1881.1 uOl fChase. 



The accordance between the nodal and the computed values is shown in 

 the following table : 



The mean orbital ^•^s viva which could be communicated to a subsiding 

 particle in any given time, varies directly as the mean gravitating accel- 

 eration, I — I , and inversely as the mean subsidence potential, | ~ J. 



The synchronism in the determination of the tos w'tiaof the two chief plan- 

 ets is shown by the proportion 



m, r^-m^r,- : h' i\ ■ n^ 1^0 (15) 



which is readily deduced from (7). The confirmation which this lends to 

 Herschel's interpretation of the nebular hypothesis is very satisfactory. 



The planets of the dense belt bear witness to an interesting combina- 

 tion of harmonic influences. The simple attraction of a principal centre 

 of condensation would tend to produce radial oscillations and very ellipti- 

 cal orbital paths. If the central force could be concentrated in a point, 

 the elliptic path would coincide with the major-axis and be rectilinear, its 



orbital time being 2-"^ — ^mj h^q mean velocity being ^ V gr ; g repre- 

 senting the acceleration of the central force at the distance r. If the rad- 

 ial oscillations are made circular, (through the mutual collision of par- 

 ticles, the exchange of molecular vis viva for vis viva of rotation or of 

 revolution, external attraction and other physical disturbances), the orbi- 



gt 

 tal velocity should be some function of the nascent velocity, ^ . 



The combined orbital vis viva of Earth and Jupiter, (1), suggests the 

 consideration of nebular subsidence from Moon's apogee towards the 

 mean centre of gravitj^ of Jupiter and Sun. In expanding or contracting 

 nebulae, rotating velocity and circular orbital vis viva both vary inversely 

 as radius. In considering ultimate particles or chemical atoms of equal 

 volume, the mass and the limiting or maximum acceleration both vary 

 as the density ; the limit of gravitating vis viva, therefore, varies as the 



cube of the density, (8 X d''^ = S^) and centrifugal vis viva varies as -^ . 



Circular orbital or tangential atomic vis viva varies directly as density and 



