202 Prof. P. E. Chase on the Correlations of Central Force. 



£. Undulations in elastic media tend to generate other un- 

 dulations in arithmetic, geometric, harmonic, and various figu- 

 rate progressions. 



o. Radial oscillations through p = mr give the central disso- 



— mr 

 dating velocity v 2/r at —7; 1 ' 



it. If we take as determinants of a parabola a vertex at — 



solar radius, or the primitive circumference of complete asso- 

 ciation (77), and an abscissa at present surface of modular atmo- 

 sphere (v) %3 5 .s73 = 35*873 x modulus, the general equation 

 p^ = £?7±?i£' n2 furnishes 27 abscissas in regular progression, of 

 which 9 are between Sun and Mercury, 9 are between Nep- 

 tune and « Centauri, and the central 9 represent points of dis- 

 sociating nebular velocity (o), as will be seen by the following 

 Table :— 



n. 



Log Xn- 



Log sec. per. 



Log mean. 



Log sec. aph. 



mr+(m-t-l). 



987322 



1-6774 



1-6806 



1-7950 



1-8855 



1 $ 



10 87322 



19099 



1-8586 



1-8905 



1-9200 



i 2 



11-87322 



21541 



21256 



2-1561 



21845 



# © 



12-87322 



2-4102 



23248 



2-3901 



2-4468 



i c? 



13-87322 



2-6779 









i Art. 



1487322 



29575 



2-9420 



2-9692 



2-9949 



1 ^ 



15-87322 



3-2488 



3-2064 



3-2447 



3-2799 



I h 



16-87322 



3-5519 



3-5217 



3-5571 



3-5897 



1 6 



1787322 



3-8668 



3-8614 



3-8678 



3 8740 



f ¥ 



36-87322 



7-6622 



76571 





7-6860 



« Cent. 



The tabular logarithms for a Centauri (7-6571 and 7-6860) 

 represent respectively the least and greatest estimates that 

 have been made of its distance. The planetary secular peri- 

 helia and aphelia are the values computed by Stockwell 

 (Smithsonian Contributions, 232, pp. 37, 38). 



p. Weber, Kohlrausch, and Maxwell have identified the ve- 

 locity which connects electrostatic with electrodynamic action 

 with the velocity of light. These accordances extend the ma- 

 thematical correlation to heat (a to e inclusive), cosmical and 

 molecular aggregation, dissociation, rotation, and revolution 

 (a to 6 inclusive), gravitation (1 to tt inclusive), and all central 

 forces (a to h and ? to 6 inclusive, f, 0). 



