1879.] "°1 [Chase. 



force were retained. The parabolic velocity is the limit between the 

 tendencies to incipient aggregation and to complete dissociation, in the sub- 

 sidence of dense nebulous particles. 



In a body which is both revolving about the centre of a system and ro- 

 tating on its own axis, every particle is subject, during each half-rotation, 

 to cyclical variations in the systematic stress, which are antagonized by the 

 constant central force of the body itself. 



In a condensing or expanding nebula, the time of rotation varies as the 

 square of radius. At any given instant, the squares ot the velocities, or the 

 living forces of different rotating particles, are proportioned to the squares of 

 their radii, or to the times of nebular rotation and synchronous revolution 

 when condensed to their respective positions. 



If the velocity of synchronous rotation and revolution is determined by 

 the aggregate resistances of the central force of the nucleus, to cyclical 

 variations of stress which may be represented by a wave- velocity, while 

 the velocity of rotation of a detached planet is determined by a force which 

 may be represented by an incipiently aggregating or parabolic velocity, the 

 representative parabolic velocity of the nucleus may be found by taking 



i/2 



- — gt; g representing the force of gravity at any past, present, or future 



iz 



equatorial limit of the nebula, or Laplace's limit of possible rotating at- 

 mosphere, and t being ^ the corresponding time of synchronous rotation 

 and revolution. I have already shown that gt, in the solar system, is the 

 velocity of light. 



Let a represent the time of synchronous rotation and revolution when 

 Sun's surface should contract so that Laplace's limit would correspond with 

 its present equatorial radius ; ,?, a mean solar day ; y, Earth's mean dis- 

 tance -i- Sun's radius ; d, a sidereal year. Then a — d -=- y? ; tang. Sun's 



1 

 apparent semi-diameter = — . 



Y 

 According to Leverrier and Hansen, Earth's present aphelion, or limit 

 of incipient condensation, is at 1.016771 rad. vec. This corresponds, within 

 j^-is of one per cent., to Stockvvell's determination of the centre of the belt 

 of greatest condensation.* The relations between the primitive solar and 

 terrestrial centres are thus simplified, so that the foregoing considerations 

 lead us at once to the following equations: 



G) 



»f 



l" (9 



* The arithmetical mean between Mercury's secular perihelion (.2974307 j and 

 Mars's secular aphelion (1.7363251) is 1.016878. 



PROC. AMEIt. PHILOS. SOC. XVIII. 104. 2w. PRINTED DEC. 31, 1879. 



