solar signs for two hours every day. As the meridian sweeps round, the first point of each solar sign meets it, or cuts it, at about two-hour intervals during the day. This gives rise in Hindū astronomy to calculations made both as to what sign was the lagna at a particular moment of a day, and as to the exact time at which a particular sign or part of a sign became lagna. The word lagna means literally "intersecting," "meeting," "coming in contact," in astronomy the cutting of one line or great circle by another; and its most common astronomical use is to designate that point of the ecliptic which at a given time is on the eastern horizon. At other times it designates the point of the ecliptic at a given time on the meridian. The horizon lagna is called kshitijē lagna, the meridian lagna is called madhya lagna. Since the solar sign remains in contact with the horizon or the meridian for about two hours each day it is clear that if a date of an inscription, besides giving us the civil day, month and year, mentions that a certain sign was lagna, we learn to within about two hours the exact time of day when the action referred to in the inscription was performed. It is as if a European inscription should state, besides the date, that the time referred to was between 10 a.m. and noon."
194. Professor Kielhorn told us (Indian Antiquary, Vol. XXV. (1896), p. 291) that, up to the time of writing, the earliest inscription known to him, bearing a Śaka date and from a genuine Indian inscription, in which the lagna occurs is one of Ś. 867 expired, A.D. 945. It is an Eastern Chalukya inscription of December 5th, A.D. 945, recording the accession of King Amma II. (Ind. Ant., Vol. XXIII. (1894), p. 123, No. 62). Mention of the lagna has, however, been found earlier than this in Cambodia.
195. Now I do not propose to devote any great space to the consideration of the problem of the lagna, for two reasons. The first is that Professor Jacobi, in his paper entitled "How to calculate the lagna," in the Indian Antiquary for July, 1900 (pp. 189–90), has given us full and ample rules for solving the problem by use of his own Tables, and to attempt here to reproduce those rules would be merely to trespass wantonly on his ground. The second is that, although undoubtedly the superstitious Hindū paid at one time and another great attention to the point, the lagna is really not a matter which greatly concerns an historian. When we are perfectly certain of the accuracy of a civil day as given in any record, it is very seldom of any consequence to us to enter into particulars as to any given hour of that day.
196. It will, therefore, I think, be sufficient if I show how to obtain a first approximation to the correct result, leaving extreme accuracy to be arrived at by use of Jacobi's own method and Tables. This approximation, which, so far as I can judge, was considered sufficient by Kielhorn, can be obtained from the Indian Calendar and the Tables in the present volume.
197. On the supposition that the earth's equator and the ecliptic are on one and the same plane, in order to find at what time a given sign, or part of a sign, becomes lagna, or rises on the eastern horizon, we have only to find (i.) the true longitude of the sun at mean sunrise on the given day; (ii.) the distance of the sun at that moment from the given lagna, measured along the ecliptic; (iii.) the time required for covering this distance. The result will be approximately, and without reference to the