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POPULAR SCIENCE REVIEW. 
its velocity at given distances from the sun. Thus, when at 
the distance of Neptune its velocity would be 4*7 miles per 
second; at the distance of Uranus, 5*9 miles per second; of 
Saturn, 8*3 miles; of Jupiter, 11*3 miles; of the asteroids, 
from 15 to 16 miles per second; and the velocity in crossing 
the distances of Mars, the Earth, Venus, and Mercury, would be 
20*8 miles, 25*9, 30*3, and 41*4 miles per second repectively. 
Now we know that the greatest velocity which any given 
planet can communicate to a body approaching it under its 
sole influence from interstellar space is very much less than the 
velocity which such planet can communicate to a body approach- 
ing it under the sun’s influence in addition to its own, for the 
communication of velocity to a moving body is a process 
requiring time, and in the latter of the two cases just con- 
sidered the body is for a much smaller time under the in- 
fluence of the planet.* And the velocity which a planet can 
the particle he supposed to come from the distance of the nearest star or 
from an infinite distance. This is easily seen from the formula 
where r represents the radius of a circular orbit described with velocity 
and V is the velocity at distance r, of a body travelling in an orbit having 
mean distance a. For regarding the earth’s orbit as unity, put 
r = earth’s distance = unity, 
v = earth’s velocity = 18*3, 
taking a mile as the unit of length, and a second as the unit of time ; 
for though we have put r = unity, this does not force us to take r as our 
unit of length, because we only require to consider the ratio in what follows.. 
Then we have — 
if a is made infinite. But if a be taken equal to half the distance of Alpha 
Centauri, say = 100,000, we have 
V = 25-9 - 0-00006475 - 0-000000000809375 - smaller terms, 
all the terms after the first being together manifestly less than 0-00007, or 
about 4^ inches. In other words, whereas a body approaching the sun from 
infinity would have a velocity of about 25-9 miles per second, a body ap- 
proaching the sun from the distance of Alpha Centauri, so that its mean 
distance may be regarded as half the distance of that star, would have a 
velocity less by 4£ inches per second, a difference so small that it may be 
regarded as evanescent. It is a curious consideration, however, that minute 
though such differences are when we are merely comparing velocities, yet 
distances due to such differences in the enormous time-intervals which the 
study of comets introduces to our consideration, are to be measured by 
thousands of miles. 
* The comparison is easily made in any given case. Take, for instance, 
the planet Jupiter, supposing it at rest, and a particle drawn towards it 
