252 Mr. P. E. Chase on the Cosmical Activity of Light. 



cipal limits of the planetary belts*. Within those limits, pla- 

 netary positions may be referred to simple circular pendulums, 

 which are so jointly related that their harmonic vibrations tend 

 to maintain the stability of the system. 



The time of rotation for a given radius varying as the f power 

 of the time of revolution for same radius, the theoretical distance 

 of each planet, in solar radii, may be found by multiplying the 

 § power of its number of pendulum units by the unit of distance, 

 which is | Sun's radius, Sun's surface being at a centre of ex- 

 plosive oscillation (fxf xf = 1). Symbolizing each pendulum 

 by its planet's initial letters, we have the following synopsis of 

 theoretical and observed distances . — 





Number of 



pendulum 



units. 



(A) Theore- 

 tical mean 

 distance. 



(B) Actual 

 mean dis- 

 tance. 



(A-B)-KB). 



Me 



15 



24 



30 



42 



105 



168 



280 



392 



83-23 



155-76 



209-74 



328-48 



1114-75 



2085-75 



4121-54 



6455 03 



8317 



155-42 



214-86 



327 38 



1117-87 



2049-51 



4121-78 



6453-06 



+•0007 

 +•0022 

 -•0239 

 + •0034 

 -•0028 

 + •0177 

 -•0001 

 + •0003 



Ve 



Ea 



Ma 



Ju 



Sa 



Ur 



Ne .. 





Column (A) exactly represents planetary positions- — although, 

 on account of orbital excentricities and joint perturbations, it 

 gives mean positions only with a very close approximation. 



If we take as our unit pendulum (^) 3 of solar radius, the 

 several planetary pendulums will represent the accordant radii 

 of solar rotation, or the radii of solar expansion at which Sun's 

 rotation would be synchronous with planetary revolution. The 

 following comparison gives two theoretical values — (I.) in which 

 the unit is -J-, (II.) in which the unit is increased by the ratio of 

 Neptune's mean excentricity, 1 per cent. : — 





No. of pen- 

 dulum units. 



I. Theo- 

 retical. 



1 875 



3000 

 3-750 

 5250 

 13125 

 21-000 

 35 000 

 49-000 



II. Theo- 

 retical. 



Actual. 



I. Error. 



II. Error. 



Me 



15 

 24 



30 

 42 

 105 

 168 

 280 

 392 



1-894 



3030 



3-787 



5-302 



13-256 



21-210 



35-350 



49-490 



1-892 



3023 



3-855 



5-287 



13-279 



20923 



35 334 



49-454 



-0272 

 -0090 

 -0074 

 -•0070 

 -•0116 

 + •0037 

 -•0095 

 -0092 



-0176 

 + 0001 

 + •0023 

 + •0028 

 -•0017 

 + •0137 

 + •0005 

 + •0007 



Ve 



Ea 



Ma 



Ju 



Sa 



Ur 



Ne 





* My harmonic anticipation of planetary or asteroidal matter at a dis- 

 tance from the sun equivalent to "269 of Earth's mean radius vector, which 

 was so promptly confirmed by the sun-spot observations of De La Rue, 

 Stewart, and Loewy, is still further corroborated by the recent papers of 

 Leverrier. 



