Chase.] '^^^' [April 15, 



24. Satellite Velocity at the Centre of Density. 



The influence of Laplace's limit appears in satellite velocity as well as in 

 velocity of rotation (Note 17), at the centre of condensation in the solar 

 system; thus lending added significance to the stellar-solar paraboloids.* 

 K I designates the limit of synchronous rotation and revolution, it is evi- 



3 JL ff^ 3 JL 



dent, from Kepler's third law, that - Z^ {gry^ ~ T' ^"^ -^'"■^'^ (6"")'^ 



1 



(1 + e) 3 ^^xelodty ofliglit. If we take Earth's semi-axis major as the 



unit-length of linear oscillation, the velocity which corresponds to the 



/2\i . , . 



mean linear t;i8 ?Ji«;a is \~o ) ; the accelerating limit of satellite velocity 



86164 

 divided by velocity of equatorial rotation is ka~o~5 = 16.9828 ; the nascent 



vis viva of nebular atmospheric condensation divided by mean orbital vis 

 viva is [r (1 -f- «)*]' ; the vis viva of terrestrial projection, in units of nu- 

 cleal condensation, is n. The projection against uniform resistance, or the 

 synchronous rotating velocity which is due to such projection, is propor- 

 tioned to the vis viva, and we find that 



(I)* 



y-j : 16.9828 :: tt^ X 1.016773 : n = 214.59 



This value of n differs by less than y\ of one per cent, from the one found 

 by Note 17. Such accordance in the successive transformations of photo- 

 dynamic energy into energy of rotation and of revolution gives new evi- 

 dence of the kinetic importance of Earth's position at the centre of 

 belt-condensation. 



If we treat e and n as unknown quantities, and find their values by com- 

 bining the methods of Notes 17 and 20, we get 1 -[- e = 1.01662 ; n = 

 214.51. This value of e differs by less than -^^ of one per cent, from the 

 observed value, 1.01677. If we treat n and the constant of aberration as 

 unknown quantities, we find n = 214.59 ; time of light propagation from 

 Sun, 497=. 423. 



25. Satellite Velocities in tTie Dense Belt. 



3 1 ft 



The equation, jzP (fry^ = i^, is true in all cases of radiodynamic cen- 

 trifugal or centripetal influence, whether cosmical or molecular. The range 

 of uncertainty respecting the masses, densities, and axial rotations of the 

 other planets, is too great to justify any attempts at precise measurement of 

 their dependence upon sethereal or photodynamic influence, but some inter- 

 esting comparisons may be drawn between the central and collateral ener- 

 gies in each of the great planetary belts, which furnish suggestive indica- 

 tions for future precise observation and analysis. If we refer the satellite 

 velocities of the dense belt to photodynamic energy at the centre of the 

 belt, by taking Earth's limiting velocity as the unit, we may designate 

 the limiting velocities for Mercury, Venus, Earth, and Slars, by fj, v^, v^, t;^, 



*Proc. Am. Phil. Soc, xii, 518; xix, 20S; ct al. 



