Prof. P. E. Chase on Undulation. 293 



radial velocity of complete solar dissociation 



4 x 214-86^7rp m 



" number of seconds in 1 year ' 



t = time of oscillation through major-axis equivalent to Sun's 

 possible atmosphere, or to J of Earth's radius vector ; Tj = 

 time of Jupiter's revolution ; t. 2 = time of Earth's revolution ; 

 t 3 = time of Earth's rotation ; p = Sun's equatorial radius ; 

 p x = Jupiter's projectile radius, or mean perihelion distance 

 from Sun ; n = special coefficient of Earth's dissociation velo- 

 city {ivKs/fr)\ n x = special coefficient of Jupiter's dissociation 

 velocity (n 1 ir\/fy'^)', 8 = Earth's mean distance from Sun ; 

 B 1 = Jupiter's secular perihelion distance from Sun ; B 2 = 

 Uranus's mean distance from Sun ; 2^ = relative radius of re- 

 volution for 2r a ; 2% = relative time of revolution for 2r a ; 



-, nn-> t -x 9 secular aphelion ,. 



1*061 = Jupiter s radius vector. 



r mean 



To illustrate the closeness of the accordances, if we substi- 

 tute in (1) the actual values, viz. \=/3-i- 2*317, \ 1 = p-'-344*15, 

 p = l, pi = 1069*62, the equation reduces to 



(^±^Y'° 029 = 1070*62; .-. ^±^ =1049*24. 



Bessel's estimate is 1048*88, differing from the theoretical 

 value only ^ of one per cent. 



The significance of Earth's position, at the centre of the 

 belt of greatest condensation, of the positions of Jupiter and 

 Uranus, as inner planets of the two exterior two-planet belts, 

 of the masses of Sun, Jupiter, and Earth, as the principal 

 masses, in the system, in the extra-asteroidal and in the intra- 

 asteroidal groups, and of the many important relations to the 

 limiting velocity of luminous undulation, is thus clearly shown. 



In the sethereal waves which are generated by the two con- 

 trolling masses, //, and fi^ we may naturally look for harmonic 

 interferences, not only in the solar spectrum, but also in ele- 

 mentary molecular groupings and in cosmical masses. If we 

 compare //, and ix x 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 a, and taking c = b(a — l) = 0*918, we may form the 



harmonic progression — — ? 9 • Q , &c, thus obtaining 



the following nodal divisors and approximations, in millionths 

 of a millimetre, to wave-lengths of Fraunhofer lines : — 



