Chase.] 2i2 [April 21, 



2. The nodal modification of Neptune's mass by Earth's secular aphelion, 

 and of the mass of Uranus by Earth's secular perihelion. 



3. The nodal modification of Neptune's mass by its own mean perihelion, 

 and of the mass of Uranus by its own mean aphelion. 



4. The modification of Uranus by Jupiter, and the corresponding modi- 

 fication of Neptune by Uranus. 



167. Earth's Modulus of Rotation and Jupiter's Eccentricity. 



Let g^ represent the sum of the gravitating accelerations of Sun and 

 Earth at Earth's equatorial surface ; t, time of Earth's rotary oscillation 

 (^ sidereal day); «„, Sun's equatorial semi-diameter; r,, Earth's semi- 

 diameter ; n , mean projection of centre of gravity of Sun and Jupiter 

 from p^; o^ -h «„, Jupiter's maximum secular eccentricity ; p.^, Eaith's 

 semi-axis major ; (j^f, Earth's modulus of rotation. Then 



S'^^' -ps-'Pa' po- 

 The photodynamic or oscillatory values of Sun's mass and distance, Note 



in / 7' \ 2 

 91. give for Sun's gravitating acceleration of Earth — ^ ( — ) = 331776 X 



-~ 92785700)2 = .000605184 of Earth's equatorial gravitating accel- 

 eration. If we adopt Everett's value for g, g^t'^ = 1.000605184 X 32.091 

 X 430822 ^ 5280 = 5643840 miles ; p^^ -^ p^ — .0608265. Stockwell's value 

 {Smith. Oont., 232, p. 38), is .0608274. 



168. Axis of Central Subsidence and Rupture. 



The influence of the interstellar photodynamic paraboloid is shown in 

 the boundaries of the belt of greatest condensation. The locus of incipi- 

 ent rupture, Mercury's secular perihelion, is about I of the locus of incipi- 

 ent subsidence, secularaphelionof Mars. Stockwell's values for the two loci 

 are .2974008 and 1.736478. This gives for the major axis of the several in- 

 cipient ellipses, described by the subsiding particles from the outer portion 

 of the belt, .2974008 + 1.736478 = 2.0338788. Let g^, g., represent equa- 

 torial superficial gravitating acceleration of Sun, Earth, respectively ; %, 

 ?%, masses of Jupiter, Earth ; ta, time of Jupiter's orbital revolution ; t^, 

 time of Earth's rotation ; ^3, Earth's semi-axis major ; p^, asteroidal radius 

 equivalent to major axis of incipient ellipses of dense belt. Then 



