W. A. Norton on the Dimensions of Donati’s Comet. 67 
the orbit, and is about 3,600,000 miles. The extreme circular 
ring on the left, or preceding side, is made up of the particles 
which are repelled from the sun by the greatest force (1'218), and 
the extreme ring on the right is composed of particles which 
have been solicited by the greatest attractive force (0:455). The 
radius of the former is 236,000 miles, and that of the latter 
338,000 miles. e middle circle is composed of particles 
which are neither attracted nor repelled; its radius is 348,000 
miles. The mean breadth of the cross-section of the tail, at the 
distance supposed, as determined from these three circles, is 
615,000 miles; and the ratio of the longest diameter to the mean 
breadth, is as 5°86 to 1. 
We have already intimated (p. 64) that the initial lateral ve- 
locity of the particles that go to the extreme concave side of the 
tail, was probably less than 0™184, and may have been very small. 
The mean breadth of the cross section was therefore probably less 
than 615,000 miles. It may not have exceeded 360,000 miles. 
At less distances from the nucleus the cross-section of the 
train, as determined upon the theory of a repulsion exerted by 
the nucleus, will deviate less from the circular form. At the 
very nucleus the cross section perpendicular to the radius-vector, 
must be almost an exact circle; unless the limiting angle of 
emission is different on different sides of that line, 
at points quite distant from the nucleus to have had a consider- 
ably greater extension in the plane of the orbit than in a direc- 
tion perpendicular to that plane. Dr. Winnecke, of the Pulkova 
Observatory, in announcing these results deduced from the ob- 
servations of Dr. Pape, remarks, ‘We are thus conducted to 
probably lies in the plane of the orbit.’ 
In what precedes we have taken account only of the outer 
envelope of the head of the comet, and of its indefinite prolonga- 
tion in a continuous stream which we have regarded as the train — 
