Chase. I Z4\) [May land 15, 



suggests a primary planetary ellipse iu which the transverse is to the 

 conjugate axis in the proportion of 2 to j/3. In such an ellipse the two 

 foci and either extremity of the transverse axis represent the extremes 

 and centre of oscillation of a linear pendulum ; parallels to the lines 

 joining the foci to either end of the conjugate axis, trisect the quadrant 

 and semicircle ; the virtual velocity of oscillation at the end of the sup- 

 posed rigid transverse axis, is to the velocity at the end of the conjugate 

 axis, as the velocity of infinite fall to the. extremity of the transverse 

 axis is to the velocity of revolution at its linear centre of oscillation. 



Let A and D represent the ends of the transverse axis, B and C the 

 foci of the hypothetical ellipse. Let a denote planetary aphelion ; p, 

 perihelion ; m, centre of gravity, at secular mean conjunction, of Nep- 

 tune and Uranus ; ?i, mean conjunctive centre of gravity of Jupiter and 

 Saturn at Jupiter's mean aphelion and Saturn's mean perihelion ; n>\ cen- 

 tre of gravity at Jupiter's mean perihelion and Saturn's mean aphelion. 

 The four principal planetary masses are so proportioned to their distances, 

 and their distances are so proportioned to those of Mars and the Earth, as 

 to give the following arrangements in the typical ellipse. 



Centre. C D 



m a 



n a 

 nip 



m p 



] 2 V 

 b_ a 



o 



It is well to ohserve that the relation of Mars' s radius vector to octave 

 nodes of the asteroidal belt is indicated by these configurations, as well 

 as by the - series in my communication of April 4th (^- 2 t{J = 2 <^). 



If we accept Newton's hypothesis, that the aether is a material medium, 

 by means of which the mutual gravitating action of masses is exerted, 

 the modulus of light may be determined by the same laws as the modulus 

 of elasticity in air, steel, or other terrestrial elastic bodies, and its de- 

 termination gives significance to the following relations : 



1. The half-modulus, is to Jupiter's distance from the Sun's surface, as 

 the Earth's distance from the Sun's surface, is to solar radius (or the dis- 

 tance of the Sun's centre of gravity from its surface). 



2. The quotient of the solar mass by the aggregate planetary mass is 

 to the quotient of the mean aphelion by the mean perihelion radius vec- 

 tor of the Solar- Jovian centre of gravity, as the velocity of light is to the 

 velocity of planetary revolution at the mean perihelion Solar-Jovian 

 centre of gravity. 



3. The aggregate mass of the Jovian System {%, \ , tj?, § ), is to that 

 of the Telluric System (©, 9 , $ , $ ), as Earth's radius vector, is to 

 Sun's radius. 



