332 Beappicker—On the Changes of the Radiation of Heat from the Moon. 
area of the solar surface was measured at sixteen equidistant positions, beginning 
with that where the solar surface is just wholly exposed, and ending with that 
where it just wholly covered. Thus sixteen points on a curve representing the 
law of increase of light between the edge of the shadow and that of the penumbra 
were obtained. 
Secondly, circles were described on another sheet, with radii proportional to 
the apparent semi-diameters of the earth’s shadow and penumbra and that of the 
moon as seen from the earth, and by means of the planimeter the area of sixteen 
zones of equal breadth and lying throughout their lengths in equal depths of 
penumbra were calculated. The moon’s light at any time was approximately 
obtained by multiplying the area of each zone by the luminosity at the centre of 
its breadth, read off from the curve, and summing up these products. This 
was done for sixteen equidistant positions, and a curve representing very fairly 
the gradations of the moon’s luminosity across the penumbra was obtained. 
This is represented in the diagram (Plate X.) by the strong full line. The 
observed heat is represented by the two other lines; the dotted one is based on 
the assumption that the heat of full moon was that towards which it seemed to 
approach on the night of the eclipse (viz. 312); the fine full line is based on the 
probable average full moon value deduced from observations previous and sub- 
sequent to the eclipse (ante, p. 328). 
In ,determining the theoretic light-curve no allowance was made for the 
acknowledged decline of brilliancy of the sun’s disc towards the limb, nor, of 
course, for any inequalities of brilliancy of the meon’s disc. The moon’s apparent 
diameter was assumed equal to the breadth of the penumbra from its exterior line 
to the edge of the shadow; the middle point of the curve is taken as that where 
one limb is as much (10”) inside of the shadow as the other is outside of the 
penumbra. The time when this occurred was carefully determined and the 
corresponding heat laid down. The rate of motion across the penumbra was 
assumed to be for our purpose constant. In obtaining the area of the zones of 
the lunar surface, they were assumed to be terminated on each side by circles of 
radius equal to that of the middle point of the penumbra and with centres along a 
radius, instead of by concentric circles of increasing and diminishing radii, as no 
appreciable error would result thereby. 
We think there can be little or no doubt that an appreciable though small 
interval passes before the moon’s surface acquires the temperature due to the light 
shining upon it at the moment, whichever of the two heat curves we take as based on 
the more probable value of the full moon’s heat. From the character of the dotted 
curve, however, especially in the neighbourhood of 0" 28™, there seems hardly any 
doubt that 312 divisions is too small a figure to assume as a full moon value. 
Birr Caste, August 26, 1885. 
