1877.1 



507 



[Chase. 



ion of each belt into two pairs, the inner belt being denser than the outer, 

 and the inner member of each pair being denser than its companion ; Mer- 

 cury being denser than Venus ; Earth, than Mars ; Jupiter, than Saturn ; 

 V Uranus, than Neptune. This arrangement towards the Sun as a principal 

 centre, appears, however, to be of more recent date than the tendency to 

 condensation in the Telluric belt, for Earth is denser than Venus, and the 

 great secular ellipticities of Mars and Mercury suggest the likelihood of a 

 quasi -cometary origin. Similar tendencies would contribute to the chemi- 

 cal grouping of atoms by pairs, which is essential for polarity and for the 

 already enumerated laws of chemical combination. 



In the "nascent state," particles may be regarded either as paraboli- 

 cally perifocal, with the velocity of complete dissociation from a given 

 centre, or as relatively at rest, and ready to obey the slightest impulses ot 

 central force. The mean vis viva of a system formed by two such particles 

 would be m x (i/2) 2-fOT><0=:2mxl, representing a change from 

 parabolic to circular orbits and a condensation of two volumes into one. 

 At the parabolic limit between complete dissociation and incipient aggre- 

 gation, if the focal abscissa Xq= V F, 

 is taken as the unit of wave-length, 

 the value of the successive ordinates, 

 as well as the velocity communicated 

 by uniform wave influence acting 

 through the entire length of the 

 ordinates, will be represented by 

 1^4 X fi; the resulting vis viva, and 

 the consequent length of path, or 

 major axis, communicable against 

 uniform resistance, by 4 a; ^ ; the 

 successive difierences of major axis, 

 by 4. Each normal, v„ f„ _^ g, equals 



the next ordinate, v„ 



+ lfn 4- 1; 



there are, therefore, triple tenden- 

 cies, both in the axis of abscissas, and 

 on each branch of the curve, to suc- 

 cessive diff"erences of 4 in the major 

 axes of aggregation, in consequence of the meeting of abscissal, ordinal, 

 and normal waves in the axis,' and the meeting of tangential, normal, and 

 abscissal waves upon the curve. At each node of aggregating collision two 

 of the wave systems are due to normally alternating rectangular oscilla- 

 tions,* the third serving as a link between the axial and the peripheral waves. 

 The bisection of the normals, by their equivalent ordinates, adds import- 

 ance to the normal major axes, and increases the tendency to aggrega- 

 tion at their respective centres of gravity. 



♦"Fundamental Propositions," 13. 



