Progression of the Planetary Distances. 599 



atrophied by disuse, to the great hindrance of the. science 

 which they endeavour to advance. This habit of mind is all 

 the more deplorable in its consequences from the fact of its 

 being unsuspected, and associated with attainments of the 

 highest order in men occupying important positions in 

 observatories and seats of learning, where the influence of 

 their peculiar idiosyncracies makes itself felt through a long 

 course of years *. 



6. Bode's law briefly stated is as follows : — The radii 

 vectores, or the relative planetary distances from the Sun, 

 proceed in multiple proportions, each one after the second 

 being double the one which precedes it, and, by adding the 

 constant 0*4 to each progression, we obtain approximately 

 the distances of the planets as shown in Table I. (p, 602). 



7. The parallelism of the discovery of new planets through 

 the law of multiple proportions of the distances, and the 

 discovery of new elementary substances through the law of 

 multiple proportions of the atomic weights, as shown in my 

 former papers f, will not fail to be evident to serious in- 

 vestigators in the natural sciences. 



8. The correlation of a series of nebular condensations, 

 represented by the planetary distances on the one hand, and 

 the further condensation of the nebular substance into well 

 defined series of elements, with their like series of atomic 

 weights and specific gravities, on ihe 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 1 and 2, containing Bode's 

 numbers, and expressed in astronomical units of the distance 

 of Mercury from the Sun. 



10. Taking the unit distance of Mercury = TOO, as a plus 

 constant, instead of the empirical number 0*4, as in Bode's 

 table, the binary progression now appears as : 



0-00 0-75 1-50 3 6 12 24 48 96 ; 



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



1-00 1-75 2-50 4 7 13 25 49 97. 



* The attacks made by astronomical writers on Bode's law have been 

 discussed at greater length in my paper published in the Manchester 

 Memoirs, vol. xxxix. (1895). 



t Manchester Memoirs, vols. 30, 39, 40, 46, 48, 52, 1878-1907 ; 

 Chemical News, vol. xxxviii. pp. 0(5, 96, 107, 1878; rhil. Map:. ((>) 

 vol. xvi. p. 824 (1008). 



