on the Planet Venus . 
*59 
projected extent too small ; and (c) that my calculations are so 
full of inaccuracies , that it would he necessary to go over them 
again , and compare them exactly with those made by my 
opponent. 
It requires, indeed, little examination to perceive, that all 
these objections are groundless. 
( a ) That I did pay attention to the penumbra, my paper 
“ on the atmosphere of Venus” shews plainly enough; and it 
is readily to be conceived, that the points of the horns, illumi- 
nated by refraction and penumbra, must project beyond the 
enlightened semicircle into the dark side. And it would also 
be easy to shew, how the points must project more beyond the 
enlightened semicircle, in proportion as the phase of Venus is 
that of a sharper crescent ; with regard to which, I will here- 
after determine, more accurately than my opponent has done, 
how much the projecting excess of the arch must be. But the 
author has not considered that, in my way of making the mea- 
surement, it was quite unnecessary to take the penumbra into the 
computation ; for I measured the faint light, of a bluish-grey 
colour, which ran on along the edge of the dark hemisphere, 
according to fig. 20, (where A D indicates a diameter of Venus, 
parallel to the line of the horns) not, as he did 3 years after, 
from A, but only from B (the extreme visible point of the 
horn, still faintly illuminated by refraction and the diameter 
of the sun) to C ; and consequently I had, by the observation it- 
self, already deducted the penumbra. It is indeed possible, that 
at B and E, where the penumbra seemed to me to terminate, 
it yet might not be quite at an end ; but the excess must be 
indefinitely small, since the whole projection of the penumbra, 
