Sanscrit Writing and Language. 133 



Brahma Gupta is more modern than Lalande ; — indeed so much more modern, 

 that the time of his existence is not yet arrived, nor will it for near four thousand 

 years to come ;* and it must have been only by some sort of prophetic anticipa- 

 tion that the Brahmans have had his tables for the last 1300 years. Again the 

 same tables exhibit the mean motion of the Moon's apogee slower than in those 

 of Lalande at the rate of 8' 3.4" in a century ; which difference also, by our 

 author's reasoning, would remove the Indian astronomer into futurity, but only 

 about half as far off from us as in the preceding instance. The tables of Varaha 

 likewise exhibit the mean motion of the Moon greater than modern ones do, 

 and, of course, he is not yet come into existence ; but on the other hand, they 

 must be above ten thousand years old, since the mean motion of the Moon's 

 apogee is given slower in Lalande's tables than in them at the rate of 42' 10.9" in 

 a century. These are a few of the absurdities and contradictions into which the 

 application of the lunar theory to Indian chronology would lead us. The mis- 

 take of M. Laplace arose, as I conceive, from his overlooking the bearing which 

 the nature of the Indian astronomy had upon his argument; — a bearing, which 

 is strictly deducible from the data that he himself has supplied. 



To return to the two articles of the English astronomer ; — upon stating that, 

 previously to the age of Brahma Gupta, the Hindoos came no nearer to deter- 

 mining the true length of a lunation than within 20' 49^" of time, he offers the 

 following remark. " This makes an error of one day in less than six years, 



* M. Laplace states that the retardation in the mean motion of either apsis of the Moon's orbit, 

 which has accrued since the time of Hipparchus, or in the course of about two thousand years, is at 

 the rate of nearly fifteen minutes in a century. " — j'en avois couclu quale mouvement du perigee 

 lunaire se rallentit de siccle en siecle, et qu'il est maintenant plus petit d'environ quinze minutes par 

 siecle, qu'au temps d'Hypparque. Ce resultat de la theorie a ete confirme par la discussion des 

 observations anciennes et modernes." — Mecanique Celeste, tom. iii, p. 274. But he has also proved 

 that the rate of retardation of the apsis is three times the rate of acceleration of the Moon herself. 

 The secular motion of the Moon, therefore, is greater now than it was two thousand years ago, by 

 about five minutes of his notation, or somewhat above two minutes and a half of the common 

 sexagesimal admeasurement ; and of course it will take about four thousand years more before she 

 acquires the further secular acceleration of 3' 38.9" ; — that is, supposing the rate of acceleration to 

 continue the same for the next four thousand years as for the last two thousand, which probably is 

 not exactly the case, but I have no occasion here to look for more than a very loose approximation 

 to the truth. 



