148 The Birth and Evolution [March, 
form the more complicated mechanism of the whole 
system. 
We thus have the solar distances of the two central 
masses — • 
mi=i:r8 7 . 
IIl6 Y 
Observation gives the densities of sun and planets. Slight 
differences of density between those observed and here 
deduced are irrelevant, for nothing is more uncertain than 
the exadt mean diameter of planets, and for density the 
error increases to the cube. 
Observation gives, if the density of the earth be taken 
as 1, that of the sun 0*252, of Jupiter 0*243. The density 
of solar and planetary mass was equal, but Jupiter remained 
1*05 this side of the point of gravitation ; so much less was 
it condensed, we have its density 1-1*05 of that of the 
Sun, or — 
0*252 
— — = 0*240 
i*05 
of that of the Earth. Observation gives the density of 
Saturn 0*140. It is— 
^ = 1-8 = 172 xro 5 = -^i. 
0*140 1*025 
The density of Saturn is so much less than that of the Sun 
as its distance is greater than that of Jupiter when divided 
by that distance which it moved beyond its ideal position. 
This farther distance increases its density, as that of Jupiter 
is less by its remaining this side of the point of gravitation. 
The density of Saturn to that of Jupiter is therefore 1 to 1*72. 
Observation gives the mass of the Jupiter system 1-1047*8 
of the Sun ; of the Saturn system, 1-3501*6. The former 
contains 3*345 more mass than the latter : 1 to 1*84 is the 
solar distance of Jupiter to that of Saturn ; i* 84 2 = 3*45, or 
inversely as the squares of distances are the masses of the 
two central concentrations, or Saturn is — 
1 
172 2 x (105 x 1025)* 
of the mass of Jupiter. 
The planetary rotation, 77*3 times more rapid than that 
of the sun, became diminished by the opposing centrifugality 
of the sun, gradually diminishing the oblateness of the 
