ON MAPPING THE SURFACE OF THE MOON. 9 
particularly of the mountain-slopes, must necessarily include the larger angle 
under which they are seen on the photogram. It is only such objects as the 
orifices of craters, rings, and generally surface-markings, that are foreshort- 
ened to a greater degree as they are removed further from the eye by the 
effect of libration. The angle under which a mountain-slope, or any object 
which is elevated above the surface, is seen, is increased by libration as it is 
earried further from, and decreases as it is brought nearer to the eye; for if 
we take a mountain-range lying E. and W, on the equator, moon in node, we 
see the N, and 8. slopes under the smallest angles. As the moon attains a 
greater N. latitude, the mountain-range is seen N. of its normal position, and 
we see more of its S. slope and lose its N. slope, the reverse taking place as 
the moon attains S. latitude. The degree of visibility of mountain-slopes or 
objects that are more or less elevated above the surface within the areas 
above mentioned is dependent more or less upon three conditions :—1°, the 
angle which the crest or longitudinal direction of an object makes with a Junar 
meridian ; 2°, the angle which the slope makes with a vertical perpendicular 
to the moon’s surface; and,3°, the angle through which it is moved by the effect 
of libration. In each case there is a maximum effect, determined by the posi- 
tion and direction of the object. The visibility of objects within a zone of 
1° 32' 9" N. or 8. of the moon’s equator is also affected by another circumstance, 
viz. the direction in which the sun’s rays fall upon such objects at different sea- 
sons of the lunar year ; for example, a mountain-range lying E. and W. on the 
moon’s equator will have its N. slope illuminated while the sun is N. of the 
moon’s equator, and its S. slope during the opposite season. The lunar sea- 
sons are easily found. When the sun’s longitude, as seen from the moon 
(which does not at the utmost differ more than 8’ from the longitude as seen 
from the earth), is equal to the longitude of the moon’s ascending node, the 
sun is vertical to the moon’s equator, passing from 8. to N. When the differ- 
ence between the longitudes of the sun and node equals 90°, the N. pole is 
enlightened, and the season is summer in the northern hemisphere. When the 
longitudes of the sun and node differ 180°, it is the autumnal equinox in the 
northern hemisphere, and when the difference amounts to 270° it is winter, 
the 8. pole being illuminated. These quantities may be thus expressed for 
the northern hemisphere :— 
O-—8= 0°+ Sun in equator ascending. 
©O-—R8= 90+ Sun in tropic, N. pole illuminated. 
©O— g=180 — Sun in equator descending. 
O— 8 =270 — Sun in tropic, 8. pole illuminated, 
Tn order to find the season, and consequently the illumination due to it of 
an object in the tropical zone 1° 32’ 9” N. and S. of the moon’s equator, nothing 
further is requisite than to find from the Nautical Almanac the longitudes of 
the sun and node: the quantity © — g will give the season as above. 
Tf the sine of the angle @ — g be multiplied into the sine of 1° 32! 9”, the 
inclination of the moon’s equator to the ecliptic, we obtain the sine of an angle 
which represents respectively the following quantities:—1°, the sun’s decli- 
nation as seen from the moon ; 2°, the inclination of the equator of illumina- 
tion to the moon’s equator ; and, 3°, the inclination of the terminator to the 
lunar meridian which it intersects. 
From the above considerations it follows that in the three areas now issued, 
and also in the corresponding areas in Quadrants I., II., and III., we see lunar 
objects of very nearly their true forms, and that libration does not materially 
affect either their forms or magnitudes. 
1868. c 
ed 
