1878. ] 295 [Chase. 
mass of Earth; /\ = density of Earth in units of Sun’s density ; 2? — 
bole 
- 4 2 A c : 
time of revolution at 2 7; 2% = radius of revolution for 2¢; 6 — Earth’s 
mean distance from Sun ; ¢= time of oscillation through major-axis equiva- 
ent to Sun’s possible atmosphere, or to 4 of Earth’s radius vector ; 4, = time 
of Jupiter’s revolution ; ¢, = time of Earth’s revolution ; 1.061 = Jupiter's 
secular aphelion ; 
radius vector, 
mean 
Sarre: ‘ : ee ta ie : 
It is evident, from equation (6), that — ea might be substituted for 
1 
A +A 
TUF i in the exponent of equation (1). 
In the undulations which are generated by the two controlling masses, w 
and p,, we may naturally look for harmonic interferences, not only in the 
light spectrum, but also in cosmical aggregations and in elementary molecu- 
lar groupings. If we compare » and y», at Jupiter’s present perihelion, we 
find that the product of Jupiter’s radius vector by its mass is 1.0153 times 
the product of Sun’s radius by its mass. Representing 1.0153 by n, and 
1 
1 
n+ a’ n+2a@ 
, etc., gives us the following nodal divisors and approximations, in 
taking a= 6  .0153 = .0918, the harmonic progression, 
nm+3a 
millionths of a millimetre, to wave-lengths of Fraunhofer lines : 
Denominators. Nodal Divisors. Quotients. Observed. 
1 1.0000 761.20 A 761.20 
m+a (f) 1.1071 687.56 B 687.49 
[1.1530 660.19] C 656.67 
n+ 2a 1.1989 634.92 
mn+3ua (f) 1.2907 589.76 D 589 74 
nm+4a 1.3825 550.60 
[1.4487 527.26 ] E 527.38 
n+5a 1.4748 516.31 6 817.70 
we Ce Cf) 1.5661 486.05 F 486.52 
n+Ta 1.6579 459.13 
n+8a 1.7497 435.05 G 481.038 
[1.7650 431.27] 
n+9a 1.8415 413.37 
[1.9180 396.87] H 397.16 
nm+10a (f) 1.9333 393.73 H! 393.59 
The harmonic interferences indicated by the series marked (7) are the 
most interesting, both on account of the closeness between the theoretical 
quotients and the corresponding observed values, and because the succes- 
sive denominator increments, are figurate. 
Of the remaining six lines, three (A, 0, G,) approximate so closely to the 
