600 Dr. H. Wilde on a neio Binary 



11. The observation distances in column 2 are in close 

 accordance with those derived from Kepler's third law, as 

 will be seen by multiplying each of the terms in column 5 of 

 the new table of distances from my former paper*, by the 

 terrestrial unit distance of Mercury, 0*3871. The additional 

 decimal place is brought in for greater accuracy not required 

 in the general tables. 



12. A comparison of the sums of all the distances in 

 column 1 of Bode's table with those of the observation 

 distances in column 2, shows that the difference between the 

 two sums only amounts to one- fortieth part of the whole. 



13. By the like comparison of the sums of the new binary 

 progression in column 4 with the distances from the new 

 table in column 5 (which are in strict accordance with 

 Kepler's third law), the difference between the two sums is 

 only one hundredth part, or two and a half times less than 

 that derived from Bode's table, and abundantly establishes 

 the validity of the binary progression of the planetary 

 distances of both tables as a law of nature. 



14. The substitution of the Mercurian radius vector for 

 the terrestrial unit of distance, brings out several variations 

 in the tables, the most conspicuous of which is the minus 

 difference, 0*417, of the distance of Uranus in Bode's table, 

 and the plus difference, 0*550, in the new table for the same 

 planet, the plus difference being accounted for by the 

 attractive influence of Neptune. 



15. The anomalous minus difference of Saturn, 0*360, 



column 6, between the plus differences of Jupiter and Uranus 



is interesting as indicat'no- the large amount of attraction 

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exercised by the enormous mass of the Jovian planet on the 

 outer side, and by the plus differences of the Earth and Venus 

 on ihe inside of his orbit from the same cause. 



16. The plus difference of Jupiter in the new progression, 

 0*437, column 6, is remarkable as showing the attractive 

 influence of the large planets, Saturn, Uranus, and Neptune. 



17. Other differences will also be seen between tiie 

 observation and calculated distances in Bode's table and in 

 the new progression, the final effect of which is to reverse 

 the order of the plus and minus differences of the total sums 

 of the distances shown in columns 1, 2 and 4, 5 of the table. 



18. The smaller minus difference of Mars would appear to 

 be caused by his proximity to the intra-Martian planets, 

 together with the interruption of the binary progression of a 



* Manchester Memoirs, vol. liii. (1909) ; Phil. Mag. (G) vol. xviii. 

 p. 523 (1909). 



