TRACT 29.

DIVISION OF THE QUADRANT.

127

at that place; therefore at the line or number 2153, or9 + 16 x 134, which would be to have the 1 more added,let the 1 be there omitted, and add it at the next line or2154, the true decimals alter the first six, for 2153, being499985, and for 2154 they are 562456. Continue thus al-ways adding 1 more at everv 16th line, except at the fol-lowing numbers, where the 1 must be omitted, and added atthe next following number; viz,

2153

12926

23683

34*56

15213

55970

43! 4

150 " ]

2/ 8 4

: 660 1

47c 58

53131

66743,

73194

6 159

17252

27989

58746

19519

6027''

6888S

75339

8020

1937"

50150

10907

51' ’ 6 4

6 2457

71033

77500

10765

21538

32295

43052

53825

64582

And thus proceed to the middle ol' the quadrant; bywhich means all the numbers will be to the nearest unit inthe sixth or last place. Also, to have a check upon thesenumbers at certain intervals, it may be proper to proceedin this manner: First find every 100th number, by addingits decimal -264803 &c, verifying them at every 10th;then find every 16th number, by adding continually•002369 &c, which will also be checked and verified atevery 25th addition by one of the former set of 100, for25 times 16 make 400, using a proper precaution to pre-serve each number true to tiie nearest unit in the 6th or lastdecimal.

As to the decimals of the numbers in the latter half of thequadrant, they will be the complements, to 1, of the cor-responding numbers in the first half; and therefore theymay be all easily found by taking each figure from 9, andthe last from 10. But it will be safest to find only every10th decimal in this way, and to fill up the intermediatenine by adding, as before, the constant decimal 062648 ;by which means they will be checked and verified at every10th number.

11. To fill up the third column, or that of sines, as wellas those of tangents and secants, it may first be observed,that the old tables of those lines to every minute, or even to