4 Wilde, New Binary Progression of Planetary Distances. 



well defined series of elements, with their like series of 

 atomic weights and specific gravities, on the other, rendered 

 it imperative that the binary progression of planetary 

 distances should again appear in connexion with the 

 Mercurian unit of distance. 



9. The solution of this problem is shown in the same 

 Table i, in columns 4 and 5, parallel with i and 2, con- 

 taining Bode's numbers, and expressed in astronomical 

 units of the distance of Mercury from the sun. 



10. Taking the unit distance of Mercury = i 00, as a 

 plus constant, instead of the empirical number 0*4, as in 

 Bode's table, the binary progression now appears as, — 

 O'OO 075 1-50 3 6 12 24 48 96; 

 and the value of each term of the new series becomes- - 

 TOO 175 2-50 4 7 13 25 49 97. 



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"387i. 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 [ 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 difTerence between the two 

 sums is only one hundredth part, or two and a half times 



"Manchester Memoirs, vol. 53, 1909, Phil. Mag., (6), vol. 18, p. 523, 1909. 



