1884, ] 597 
| Chase. 
In other words the Sun would weigh 328002 times as much as the Earth, 
if Harth’s orbit were always circular.* The remarkable accordances 
among the various harmonic estimates which are deduced from the corre- 
lations of mechanical, electrical, chemical, luminous and other forces, in- 
dicate an amount of probable error which is much smaller than those of ordi- 
nary astronomical estimates. 
431. Lunar Mass. First Estimate. 
Ferrel (Methods and Results, p. 20) gives '7989 metres as the height of 
the homogeneous atmosphere. The equilibrium of atmospheric elasticity, 
between the mutual interactions of Barth and Moon (Notes 8, 316), gives 
the following proportion : 
(20000000 + x) :'7989 : : 7, : 00125497, : : (x? x 80.74) 21 
432. Lunar Mass. Second Estimate. 
The estimates of the height of a homogeneous atmosphere differ for 
different latitudes and for slight variations in the elements of the calcula- 
tion, It may, therefore, be more satisfactory to deduce the Moon's mass 
from the simple principles of oscillation. 
From Notes 8, 162, 246, we find: 
t\? 2.08776 
l=g (=) = “Fag9  X (48082.04)? +- x? = 1142874 miles 
for the length of Harth’s theoretical pendulum. From this equation we 
deduce the ratio of Eurth’s mass (ms) to Moon’s mass (u), by the propor- 
tion : 
pg tbls ms tm. 
92524100 : 1142874 : : 80.957: 1 
433. Harth’s Secular Hecentricity. 
The harmonic relations of the Earth and Moon are still further shown 
by the evidences of original terrestrial projection before the Moon sepa- 
rated from the Earth. If we designate Harth’s secular perihelion radius 
vector by p's, we have the proportion, g, 7, (m5 ++ 2) : (Jy ty)? my 3: ere 
In other words, the orbital vis viva of original solar projection, for the 
combined masses of Earth and Moon, is represented by the mean radius 
vector, while the limiting oscillatory vis viva of the Earth alone is repre- 
sented by the radius vector of secular perihelion. Substituting in the above 
proportion the harmonic values which we have already found, we have 
269.766? X 81.957 ; 261.8194? x 80.957 :: 1 : 930462 
this gives, for Harth’s secular eccentricity, .069538, 
Stockwell’s estimate of this eccentricity for the value of Barth’s mass 
which we have deduced from its harmonic oscillation is .06901. The dif- 
* See Note 434, 
