Progression of the Planetary Distances. 601 



major planet revolving in the orbit of the asteroids, of which 

 Ceres is the chief representative. 



19. It will be further observed that, while the plus and 

 minus differences in the distances are irregular in amount, 

 they are rectified by the mutual attraction of the planetary 

 bodies among themselves, to effect an approximate ratio of 

 equality between the binary progression of the distances, 

 shown in columns 1 and 4, and those derived from obser- 

 vation. 



20. Turning now to the anomalous departure of the 

 distance of Neptune from the binary progression of distances 

 of the other members of the solar system; it will readily be 

 admitted that, had the agreement between the numbers of the 

 binary progression and the observation distances, as shown in 

 the table, been absolute, the outstanding minus difference of 

 the distance of Neptune, 19'410, would have still remained 

 an exception to the law. 



21. In my former paper on the multiple proportions of the 

 atomic weights, it was laid down as a general principle of 

 philosophic reasoning, that, when a number of recurring 

 instances was sufficient to establish the relation of cause and 

 effect, or, in other words, the general accuracy of a law, the 

 road to further discovery was rather in the direction of ex- 

 plaining the anomalous departures from it, than in challenging 

 the truth of the law itself *. 



22. That the distance of Neptune, at the genesis of its 

 history, was the first and exact term of the binary progression 

 is an inference justly to be drawn from the like progression 

 observable in the distances of the other planetary bodies, and 

 it was on this same distance (38'4) that Adams, in 1845, 

 based his first determination of the then unknown planet. 



2'6. The Astronomer Royal (Sir George B. Airy) in his 

 historical review of the circumstances connected with the 

 discovery of Neptune says that, "if the mathematicians, 

 whose labours I have described, had not adopted Bode's law 

 of distances (a law for which no physical theory of the rudest 

 kind has ever been suggested), they would never have arrived 

 at the elements of the orbit" f, or, in other words, would 

 never have discovered Neptune. 



24. The most probable, as well as the most obvious, cause 

 of the anomalous minus difference in the binary progression 



* Manchester Memoirs, vol. xxxix. p. 71 (1895). 

 t Proc. Key. Astronomical Society, Nov. 13 (1846); Phil. Mag. (3) 

 vol. xxix. pp. 520, 537 (1846). 



