THE PHASE OF THE MOON A rule for calculating the phase of the Moon: 5(ii)-7. (In the light half of the month) multiply (the diameter of) the Moon's disc by the Rversed-sine of the difference between the longitudes of the Moon and the Sun (when less than a quadrant) and divide (the product) by the number 6876: the result is always taken by the astronomers to be the measure of the illuminated part (of the Moon). When the difference between the Moon and the Sun exceeds a quadrant, then the Moon's illuminated part is calculated from the Rsine of that excess increased by the radius.¹ After full Moon (i.e., in the dark half of the month) the unilluminated part of the Moon is determined from the Rversed- sine or Rsine of (the excess over six or nine signs respectively of) the difference between the longitudes of the Moon and the Sun in the same way as the illuminated part is determined (in the light half of the month). Let the longitude of the Moon minus the longitude of the Sun be denoted by D. Then according to the above rule- (1) In the light half of the month, the illuminated part of the Moon Rversin D X Moon's diameter 6876 if D <3 signs, i.e., if it is the first quarter of the month; and [R+Rsin (D-90°)] x Moon's diameter 6876 if D>3 signs, i.e., if it is the second quarter of the month. 187 if D> 6 signs, i.e., if it is the third quarter of the month; and [R+Rsin (D-270°)] x Moon's diameter (2) In the dark half of the month, the unilluminated part of the Moon Rversin (D-180°) x Moon's diameter 6876 = , 6876 if D> 9 signs, i.e., if it is the last quarter of the month. 1 This rule is found to occur also in BrSpSi, vii. 11(ii)-12 and SiDV, I, ix. 12.
