Indian Science and Technology in the Eighteenth Century: Some Contemporary European Accounts c9.172

c9.172

If, therefore, m be the motion of the moon for a century in the last mentioned tables, m (x - y) - 9" (x² - y²) will be the mean motion for the interval x - y in the tables of Chrisnabouram. If, then, a be any other interval, as that of 43.83 centuries, the mean motion assigned to it, in these last tables, by the rule of proportion, will be (ma(x-y)-9"a(x²-y²))/(x-y) = ma - 9a(x+y) Let this motion, actually taken from the tables be = na, then ma - na = 9a(x+y) or x+y = (m-n)/g = 52.19 in the present case It is certain, therefore, that whatever supposition be made with respect to the interval between x and y, their sum must always be the same, and must amount to 5219 years. But that, that interval may be long enough to give the mean motions with exactness, it can scarcely be supposed less than 2000 years; and, in that case, x = 3609 years, which therefore is its least value. But if 3609 be reckoned back from 1700, it goes up to 1909 years before Christ, nearly, as has been said.