58 W. A. Norton on the Dimensions of Donati’s Comet. 
determinations of the positions on Oct. 54-0776, (W. M. T.) of 
particles which emerged from the sphere of influence of the 
nucleus on several previous dates. ‘To these particles were at- 
tributed various repulsive and attractive ett epee: due to the 
sun’s action, between certain limits, and also various initial late- 
ral velocities answering to different. iobibndiotia to the radius- 
vector, of the jets proceeding from the nucleus. It will a seen, 
when we come to investigate the form of envelope that should 
result from the combined repulsive actions of the nucleus and 
sun, that if we conceive the ratio of the efficient sem of 
the two bodies to be constant for all points of the nucleus from 
which the jets proceed, the maximum inclination of 2 a oe to the 
radius-vector, which answers to the observed form of the come- 
tary en velope, i is about 19°; and that if this ratio be supposed 
to vary from one point of the surface of the nucleus to another; 
its law of variation, and that of the effective repulsion of the 
nucleus, must be such that the greatest lateral velocity of a re- 
ceding particle is nearly the same as if the ratio in question re- 
mained constant, and the limiting angle were 19°. The initial 
lateral velocity of a jet of cometary matter, it is to be observed, 
increases with the intensity of the effective repulsion of the nu 
cleus. In fact it appears from equation 9, given in the format 
rt of this memoir, that it varies, for a given angle of emis- 
a a, ng a as the square root : the “Araceae repulsion, p. 
tive repulsive force by w shih is urged 
away oer! the nucleus is the excess of i iat repulsion of the 
nucleus over its airs The same is true of the effective 
repulsive force of the sun. The actual repulsions must ac- 
sordingty be dininguiated thei the efficient done forces by 
which the particle is solicited. It is assumed, as a fundamental _ 
principle, in our investigations, thatthe actual fepulsive actions 
of the sun and nucleus upon any particle vary simply by reason 
of some change in the condition of the particle; and therefore 
that the ratio of these actions must remain unalterably the same, 
oe whatever range their actual intensities may be supposed 
Ts elebicris of the orbit of Donati’s comet employed in the 
arteeyniy were computed by Mr. Searle, of the Dudiey Obser- 
and are as follows :—Per. pass. Sept. 298 ‘7523 W.M.T.; 
= = 88! 1 2' 21”; 2=165° 18’ 46”; 7=116° 57’ 46”; »=85° 
21’ 21”; oe q= =9°762236. 
The process of calculation of the position at a given instant, 
of an individual particle supposed to have left the sphere o 
influence of the nucleus at a certain previous date, is as follows: 
Equs. (10) and (11) give the ian circumstances of motion of 
the particle. The computed value of V’ is the initial velocity of 
the particle, resulting from the atin of the nucleus. This is in 
