CONTENTS 



N.B. The references are to the articles, not to the pages. 



SECTION I. 



Introductory statement, 1. 



Correction of data, 3. 



Table (A) of periodic times, distances, and masses of planets, respectively, 3. 



SECTION II. 



First approximation to a Law of planetary distances, with an approximate tabular arrangement 



of the system, 5. 



Half-planet characteristics of the Earth and Venus, 6. 



Half-planet characteristics of Uranus, 7. 



Ratios for half-planet terms; viz : — 



Neptune Mars Mercury in aphelion , , ,. 



-yf 1 7^ — -pT' and also vj^ ■■ r— t^ — ; which, with r for the leadinpr ratio of the 



Uranus Earth, Mercury m perihehon/ '^ 



system, all approximate to H: also ratio , approximating to ri Symbolical arrange- 



Venus 



ment representing planetary ratios, 8. 



Mode of computation of terms, 9. 



Laws of planetary distances, involving leading ratio r, also r', and rK 2cZ Approximate Arrange- 

 ment of the system, 10. 



Question of regular variation of ratio r considered^ 11. 



Subnidiai-y Induction in the region from Saturn to Mars inclusive, 12. 



Specific values of r in the Planetary System, 13. 



Completed Arrangement of the Planetary System; exhibiting the correspondence of Law with Fact, 

 in Table (B), 14. 



System of Saturn, 15. 



Centre of gyration of a thin homogeneous ring is in the circumference of a circle bisecting the area 

 of the ring, 16. 



A formula for the centre of gyration of any two equal masses similar to the reduced formula for the 

 homogeneous ring, IT. 



Definite Arrangement of the Saturn System in Table (C) ; the rings {referred to their centres of 

 gyration) claiming their places as satellites, 18. 



Other relations ir Saturn's System, 19. 



Definite Arrangement of Jupite7-'s System, in Table (D), 20. 



Approximate Arrangement of the System of Uranus, in Table (E), 21. 



Summing up of the preceding relations of distances in all the four systems, 22. 



Additional feature of resemblance of half-planets, 23. 



(V) 



