with Remarks on the Construction oj its different Parts. 135 
appearance of the bright envelope ; but this, it will be seen, is 
the immediate consequence of the great depth of light near 
the circumference, contrasted with its comparative thinness 
towards the centre. The 6th of October, for instance, the 
radius of the envelope was 9' 30" on the outside, and 7' 30'' 
on the inside ; and as the greatest brightness was rather nearer 
to the outside, we may suppose its radius to have been about 
8'-|. Then if we compute the depth of the luminous matter 
at this distance from the centre, we find that it could not be 
less than 248 thousand miles ; whereas in the place where the 
atmosphere was darkest, its thickness would be only about 50 
thousand ; so that a superior intensity of light in the ratio of 
about 5 to 1, could not fail to produce the remarkable appear- 
ance of a bright semi-circle, enveloping the head of the comet 
at the distance at which it was observed.* 
I have entered so fully into the formation of the envelope, 
as the argument, by which its construction has been analysed, 
will completely explain the appearance of the streams of light 
inclosing the tail of the comet, and indeed its whole con- 
struction. 
The luminous matter as it arises from the envelope, of which 
it is a continuation, is thrown a little outwards, and assumes 
the appearance of two diverging bright streams or branches ; 
but if the source from which they rise be the circular rim of 
* From the measure of the envelope, whose diameter the 6th of October was 643032 
miles, we have the radius ab } Plate III, 321516. Then if cd be 25000, we find 
the angle bac, of which a c is cosine 22 0 44' 37" ; and the sine b c, which is the depth, 
will be to the versed sine cd, which is the thickness, as 4,972 to 1. And if a d is 9' 30", 
the greatest brightness which is at c will give the distance ac equal to 8' 45*,7. This 
calculation being made for that part which is convex towards us, the addition of the 
concave opposite side will double the dimensions of the depth and thickness. 
