6 The Saturnian System. (January, 
with distance ;* but the latter is, as it were, accidental, since 
there is no necessary connection between the mass of any 
planet and the distance at which it travels. It is worthy of 
notice, as a convenient aid to the memory, that while the 
area swept out by Saturn is about ninety times that swept 
out by the earth, and solar heat, light, and gravity at Saturn 
about one-ninetieth less than at the earth, the mass of 
Saturn exceeds that of the earth about ninety-fold. It is 
manifest, then, that Saturn must be regarded as a much 
more efficient ruler over the region of space along which he 
circles than the earth can possibly be over the region 
of space through which she travels. Or rather, it is 
manifest that the range of Saturn’s influence is much 
wider. So feeble is the earth, so narrow is the sphere 
of her special influence, that even her own moon is far 
more fully under solar influence than under terrestrial 
rule. In fact, if we remember that the sun’s mass is about 
315,000 times that of the earth, we see that his influence 
equals hers at any point whose distance from the sun is to 
that from the earth as the square root of 315,000 to unity, 
or about as 561 tor. Now since the distance of the earth 
from the sun is about 91,500,000 miles, a point on the line 
joining the earth and sun (and between these bodies) 
must be distant from the earth 1-562nd part of this distance 
to be equally influenced by the sun and earth. This 
distance is rather less than 163,000 miles, whereas the 
moon’s distance from the earth amounts to 238,800 miles. 
A point beyond the earth on the line joining the sun and 
earth produced should be at 1-560th part of g1,500,000 miles 
from the earth, to be equally influenced by the earth and 
sun, that is about 164,000 miles. This is the farthest point 
from the earth at which her influence equals that of the 
sun; and if a sphere be described in space at any instant, 
having the line joining this last-named point and the one 
before determined (163,000 miles from the earth’s centre 
towards the sun) as diameter, then at all points within this 
sphere with its diameter of 327,000 miles or thereabouts, 
the earth acts more potently than the sun; but everywhere 
else she acts less potently. Now let us apply a similar 
process to Saturn, in order to ascertain the dimensions of 
the sphere over which his power is, as it were, supreme, and 
* Since the area swept out by a planet in completing its orbit varies directly 
as the square of the mean distance, while light, heat, and gravity vary inversely 
as the square of the mean distance, it follows that the light, heat, and attraction 
influencing bodies revolving around the same central sun vary inversely as the 
area of their orbits. 
