124
PROJECT FOR A NEW
TRACT 29.
3. I would assume the radius equal to 100000, or supposeit to be divided into 100000 equal parts. Then it is wellknown, that the semi-circumference will be 314159*26536nearly, and consequently the quadrant nearly 157079-63268of the same equal parts, which is less than 1S7080 by•36732, or nearly of a unit, or nearer -§. = -375, or nearer•/ T = -3636, or still nearer = -3684, or still nearer -J-J. =•36666 &c. And the half quadrant, or -j. of the circle,78539-81634 which is less than 78540 by only -18366, ornearly only of any of the above-mentioned fractions.
4 . The table may consist of 5 or more columns; the firstcolumn to contain the regular arithmetical series of arcs,differing by unity, from the beginning, in this manner,1, 2, 3, 4, 5, &c, up to half the quadrant, the next lesswhole number being 78539 ; then for the higher numbers,or those in the latter half quadrant, besides adding 1 con-tinually, there must be at the first added the decimal*63268, which will make all the numbers in this half becomethe exact complements of the first half, which consists ofwhole numbers only ; and these will be the lengths of thearcs. Or, in order to include the qnadrantal arc 78539-81634,the first column may be continued up to 78540. The se-cond column to contain the corresponding degrees, minutesand seconds, to the nearest second, or to the true secondsand decimals of a second, for the convenience of easilychanging the tables from the one measure to the other, orto make them answer to both methods ; and the 3d, 4th, 5tb,&c columns, to contain the corresponding sines, tangents,secants, &c.
5. The tables may be disposed as at present, namely,continuing them downwards by the left-hand side of thepages, as far as to the middle of the quadrant, and then re-turning them again backwards and upwards by the right-hand side of the pages.
6. In this disposition, the numbers on the same line, theone on the left and the other on the right, will be exactcomplements of each other to a quadrant, and the decimal