Indian Science and Technology in the Eighteenth Century: Some Contemporary European Accounts c9.85

c9.85

They do so, however, only nearly; and it will be found on trial, that there is, in the numbers of the table, a small, but regular variation from this law, which is greatest when the argument is 30°, though even there it does not amount to a minute. The sun's equation, for instance, which, when greatest, or when the argument is 90°, is, by these tables, 2°, 10', 32", should be, when the argument is 30°, just the half of this, or 1°, 5', 16", did the numbers in the table follow exactly the ratio of the sines of the argument. It is, however, 1°, 6', 3"; and this excess of 47" cannot have arisen from any mistake about the ratio of the sine of 30° to that of 90°, which is shown to be that of 1 to 2, by a proposition in geometry⁷⁴ much too simple to have been unknown to the authors of these tables. The rule, therefore, of the equations, being proportional exactly to the sines of the argument, is not what was followed, or intended to be followed, in the calculation of them. The differences, also, between the numbers computed by that rule, and those in the tables, are perfectly regular, decreasing from the point of 30°, both ways toward the beginning and end of the quadrant, where they vanish altogether.