[ 452 ] 
Then If from C the line CK be drawn from the 
centre of this circle, K will be the place of the moon 
at the greateft obfcuration. The beft method for 
alligning this point K is to defcribe the arch of a 
circle to the center C with any interval, whereby it 
may cut the arch GHl, as in N and O; for the 
point K bifefts the intercepted arch N KO. Again, 
if CL, C M be applied from C to the arch I H G, 
each equal to the fum of the femidiameter of the fun, 
and apparent femidiameter of the moon, L will be the 
place of the moon’s center at the beginning, and M 
the fame at tlie end of the eclipfe. 
In the laft place, for finding the time, when the 
moon fhall be in each of the points L, K, M, mea- 
fure the chords of the arches HG, HL, HM, HI, 
as not fenlibly differing from the arches themfelves. 
Then A denoting H L or H M, and B the fum of G H 
and H I, the time fought for the greater chord may be 
confidered equal to X the time of 
the moon’s pafling from G to H, or from H to I. 
The time for the leffer chord will be^x 3^ 
2O ^£>1 J3 
X the time above named j and in the laft place, the 
time of the moon’s paftage between H and K equal 
to 
HK_Hk 
b GHc/jHI 
' X 
2IJ 2^ 
B 
X the time fpecified. 
This calculation I deduced from Sir Ifaac Newton’s 
Differential Method j and in the laft cafc' — ^or 
K 
X , &c. is to be taken, as K fliall fall within the 
greater or leffer of the arches G H, H I : but for the 
moft part the term may be wholly omitted. 
If 
