126

PROJECT FOR A NEW

TRACT 29.

to above -i a second ; and then the 3" must be added at every16 afterwards, viz, at 24, 40, 56, 72, 88 , 104, &c.

10 . But, besides the constant addition of 2" every time,and of l" more every 16th time, there must be l" moreadded for every 6753-4 time, on account of the excess ofthe fraction •062648062470964 over the fraction ’0625 or1 % : for that excess is ’000148062470964, which is =

g^-p. And the easiest method of making this last addition

of 1 at every 6753 4 , will be to make the [increase of the 1,on account of the at a unit sooner for every 422 T 3 T ;because 16 is 422 T 3 T times contained in 67534; by whichmeans the incremental units, for the T '- 6 , will become 1more at that number 6 7534-, which last unit may be consi-dered as the increment of the former increment for the -fe ;and so proceed up to the quadrant; which will completethe second column of arcs to the nearest second in eachnumber. Or this second column may be exactly computedto as maty decimals as we please, by adding continually the2 " and decimals, viz, 2-062648062470964. But at the mid-dle of the quadrant, where the numbers return again up-wards by the right-hand, there will for once be to be addedonly the seconds and decimals answering to the arc '63268,viz, 1’30499618 seconds, that number being necessary tomake the numbers on the right-hand to be the exact com-plements of those on the left. Or it will perhaps be properto make them to the nearest unit, in the 6 th place of deci-mals. And to fill up the second column to this degree ofaccuracy, add continually 2-062648 seconds, but at the 9 thline add 1 more, or 2’062649, because 9 times 062470964amounts to 56223867, or more than half a unit at that place;and after that add 1 more than 2’062648 at every 16th line,viz, at 25, 41, 57, 73, 8 tc, because 16 times ’062470964amounts to "99953542, or nearly 1 , it being only ’00046458less than 1 . And this number ’00046458, thus added toomuch, will, in 134 times adding it, amount to more than06223867, the excess of 56223867 above 5, or half a unit,