Page:The Construction of the Wonderful Canon of Logarithms.djvu/52

28 CONSTRUCTION OF THE CANON,

HUS, let the greater of the given sines be 9999975.5000000, and the less 9999975.0000300, the difference of these .4999700 being multiplied into radius (cyphers to the eighth place after the point being first added to both for the purpose of demonstration, although otherwise seven are sufficient), if you divide the product by the greater sine, namely 9999975.5000000, there will come out for the less limit .49997122, with eight figures after che point; again, if you divide the product by the less sine, namely 9999975.0000300, there will come out for the greater limit .49997124; and, as already proved, the difference of the logarithms of the given sines lies between these. But since the extension of these fractions to the eighth figure beyond the point is greater accuracy than is required, especially as only seven figures are placed after the point in the sines; therefore, that eighth or last figure of both being deleted, then the two limits and also the difference itself of the logarithms will be denoted by the fraction .4999712 without even the smallest particle of sensible error.

Write down the sine in the First table nearest to the given sine, whether less or greater. Seek out the limits of the table sine (by 33), and when found note them down. Then seek out the limits of the difference of the logarithms of the given sine