Chase. ] 110 [July 20, 
less than four ten-millionths of a millimetre, and, therefore, very far 
within the limit of probable errors of observation. 
My papers on planetary harmonies have shown that alternate planetary 
positions manifest the greatest simplicity of law, intermediate positions 
being modified by requirements of mutual equilibrium, which help to give 
stability to the system. The same thing seems to be true of the Fraun- 
hofer lines. The ‘‘figurate’’ symmetry of the above divisor differences 
(1a, 3a, 6a, 10a) is especially noticeable, and suggestive of my equation 
between the principal planetary masses : 
(Neptune) 'x (Uranus) *x (Jupiter) °x (Saturn) —'=1. 
After finding this relation among the most important lines, I sought for 
traces of the ‘‘morning-star’’ music among the subordinate lines, with the 
following result: I have introduced Kirchhoff’s scale-measurements, in 
order that the lines may be identified without the necessity of reference to 
Dr. Gibbs’s papers. 
Divisors. Quotients. Observed values. Scale measurem’ts. 
n+ 2a 635.07 634.05 783.8 
n+ 4a 550.72 550.70 1306.7 
n+da 516.42 517.15 1655.6 
n+ Ta 459.22 458.66 2436.5 
n+ 8a 435.12 435.67 2775.7 
n+9a 413.43 (413.76) (2) 
There is no single line corresponding to the harmonic denominator 
n+ 9a. The bracketed number is the arithmetical mean between Kirch- 
hoff line 2869.7 —= 430.37, and H = 397.16. This again, may either indi- 
cate a bright line, or it may await future discovery for a true inter- 
pretation. 
The equality, which I had previously pointed out, between the average 
limiting velocities of solar centrifugal and tangential dissociation, and the 
velocity of light, induced me to apply the same harmonic series to the solar 
system. In some of the papers on cosmical and molecular force, which I 
have had the honor of communicating to the society (Proc. Soc. Phil. 
Amer. vol. xiii.), I had taken steps in this direction, but they were com- 
paratively feeble, for want of sufficient definite guidance. They had, how- 
ever, shown very clearly, that, in ultimate physical generalizations, the 
study of elastic reaction is quite as needful as the] study of centripetal 
action, and vice versa. One of the most important facts, in connection 
with such comparative study, is the variation of elastic density in geomet- 
‘rical ratio, when distance varies in arithmetical ratio. In making an 
operative application of the spectral harmonic series, the several terms 
should therefore be taken exponentially, and the greatest activity should 
be looked for at inter-nodes, and presumably nearly midway between suc- 
cessive nodes. The Sun’s radius was naturally suggested as a fundamental 
unit. 
The process of calculation is nearly as simple as Columbus’s egg, but, on 
