BS cy Dr. Hut TON’ s Proj A fora 
caution to preferve each number true to the neareft unit in the’ 
6th or laft decimal. Wheres iets 
As to the decimals of the numbers in the latter half of the 
quadrant, they will be the complements, to 1, of the corre= 
{ponding numbers in the firft half; and therefore they may be: 
all eafily found by taking each figure from g, and the laft from: 
10. But it will be fate to find only every :6thdecimal in this: 
way, aud to fillup the intermediate nine by adding, as before,’ 
the conftant decimal 062648; by which means they — bé 
checked and verified at every roth number. | 
11. To fill up the third Colunte,| or that of fines, as well as: 
thofe of tangents.and fecants, it may firft be obferved, that 
the old tables of thofe lines to every mimute, or even to every ten: 
feconds of the quadrant, cannot be of fo much ufe as. it'might: 
ieem at firft fight; as the very near coincidence of the nume. 
bers in the new and old divifions appear very feldom to happen. 
i find, indeed, that our arc 1369 anfwers nearly to 45 minutes, 
tliat arc excecding 4 45" by only *00632363 or 3, part of a fe- 
cond nearly, and fo.in proportion for their equi multiples.’ But 
although this degree of coincidence may be-fufficient for check- 
ing the correfpanding values of the arcs in the firft-and ‘fecond 
columns, we are not thereby authorifed to confider the fine, 
tangent, or fecant of 1309 asaccurately equal to that of 45° i 
all the feven places of figures, but differing from it by nearly the 
\., part of the difference correfponding to 1/’, which:1s about 
‘of an unit in the fines and tangents, though next to nothing 
in the fecants. This, therefore, although it makes:no fenfible 
difference, in this particular cafe, will caufe a difference that 
muift not be negleéted in the equi-multiples of 1309 and 45’, 
the fines and tangents of which wil differ by half a unit-or 
3 more, 
