1881.] 4:51 [Chase. 



fying action of its constituent bodies is concerned. The particles of a star 

 or nebula, exposed to sethereal oscillations, are solicited simultaneously 

 towards the local and towards the universal centre of gravity. The accel- 

 erations, relatively to the stellar or nebular centre, on the side towards the 

 universal centre, and the retardations on the opposite side, necessarily 

 produce rotation. The duration of the rotation must be such as to main- 

 tain cyclical equilibrium among the three activities of general luminous 

 undulation, general gravitation and local gravitation. 



Ectuality of action and reaction should lead to harmonies of vis viva and 

 of mass, which may become especially prominent when there are two 

 largely preponderating bodies in a system, as in the case of Sun and Ju- 

 piter. Their mutual actions and reactions, being exerted through a com- 

 mon radius, are proportioned to their masses. The mean vis viva of rotation 

 being represented by a virtual projection of mass through Ar, if Ave con- 

 sider the modulus of light as the virtual projection due to Sun's mass dur- 

 ing the cyclical disturbances of equilibrium, we may suppose 

 Sun's mass : Jupiter's mass : : Modulus : .4 Jupiter's semi-axis major. 



1047.879: 1 :: 474657.14 : 453 



Jupiter's semi-axis major is 5. 2028x214.45 = 1115. 74; .4 of 1115.74 = 446.3. 



The theoretical projection is, therefore, 1.0149525 times the mean-pro- 

 jection, and there is an exact accordance, twice during each revolution of 

 Jupiter around the Sun. For, according to Stockwell,* the secular mini- 

 mum value of Jupiter's eccentricity is equal to .0254928. Neptune's 

 maximum eccentricity, according to the same authority, is .0145066, and 

 ^ of the mean eccentricity of Uranus is .0149538. These accordances seem 

 significant, in view of Jupiter's central nebular position between Uranus 

 and Neptune, at their opposition. 



49. Further Stellar Relations of Mass. 



The paraboloidal formula, x^^ = rr,"C", may be expressed under the form 

 x^ = ^ (yj ^^" ^™ the successive terms being found by the product of cor- 

 responding terms of two geometrical series. They may, therefore, be 

 taken to represent the mutual actions and reactions of two co-ordinate 

 masses, like Sun and Jupiter. The geometric variations of density, which 

 accord with arithmetical variations of distance, suggest the proportion, 

 (Note 46) : 



Sun's mass : Jupiter's mass : : a-^g : 39 X Jupiter's semi-axis major. 

 1047.879 : 1 : : 46379946t : 44260.8 



This gives, for Jupiter's theoretical semi-axis major, 44260.8 -=- 39 = 

 1134.9, which is 1.017165 times the estimate of the British Nautical Al- 

 manac (Note 48). This is less than the secular minimum aphelion of 

 Jupiter, so that the locus is traversed twice during each revolution of Ju- 

 piter about the Sun. 



* Smithsonian Contributions, 232, p. 38. 



t The logarithm of 3:39 being 7.6663302, the abscissa itself is 46379916 ?'o. 



PROC. AMER. PHILOS. SOC. XIX. 109. 3e. PRINTED JULY, 16. 1881. 



