54  W.A. Norton on the Dimensions of Donati’s Comet. 
Art. XI.—Theoretical Determination of the Dimensions of Donati’s 
Comet; by Prof. W. A. Norton. 
(Continued from this Journal, vol. xxix, No, 87, p. 886.) 
Let D= the perihelion er of the comet, and V= the 
velocity at the perihelion; v= the velocity, 6,= the true anom- 
aly, and r, =the radins-vedive of the comet at any point of its 
orbit ; and. 6 = the inclination of tangent to orbit, to the radius- 
vector: 
t =the interval of time from assumed date to that of the peri- 
helion passage of the comet 
the acceleration due to the effective repulsion of the sun, 
expressed in in fractional parts of a mile, at the perihelion distance 
of the c 
R= the Rathi from the sun, and 9,= the true parabolic 
anomaly of the cometary canis at the instant of its leavin ng 
the sphere of influence of a leus : 
V'= the initial velocity Ke the particle, in a direction parallel 
to tangent to orbit of co 
= the angle included Sead the line # and the axis of the 
nyperboss orbit of the particle; 4= the angle included between 
this axis and the axis of the pare arabolic orbit of the nucleus; P= 
perihelion distance, p, = the half-parameter, e = the eccentric city, 
and A= the semi-transverse axis of the hyperbolic orbit; T= the 
interval of time from assumed date to the instant of the perihe- 
lion passage of the oe particle; y= the inclination o either 
pg Ani to the 
= the true aneahaly, and += the radius-vector of the particle 
at res interval of time, ¢, after its perihelion passage :, 
y= the angle incl uded, betwneap tlse.andiunseokonat ten parti- 
cele and the axis of the comet's orbit, 
Let a and ¢ represent certain —- 
The intervals of time, z, 7, and ¢, are xp ressed in days and 
fractional parts of a day. The vepeigen V’, and », are ex- 
pressed in miles and fractional parts of a mile, per second. 
Rand ©, may be taken, with slight error, Se to the values 
of r, and 6, , found for the same instant of tim 
sebtis 
= =. D3(tang. * © smal i. ae 
D D 180°— 6 
ZL ecaeess 6, > Vi=V es dati dads » (11) 
2_i 
cos > 1 
2 2 
Lett D.k’=n; uw VWs Whoo cae 
