1880,] «' [Chase. 



uo\y generally adopted bj"" astronomers. The semi-axes major are repre- 

 sented by p ; the superficial equatorial acceleration of gravity, by g ; the 

 densit}^ by 8 ; Earth's values being assumed as the units. In tlie expres- 

 sions for g of Saturn and Uranus, p^ = 8.539 ; t = 16.9823 ; p-^ being the 

 mean distance between tlie centre of the belt of greatest condensation 

 (Earth) and the primitive centre of rotary inertia (Saturn); i being the 

 ratio between the time of Earth's rotation (a sidereal day) and the limiting 



time of satellite-revolution f 2~-J — , at Earth's equatorial surface J. It is 



impossible, at present, to assign any more probable values for the planetary 

 radii than those which I have given under ?'(II). From those values and 

 the masses, g and d are readily found by tlie proportionalities, 8 oc m -=- r^; 

 g oc m H- r'^. The relations of ^ to simple functions of the semi-axis major 

 would be very striking, even if they were only approximately true. 

 Although we cannot ascertain whether the relations are exact or not, the 

 following considerations seem to increase the probability that they are cor- 

 rect indications of normal harmonic modifications of gravitating force by 

 distance and time. 



In comparing the gravitating force at the principal centres of early nebu- 

 lar activity, we may, tben, acknowledge a strong probability : 



1. That the force at the centre of reciprocity (Neptune), is one half as 

 great as at the centre of the belt of greatest density (Earth). 



3. That the force at the centre of rotary inertia (Saturn), is to the force 

 at the centre of density, as the rotary centripetal force at Sun, is to the ro- 

 tary centripetal force at Earth, the rotating tendencies being referred to 

 Saturn as a centre. 



3. That the force at the centre of nebulosity (Jupiter), is to the force at 

 the centre of densitj-, as the combined influence of the gravitating force at 

 the centre of reciprocity and the rotary centripetal force at Jupiter, is to 

 the combined influence of the corresponding forces at Earth. 



4. That the force at the centre of nucleation (Sun), is equal to the 

 velocity of light, divided by the time of a half-rotation ; the half-rotation 

 indicating the alternate oscillation of equatorial particles, from and towards 

 the centre of gravity of Sun and Jupiter. 



In extending the comparison to the subordinate centres within the belt 

 of greatest condensation, we find a like probability ; 



5. That the force at Mars is to the force at the centre of density, as the 

 combined force of gravitating vis viva at the centre of reciprocity and 

 rotary centripetal force at Mars, is to the corresponding combined in- 

 fluences at Earth. 



6. That the force at each of the inferior planets (Venus and Mercury), is 

 represented by the ratio of projectile living forces to times of revolution. 



Leaving the outer and somewhat doubtful territory, and entering upon 

 surer ground, let us consider some of the obvious results of conversion of 

 primitive force, with reference to centres of condensation. 



