On the Great Comet of 1843. 205 
nomena observed respecting that comet. Olbers supposes that 
any particle composing the surface of the comet, or approaching 
from the frozen regions of space within a certain distance of the 
sun, is affected with a new repulsive force resembling that which 
drives off substances from an excited prime conductor. These 
particles thus polarized he supposes to be thrown off from the 
head of the comet with a force proportioned to the mass of this 
head or nearly solid portion of the comet, and inversely as the 
square of the distance from the centre of this head. The same 
particle in acquiring polarity with reference to the comet, acquires 
also polarity with reference to the mass of the sun, and is repel- 
led by that mass, instead of being attracted by it with a force al- 
so varying inversely as the square of the distance from the sun. 
The origin of this polarity may be ascribed to the action of the 
sun’s light or heat, or both. ‘This particle thus endued with one 
repulsive force acting in the direction of the prolongation of the 
radius vector from the sun, and inversely as its square, and with 
another repulsive force acting in the direction of the prolongation 
of its radius vector from the centre of the comet and inversely 
as its square, and with its original tangential velocity, at the time 
of parting with its actual cohesion with the comet, moves away 
in space in such a manner as not to return. Now the geocentric 
position in the heavens with respect to the head of the comet, of 
any such particle for any given elapsed time after it is thrown off 
from the comet’s surface, may be readily computed, from the 
known tangential direction and velocity for any assumed values 
of the two repulsive forces of the comet and sun, for a unit of 
distance—say the earth’s mean distance from the sun. Olbers 
remarks that the heliocentric orbit of such a particle must be an 
hyperbola, moreover that the points in space where the two repul- 
sive forces of the sun and comet make equilibrium, for any ori- 
ginal direction of repulsion from the surface of the head, must 
have the portions of expelled matter more condensed than any 
portion of space between such points and the comet’s head, thus 
form apparently a hollow envelope or nebulosity, in the shape 
of an hyperboloid having the head of the comet in its internal 
focus, and its apex towards the sun, the continuation of this hol- 
low hyperboloid from the sun beyond the parameter, (so to speak, ) 
forms the tail of the comet. The shape of the hyperboloid, and 
consequently of the tail, depends upon the ratio of the repulsive 
