Chase.] 144 [March V. 



each term of which is within the limits of secular variation. The second 

 and third series (B, C,) represent the mean perihelion and aphelion 

 planetary distances. The fourth series (D) gives the mean distances : 

 and the fifth (E) is derived from the first by simple systematic modifi- 

 cations. 



Theoretical and Observed Planetary Positions. 



32 



- + J 



32 



l 9_2 



32 

 -f- 3?r 2 



32 



* + 5* 2 

 32 



- + 9* 2 



32 



- + w 



32 



- + 33~ 2 



32 



7T + 65 *" 



32 



7T + 97^ 



32 



I have already spoken of corrections that seemed to be requisite in 

 many of my analogies, on account of planetary eccentricities. If the A 

 series be divided by a mean proportional between the average (major -=- 

 mean) radii vectores of Earth and Jupiter, the results will differ less from 

 the actual planetary positions than those given by Bode's Law. The 

 remarkably close approximations of the E series wei - e obtained by using 



E°, E 3 , E5, E 1 as divisors, (E — 1.079065 = average ™J£^ radius vec- 



mean 



tor of Mars.*) 



The planetary deviations are grouped in pairs, and also in exterior and 

 interior systems. Neptune and Venus are not materially shifted ; Mer- 

 it J- 

 cury and Uranus are divided by E 3 ; Earth and Jupiter by E 3 ; Mars and 



Saturn by E 1 . The ratios of the divisors to radius vector, time, and 

 velocity, may have important bearings. 



•The values of the mean planetary eccentricities were taken from Stockwell's recent paper 

 on ' * Secular Variations of the Elements of the Orbits of the Eight Principal Planets. ' ' 



