Here we see that, with the exception of the first step from Neptune to Uranus which is only 1·9577, we have an average gradation of acceleration of 2·5898 times, from one planet to another, from the outermost as far in as Mars; and that had Neptune had the period of revolution sought for by Leverrier in his discovery of that planet, viz. 217·387 years, or 79,399·602 days, the average rate of acceleration would have been 2·5896 times, from planet to planet, as far in as Mars. This, we think, is pretty strong evidence that one law of acceleration was in force from the beginning of the separation of rings from the nebula up to the time when the ring for Mars was separated--the departure from it in the case of Neptune, notwithstanding--and goes far to prove that part of the nebular hypothesis which implies that each of the planets is now revolving round the sun in the orbit, and with the velocity, belonging to the centre of gyration of the ring out of which it was formed. From Mars to Venus the law--the areolar law, of course--had changed to a variable decreasing law, as seen from the foregoing register, which then again changed into an increasing one, till at Mercury the rate of acceleration rose again to 2·5543 times from Venus, or very nearly the same rate of increase that existed from Uranus to Mars. The causes of these changes may or may not be able to be accounted for--we shall have to return to them hereafter, in the cases of Neptune, the earth and Venus--but there is one thing of some importance that is deducible from the register, which we shall endeavour to make clear.
BODE'S LAW EXTENDED. --------------+----------+----------+----------+-----------+----------- ---- | Mercury. | Venus. | Earth. | Mars. | Asteroids. --------------+----------+----------+----------+-----------+----------- Numbers in }| | | | | progression }| 0 | 3 | 6 | 12 | 24 | | | | | Add 4 to each}| | | | | for distance }| | | | | from sun, }| 4 | 7 | 10 | 16 | 28 Earth's = 10 }| | | | | | | | | | Distance from}| | | | | sun according}|37,186,000|65,075,500|92,965,000|148,744,000|260,300,000 to the law, }| | | | | (Miles) }| | | | | | | | | | Actual |35,987,000|67,245,000|92,965,000|141,650,000| .. distance | | | | | | | | | | Percentage }| | | | | of distance }| .. | 3.34 | .. | .. | .. beyond law }| | | | | | | | | | Percentage }| | | | | of distance }| 3.22 | .. | .. | 4.77 | .. within law }| | | | | --------------+------------------------------------------------------- ---- | Jupiter. | Saturn. | Uranus. | Neptune. --------------+-----------+-----------+-------------+----------------- Numbers in }| | | | progression }| 48 | 96 | 192 | 384 | | | | Add 4 to each}| | | | for distance }| | | | from sun, }| 52 | 100 | 196 | 388 Earth's = 10 }| | | | | | | | Distance from}| | | | sun according}|483,418,000|929,650,000|1,782,114,000|3,607,042,000 to the law, }| | | | (Miles) }| | | | | | | | Actual |483,678,000|886,779,000|1,783,383,000|2,794,000,000 distance | | | | | | | | Percentage of}| | | | distance }| 0.05 | .. | 0.07 | .. beyond law }| | | | | | | | Percentage of}| | | | distance }| .. | 4.50 | .. | 22.54 within law }| | | | --------------+-----------+-----------+-------------+-----------------