40 H. M. Parkhurst-—Tails of Comets. 
A diagram I have constructed illustrates several results 
necessarily depending upon the hyperbolic theory. The black 
line represents the orbit of the comet of 1848, so far as included 
within the radius of the earth’s orbit. The red lines, starting 
from the orbit, and after passing their perihelion points radiat- 
ing in nearly straight lines from the sun, represent the hyper- 
bolic orbits of particles of matter, leaving the head of the 
comet at the given times. 
' In these computations, also, I have adopted 1 as the ratio of 
repulsion. Had Coggia’s comet possessed sufficient luminosity 
to be visible on July 24, it would have afforded a test of the 
true amount of repulsive force; but as its plane was still 
turned almost directly toward us when the tail was last seen, a | 
variation in the assumed amount of the repulsive force makes 
no appreciable difference in its position ; and the streamers seen 
extending from the convex side of the tail of Donati’s comet 
suggest the theory that upon every formation of a new envel- 
ope, a small portion of the matter was endowed with a repul- 
sion at least ten times that of the rest of the matter forming 
the tail. 
The blue lines circling around the sun connect the positions 
of the particles in their hyperbolic orbits at given times, and 
therefore represent the visible and the invisible tail of the 
comet. The particles leaving the head of the comet thirty days 
before it reaches its perihelion, follow nearly behind it, with 
continually retarded motion, and when the head of the comet 
reaches the sun, those particles have only passed over half that 
distance, and are just about to commence their outward course. 
ead of the comet exactly at the perihelion, pursue a line al- 
most directly from the sun, but about 66° from the axis of the 
comet's orbit. These particles commence their outward course 
with a velocity sufficient to carry them outside the earth’s orbit 
in a little over two days; and that velocity remains nearly 
uniform in consequence of the sudden removal of the matter 
beyond the sphere of the sun’s forcible action. Consequently, 
