1873.] J-"* 3 [Chase. 



The theoretical distance of Xeptune (in column A) appears to be an 

 exact mean proportional between Mercury's theoretical distance and the 

 modulus of light. That modulus, according to this determination, is 

 470,198 X Sun's radius ; according to Struve's value of the constant of 

 aberration, it is (475,969.23 ± 258.45) X solar radius. 



The theoretical series is symmetrical, in having three terms in arith- 

 metical progression at either extremity. This analogy is more nearly car- 

 ried out in the actual positions of the three exterior planets, which have 

 been regarded as exceptional, than in those of the three interior planets, 

 which have been considered normal. 



The theoretical positions of Mercury and Venus, are at centres of 



direct and reverse oscillation between Earth and — ; those of Uranus 



and Saturn, at similar centres between Sun and Xeptune. 



The successive doubling of the differences, places each of the theoreti- 

 cal intermediate planets at a centre of oscillation between the next in- 

 ferior and the next superior planet. 



The deviations from theoretical positions, in consequence of mutual 

 planetary disturbances, distribute the planets in various symmetrical 

 ways. 



The exponents of the divisor, E, are arranged symmetrically in pairs. 

 (3. o-J- 1 • & l-z ) 



V3» u 5 3' x ) 3> x ) 3' ""/ 



The four central planets are grouped, by their divisors, in alternate 

 pairs ; Earth, Jupiter ; Mars, Saturn. 



The four terminal planets are similarly grouped ; Xeptune, Venus ; 

 Uranus. Mercury. 



If the division by r. be thrice repeated, below the theoretical position 

 of Mercury, we obtain, very nearly, (~-l) X solar radius, or the diameter 

 of the circle described by the centre of gravity of Sun and Jupiter. 



ROTATION OF THE SUN AND THE INTRA-ASTEROIDAL 



PLANETS. 



By Pliny Earle Chase. 



(Read before the American Philosophical Society, March 7th, 1873.) 



The well known tendency to synchronism in concurrent vibrations, has 

 encouraged me to look for some significant harmony between the lengths 

 of solar and planetary days and times of fall to the centre of the system. 



The middle term in my series of alternate planetary distances, differs 

 from the others in having a multiple significance, representing, as it does, 

 a mean position in the asteroidal belt and the orbital major axis of Mars. 

 It has also simple relationships to the distances and rotation-times of the 

 intra-asteroidal planets, which serve to connect the diurnal with the 

 annual motions, and both with the equilibrating forces of the Sun. 



Since the velocities of falling and oscillating bodies are proportioned 

 a. p. s. — vol. XIII. s 



