272 ON THE LIGHT OF THE MOON AND OF THE PLANET JUPITER. 
At the same date, the intensity of sunlight at Jupiter and at the Moon was as 
1: 27.9. Hence, 
D xu). wu) 
81 1 
would be the proportion of the albedos of the two surfaces, provided that they received 
and reflected the incident light under similar conditions. This, however, is not the 
case. "The area of the Moon, included by the aperture in the focus diaphragm, is so 
small that it may be considered as being illuminated sensibly at the same angle of inci- 
dence throughout. If we take 60° as the mean value of this angle for the parts of the 
Moon compared and regarded at this date as noticeably brighter than the rest, we must 
diminish the above proportion in the ratio sin. 60°: 1, to represent the effect of the 
increased quantity of sunlight which would reach the same surface at perpendicular 
incidence. On the other hand, the aperture admits nearly the whole of the light of 
Jupiter, and the sunlight, on account of the curvature of the surface of the planet, 
being received at very different angles, it should present a gradation in the intensity of 
its light, proceeding from the centre towards the circumference. It is difficult, or 
rather quite impossible, to define precisely the rate of this decrease; but, from facts 
which will be elsewhere stated, it is certain that its light near the margin is much 
fainter than towards the centre. According to the best estimates which I have been 
able to make, the coefficient to be applied in order to reduce the mean brightness of 
a central disc of Jupiter, 327.47 in diameter, to the mean brightness of the whole disc 
on March 2d, is y Again, to reduce the mean brightness of the illuminated hemi- 
sphere to that of the central element presented at right angles to the direction of illu- 
mination, we must apply the coefficient E = 1.48. These numbers do not mate- 
rially differ from those which would result from supposing, as Lambert has done, that 
the intensity varies as the sine of the angle of incidence of the sunlight. 
, Applying the above, we should have, from the observation of March 2d, a value of 
` which would represent the relative albedo of Jupiter compared with the Moon's 
brighter regions, if both bodies are supposed to reflect light conformably with the same 
law of dispersive reflection, which, according to Bouguer and Lambert, holds approxi- 
mately for the generality of opaque bodies; viz. that the quantity of light emitted 
towards a given point from each element is proportional to the solid angle subtended 
at the point by the element. However, we have seen, in the case of the Moon, that it 
has the property of returning an undue amount of light towards the Earth at the time 
of full Moon, which would cause the other phases to appear dispr oportionately faint. 
