i,5 6 Dr. Herschei/s Observations of a Comet , 
by calculating in the next place the radius vector of the 
comet, and having likewise the distance of the earth from the 
sun, we find by computation that the distance of the comet 
from the earth at the time of observation was 1,169192, the 
mean distance of the earth being 1. Now since the disk of 
the comet was observed to subtend an angle of 1", which 
brought to the mean distance of the earth gives 1", 169, 
and since we also know that the earth’s diameter, which, 
according to Mr. Dalby, is 7913,2 miles,* subtends at the 
same distance an angle of 17", 2 we deduce from these prin- 
ciples the real diameter of the comet, which is 538 miles. 
Having thus investigated the magnitude of our comet, we 
may in the next place also apply calculation to its illumination. 
The observations relating to the light of the comet were 
made, from the 4th of October to the 19th. In all which 
time the comet uniformly preserved the appearance of a 
planetary disk fully enlightened by the sun : it was every 
where equally bright, round, and well defined on its borders. 
Now as that part of the disk which was then visible to us, 
could not possibly have a full illumination from the sun, I 
have calculated the phases of the comet for the 4th and for 
the 19th, the result of which is, that on the 4th the illumina- 
tion was 119 0 45' 9" as represented in figure 1, and that on 
the 19th it had gradually increased to 124 0 22' 40'', of which 
a representation is given in figure 2. Both phases appear to 
me sufficiently defalcated, to prove that the comet did not 
shine by light reflected from the sun only ; for had this been 
* See Phil. Trans, for 1791, page 239, Mr. Dalby gives the two semi-axes of the 
earth, from a mean of which the above diameter 7913,1682 is obtained. 
