188 RISING, SETTING AND CONJUNCTION OF PLANETS Consider Fig. 22. The sphere centred at M is the Moon's globe, and E is the centre of the Earth. The lines MS' and ES (which are approximately parallel to each other) are directed towards the Sun. Half the globe of the Moon bounded by the circle ABCD and lying towards the Sun is illuminated by the rays of the Sun, and half the globe bounded by the circle LBTD and lying towards E is visible from the Earth. An observer on the Earth will, therefore, see only that part of the Moon's illuminated surface which lies between the semicircles BCD and BTD. In fact, he will see the projection of that on the plane of the circle LBTD. Let BZD be the projection of the semicircle BCD on the plane LBTD. Then the observer will see that part of the Moon's disc illuminated by the Sun which lies between BTD and BZD. This illumi- nated part of the Moon's disc is measured by the length ZT of the Moon's diameter. From the figure, it is evident that Rcos LCMZ X MC R LCMZ = L FMS' = L MES, so that from the plane triangle CZM right-angled at Z, we have MZ- Therefore ZT =MT-MZ F (R-Rcos L. CMZ) x MC R Rversin CMZ x MC R Rversin MES X MC R E Fig. 22 TO SUN TO SUN Hence the rule. A rule for the determination of the Moon's true declination, i.e., the declination of the centre of the Moon's disc: 8. Take the sum of the arcs of the Moon's declination and (celestial) latitude when they are of like directions; in the
