1874.] The Saturman System. a 
we shall at once perceive how different is his position as a 
ruler of matter compared with that of the earth. The mean 
distance of Saturn from the sun amounts to 872,137,000 
miles, and his mass is about go times the earth’s, or about 
I-3500th of the sun’s mass. Hence the sun’s influence 
equals Saturn’s at any point whose distance from the sun 
is to that from Saturn as the square root of 3500 to unity, 
or about as 59 to £. Hence a point on the line joining 
Saturn and the sun, and between these bodies, must be 
distant from Saturn 1-60th part of the distance of Saturn 
from the sun to be equally influenced by the sun and 
Saturn. This distance is about 14,500,000 miles from 
Saturn on the side towards the sun. On the farther side, a 
point equally influenced by Saturn and the sun would lie at 
a distance from Saturn equal to 1-58th part of Saturn’s 
distance from the sun, or at a distance of about 15,000,000 
miles. Hence the sphere over which Saturn bears supreme 
sway has a diameter of 29,500,000 miles. We have seen 
that the sphere over which the earth bears supreme sway 
has a diameter of only 327,000 miles. Hence Saturn’s 
sphere of rule is to the earth’s, in diameter, as 29,500 
to 327, or is about go times greater.* Here strangely 
enough the proportion go to I comes in yet again, not as 
the reader might imagine at a first view, as a necessary 
consequence of the same proportion go to I in the mass of 
Saturn compared to the earth’s, and in the square of his 
mean distance to the square of the earth’s, but inde- 
pendently—since it would not have appeared as the result 
of our calculations did not the sun’s mass bear to Saturn’s 
the proportion 3500 tor. The volume of the sphere ruled 
over by Saturn bears to the volume of the sphere ruled over 
by the earth a proportion of about 730,000 to unity; and it 
* It may be interesting to determine in the same way the extent of the 
sphere over which Jupiter bears sway. His mean distance from the sun 
amounts to 475,692,000 miles, and his mass is equal to about one ,,,,th part 
of the sun’s. Hence the influence of Jupiter and the sun are equal at any 
point, whose distance from Jupiter is to its distance from the sun as I to the 
square root of 1048, or as 1 to about 32. Hence we must take from Jupiter 
on the side towards the sun a distance equal to ,',rd part of Jupiter’s distance, 
and on the side away from the sun a distance equal to ,st part of Jupiter’s 
distance. These distances are respectively about 14,400,000 miles, and about 
15,300,000 miles; so that the sphere over which Jupiter bears superior sway 
has a diameter of about 29,700,000 miles, which may be regarded as about 
equal to the diameter of the sphere over which Saturn bears superior sway, 
I have spoken of the region over which a planet bears special sway as a 
sphere, and this is actually the case. It is manifest from the reasoning that 
the planet is not centrally placed within the sphere, but is nearer the side 
towards the sun. The sphere is manifestly not constant in dimensions, being 
larger or smaller, according as the planet is farther from or nearer to the sun. 
