56 W. A. Norton on the Dimensions of Donati’s Comet. 
The values of r and 7 having been found for the position of a 
particle at any instant of time, we may readily obtain the right 
ascension and declination of the particle at that instant. 
he following equations serve to determine the position of the 
particle with respect to the axis of the orbit of the comet, and 
another axis perpendicular to this drawn through the position of 
the sun. 
evouy 3". (883 Fares. 
The relative position of any two different particles may be 
obtained by the equs. 
9 Y's or y’~—y y__ %—2, or 2! —2 
baa er pry cr a (27.) d cone gi. ci { 28.) 
in which «= the inclination of the line connecting the two par- 
cles to the axis of the orbit, and d=the distance between the 
particles. 
The same equations will make known the relative position of 
any particle and the nucleus, at the same instant of time, if 2 
and y’ be taken to represent the codrdinates of the nucleus. 
The former part of this memoir, published in this Journal, 
vol, xxix, p. 883, together with the formulas just given, was pre- 
pared, and the greater portion of the results of computation now 
to be published, were obtained more than a year since 
‘esults es 
The general topic that will first be considered, from our theo- 
retical point of view, is the Dimensions and Form of the Tail of 
the Comet. A similar numerical investigation will then be made 
relative to the envelopes of the head. An inquiry will after- 
wards be instituted into certain special facts and phenomena, 
with reference to which careful measurements were made by 
astronomical observers; and an approximate determination given 
of the period of rotation, and position of the axis of the nucleus. 
In the light of all the quantitative results obtained, we may per- 
haps be able to form an adequate conception of the physical 
processes of development through which the great comet of 
5 as it swept with its “trailing garments” of light 
through our firmament. We may also obtain some notion of the 
probable nature of the forces in 2 ene whose general char- 
acter is distinctly made out, and whose laws and limits of vary- 
ing intensity are determined. It will be seen that while from the 
eneral conception of the repulsion of the nucleus, combined with 
that of the sun, each varying in intensity for different cometary 
particles between certain limits, we may deduce the observed 
