W. A. Norton on the Dimensions of Donati’s Comet. 59 
a direction parallel to the tangent to the parabolic orbit of the 
comet, which makes the angle with the radius-vector, In case 
the particle is emitted from the nucleus in a direction inclined to 
the radius-vector it has a certain velocity imparted by the repul- 
sion of the nucleus, relative to the radius-vector. This lateral ve- 
locity, as it may be termed, is calculated from equs. (7) and (8), 
and is added to the velocity V’ already determined, or subtracted 
from it, according as the jet proceeds from the preceding or follow- 
ing side of the nucleus. The result is the initial velocity to be at- 
tributed to the particle. The particle having the initial, or pro- 
Jectile velocity, thus determined, is urged away from the nucleus — 
into remote space by the repulsive force of the sun, and describes 
a hyperbolic orbit having the sun in its outer focus. If we sup- 
posed it to set out in this orbit at the instant of the perihelion 
passage of the comet, the sets of equs. (12) and (18) serve for 
the determination of the orbit; ef equs. (17) and (18) make 
known the true anomaly and radius-vector of the particle in its 
orbit. If the particle be supposed to leave the nucleus either 
D=55,000,000"; V=85"-166; =90°. 
l= of a mile; n=D.W=1122907. (The value of n, 
as first found, and used in the following caleulations, is 1122°95). 
oes = 1101250; e=m+1=2101250; P= 55,000,000; 
P2=m. D=60,568,700. 
