Prof. P. E. Chase on Undulation. 295 



The following Table shows that, in planetary aggregation, 

 the interference-waves have manifested their influence most 

 strikingly at luminous intervals. The denominators are ex- 

 ponential, indicating roots which are to be extracted, instead 

 of divisions which are to be made. This is a natural conse- 

 quence of condensation in and through an elastic medium. It 

 will be noticed that the first six exponential denominators are 

 arithmetical means between the nodal divisors in the foregoing 

 Table, and that the others are formed by successive denomi- 



nator-increments of § c 



. 



Exponential 



~R nnfci 



denominators. 



J.iUV/tlJi 



1-0000 



6453 



1-0536 



4130 



1-1530 



2015 



1-2448 



1150 



1-3366 



708 



1-4284 



465 



1-5202 



321 



1-6350 



214 



1^7497 



150 



1-8644 



111 



1-9792 



84 



2-0939 



66 



2-2087 



53 



Observed. 



6453 



Neptune. 



4122 



Uranus. 



2050 



Saturn. 



1118 



Jupiter. 



728 



Freia. 



473 



Flora. 



327 



Mars. 



215 



Earth. 



155 



Venus. 



110 



Ven.-Mer, 



83 



Mercury. 



64 



„ s. p. 



53 



„ c. 0. 



The observed values are the mean planetary vector radii, in 

 units of Sun's radius. " Ven.-Mer." is the arithmetical mean 

 between Venus's mean distance (155) and Mercury's secular 

 perihelion (64). Mercury "c. o." is the centre of spherical 

 oscillation (\/ *4) of a nebula extending to Mercury's mean 

 distance. 



The following comparisons show a few of the many har- 

 monies which are found in the prominent lines of chemical 

 elements. The wave-measurements in all the spectra, both 

 solar and chemical, are taken from the papers of Prof. Wolcott 

 Gibbs, in the ' American Journal of Science', second series, 

 vols, xliii., xlvii. KirchhofF's lines are indicated by K ; Hug- 

 gins's by H; Gibbs's groupings of corresponding lines in 

 the groupings of both KirchhofF and Huggins by KH — the 

 left-hand columns containing Kirchhoff's estimates, and the 

 right-hand columns those of Huggins: — 



