CLASSIFICATION OF COMETS. 
357 
communicate under any circumstances represents the velocity 
which, under similar circumstances, the planet can withdraw 
from a moving body. So that Jupiter, Saturn, Uranus, and 
Neptune, are severally unable to deprive a particle which, drawn 
in by the sun’s attraction, passes near to them, of more than a 
portion of the velocity which these planets are respectively able 
to communicate to a body approaching them from infinite 
space. Taking, for example, the case of Jupiter, we may regard 
40 miles per second as a sort of negative fund from which Jupiter 
would have the power of drawing, to reduce the velocity of 
Todies moving from him, if Jupiter were the sole attracting 
influence under which such bodies had acquired their velocity ; 
but in the case of bodies which have been drawn inwards by the 
sun’s attraction, the fund is reduced, as shown in the note be- 
low, to about 30*3 miles per second. Now this might seem 
•ample when we remember that the velocity of a body crossing 
the path of Jupiter under the sun’s influence alone would be but 
11*3 miles per second. But it is to be observed that the estimate 
only applies to bodies moving all but directly from Jupiter, and 
•coming all but into contact with his surface. The power of 
Jupiter in this respect diminishes rapidly with distance from 
the surface. At a distance from Jupiter’s centre equal to four 
times his radius, his power is already diminished one half, and 
this distance is far within that of even his nearast satellite. 
Moreover, it is to be noticed that a body which moves in such 
from an infinite distance under the combined influence of the sun and 
planet (the particle lying originally on the side away from the sun). We 
readily obtain for the velocity V of the particle just as it is reaching the 
surface of Jupiter the equation 
F 3 = 2 M • 
J +J j ’ 
where M represents the sun’s attractive influence at a unit of distance, and 
m Jupiter’s, while J represents Jupiter’s distance from the sun, and j the 
.radius of Jupiter. Tor the velocity v of a particle under Jupiter’s sole in- 
fluence we obtain the equation v 2 = ?L^1, Now it is easily calculated that 
-- 2 -j f T - = (1T3) 2 , while ^ = (40) 2 nearly. Hence the velocity 
J + J J 
V = s/ (11*3)* + (40) 2 = less than 4T6 ; while v = 40- so that a body 
•approaching the sun under his sole influence would have, at Jupiter’s dis- 
tance, a velocity of 11-3 miles per second ; one approaching Jupiter under 
the combined influence of the sun and planet would reach Jupiter’s surface 
with a velocity of 41*6 miles per second; and a body approaching Jupiter 
under his influence alone would reach his surface with a velocity of 40 
miles per second. So that Jupiter helping the sun adds a velocity of 30*3 
miles per second as compared with the velocity of 40 miles per second, 
which he can communicate to a body approaching him from infinity. 
