W. A. Norton on the Dimensions of Donati’s Comet. 69 
the motion of a particle with respect to the nucleus we must 
regard it as subject to the actual rather than the effective repulsion 
of the sun, because both the particle and the nucleus must be 
considered as gravitating toward the sun. The value of &, for 
the particles of the outer envelope, is then 1:218+1=2-213, or 
0™-0000249 per second. According to Professor Bond’s meas- 
urements the greatest value of H may be taken at 14,000 miles, 
and ras 200 miles (it may possibly be less than this). Thus 
P=70k=0™-0017480. If now we regard the density of the solid 
nucleus as equal to that of the earth, the force of gravity at its 
surface will be equal to 27:37 .4; A denoting the sun’s attraction 
of gravitation at the distance of the perihelion of the comet 
(55,000,000), Let R denote the greatest actual repulsion of the 
nucleus and a its actual attraction, both as exerted at the surface 
of the nucleus, then p= R—a= R—27°37 A; and, for the particles 
— energetically repelled, we have 
“eng AS ll 3 R—27:37 A igs 
22134 Rap lO; OF Cie ae 70. Thus R= 182-28 A. 
Now, for the particles subject to the least actual repulsion from 
the sun, and to an effective attraction, 0°455 A, as they move off 
in their hyperbolic orbits, and which as we have seen go to make 
up the following side of the tail, we must take k= A—0-455 A= 
0545.4; and aeas 4=4060. For these particles we have 
p'='—a; and since we must suppose that the actual repulsive 
action of the nucleus will increase or decrease with the changing 
physical condition of the particle, in the same ratio as that of the 
R 18228 A 
sun ih ae, ee 
» we shall have R'= Por gar 44-9 A. Whence 
P= Rh —a=44:90 A~2737 A=1758.4. It thus nisin that if 
We assume its density to be the same as that of the earth, the 
nucleus would still exert an effective repulsion upon the particles 
Which gravitate toward the sun with the force 0:455 A, and are 
found distributed along the following side of the train. If we - 
Suppose the density of the nucleus to be 1-75 instead of 1, we 
obtain for the value of »', 2°05.A. But if it be assumed equal to - 
twice the density of the earth, we getp’=—310 4. Thus upon 
this supposition the effective action of the nucleus becomes an 
attractive force, and hence the particles under consideration could 
hot leave the nucleus. : 
It is to be observed that if p’ comes out a feeble pi eg force, 
as in the case in which the density is taken equal to 1°75, the 
Initial lateral velocity of the particles subject to its action must 
much less than the velocity (0™184) employed in our calcula- 
tions for the concave side of the tail, and that if a smaller lateral 
velocity be adopted the observed form and position of the con- 
