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LVII. On the Nebular Hypothesis. — X. Predictions. By 

 Pliny Earle Chase, LL.D., S.P.A.S., Professor of Phi- 

 losophy in Have) ford College*. 



IN accordance with a suggestion of Professor Robert E. 

 Rogers, I endeavoured to find what modes of central 

 force will best represent some of the most general forms of 

 chemical activity, more especially those which are the base of 

 the law of Avogadro and Ampere — of combination by volume, 

 and of approximate constancy in the product of atomic weight 

 by specific heat. 



The simplicity of the ratio between the energy of H 2 and 

 the solar energy at Earth's mean distance f furnishes good 

 grounds for such an investigation, while the record of a para- 

 bolic orbit connecting the Sun with the nearest fixed stars J 

 indicates a proper course for conducting it. Although there 

 may be some doubt as to the degree of certainty which belongs 

 to the recent hypotheses of internal gaseous structure, there 

 can be none as to the graphic representation of orbital activi- 

 ties under forces varying inversely as the square of the dis- 

 tance. Circular orbits denote constancy of relations between 

 radial and tangential forces ; elliptic orbits, variability of rela- 

 tions accompanied by cyclical oscillations ; parabolic orbits, 

 variability of relations without cyclical oscillations ; hyperbolic 

 orbits, variability of relations complicated by the action of 

 extraneous force. 



In a rotating mass, the orbits of the several particles are 

 circular. If the uniform velocity of any particle in the equa- 

 torial plane is less than s/fr, the mean action of the central 

 force is impeded by internal collisions or resistances. If the 

 velocities of all the particles in the plane vary precisely as *Sfr, 

 there is a condition of perfect fluidity, marking a limit between 

 complete aggregation and incipient dissociation. Any cyclic 

 variations of velocity between constant limits indicate elliptic 

 orbits, with tendencies to aggregation through collisions near 

 the perifocal apse. A perifocal velocity of s/ 2fr marks a pa- 

 rabolic orbit, and a limit between complete dissociation and 

 incipient association. A velocity greater than n/2/t is hy- 

 perbolic, indicating the intervention of a third force in addi- 

 tion to the mutual action between the two principal centres of 

 reference. 



If all physical forces are propagated by aetherial undulations 



* Communicated by the Author. 



t Proc. Soc. Phil. Amer. xii. p. 324; xiii. p. 142. 



X Ibid. xii. p. 523, and subsequent papers. 



