1884.] 599 [Chase. 
487. Mass-Relation of Harth and Venus. 
The simplicity of the harmonic mass-relations between Sun and Earth, 
as well as between Jupiter and Saturn, increases the likelihood of similar 
relations, which are equally simple, between Earth and Venus; but the 
wide range of discrepancy among the estimates of different astronomers 
makes it somewhat difficult to ascertain what rhythmic influence has 
prevailed, Stockwell’s estimate of Venus’s mass is about .945 of Earth’s 
mass ; Hill’s is only .831 ; Leverrier’s mean of two estimates, .872. The 
value which would give Harth and Venus equal orbital momenta is .85049. 
We may, therefore, claim a great probability for the proportion, mp : mg 
: 1 (829196 -- .85049 = 887066) : 1. 
438. Mass-Relation of Neptune and Uranus. 
In the exterior twin planet belt, we find a harmonic mass relation which 
is no less striking than those that have already been given. It is es- 
pecially interesting, as pointing to an early stage of nebular condensation, 
as well as to a blending of external and internal influences which accounts 
for retrograde satellite rotation and revolution. The gravitating accelera- 
tions, which are due to the actions and reactions between two cosmical 
masses, are proportioned to the respective masses. The vis viva of gravi- 
mv 
tating subsidence ( 5 ) is, therefore, proportioned to the cube of the 
2 
masses. We find, accordingly, that 
Me sm? +3 pg! : py 
In this proportion ps’ Yrepresents the locus of incipient subsidence, or 
secular aphelion of Neptune, while p; represents the mean radius vector 
of Uranus. The values which satisfy this proportion are very exact, as 
will be seen by the following comparison : 
Harmonic, Newcomb. 
Sun -+- Neptune 19872.86 19380 -+ 70 
Sun + Uranus 22603.88 22600 +: 100 
439. Mass-Relation of Mars and Mercury. 
The Earth appears to have exercised an influence upon the two ex- 
terior planets of the belt of greatest condensation, analogous to that which 
the Sun has exercised upon Neptune and Uranus. We find, accordingly, 
MPs mP ss py? pr 
In this proportion, if we let , and p, represent the mean distances of 
Mars and Mercury, respectively, the mass of Mars would be 1.5789 times 
that of Mercury. Adopting Hall’s estimate of Sun +- Mars = 3093500, 
we find Sun + Mercury = 4884366. Encke’s estimate is 4865751. These 
estimates are based upon the hypothesis that Sun + Earth = 854936. If 
we substitute the harmonic value, 829196, we get Sun ~ Mars == 2869151 ; 
Sun + Mereury = 4530150. 
PROC. AMER. PHILOS. 800, xxt. 116. 8x. PRINTED JuLY 381, 1884. 
