CERTAIN HARMONIES OF THE SOLAR SYSTEM. 5 



(6) An inspection of what is here exhibited will at once reveal the fact that 

 the Earth and Venus seem to have characteristics of half-planets ; the one term, 

 0.884 (in the series), pertaining to them, being indicative of a distance between 

 those of the two planets at which their masses should be united; and which is 

 designated as limit (© 9 ). 



[To avoid circumlocution, such an arrangement as this, will be termed a half- 

 planetary arrangement, and the planets subject to it, be, at times, designated as 

 half-planets; those situated, as Uranus and the Earth are, without the intervening 

 limit, being styled exterior half-planets; while those, like Venus, within tlie limit, 

 are specially designated as being interior half-planets; Uranus being regarded as 

 an exterior half-planet as well as the Earth. For the ratio of the mean distance 

 of Neptune to that of Uranus is very nearly the same as that of Mars to tlie Earth's ; 

 viz., a very little greater than the ratio of 1| to 1. And so^ the limit (u) in the pro- 

 gression is very nearly the same fraction of the term for Uranus in the column of 

 Fact, that the limit (© 9) is of the Earth's distance; viz. very nearly y\, in both 

 cases.] 



(7) Uranus, then, like the earth, has the characteristics of an exterior half- 

 pilanet ;"- though there is no other half-planet (analogous to Venus) apparent between 

 limit (u) and Saturn. But the region of the system where the appropriate term for 

 such a half-planet should be found has been marked in the tabular arrangement, 

 and its symbol (Si) shows that it would belong to a half-planet interior to Uranus; 

 such as Venus is in the region interior to the Earth's place. 



(8) Now the ratios for the mean distances from the Sun of the exterior half- 

 planet terras, are as follows: — 



*^^= 1.56681 

 Uranus 



Mar<i 

 -£^= 1.52369 \ Mean= 1.53606; 



Mercury hi aphelion 



1.51768 



Mercury in perihelion 



while it is also true, with respect to the ratio for other than half-planet distances 

 [which = I or 1^ very nearly], that 



(1.8)f = 1.55401, 



agreeing very nearly with the preceding; so that, r being the ratio for other than 

 half-planets, the ratio for the exterior half-planets is ri . 

 Also, as again respects mean distances from the Sun, 



Earth 



Venus 



= 1.38249. 



' Having all the while in view the table of the first Approximate Arrangement under discussion. 



' This was not discerned until just before the Meeting of the American Association for the Advance- 

 ment of Science, in Baltimore, in 1858. It is jnst the non -perception of a half-planet relationship, 

 that has seriously troubled most of the investigations into the arrangements, etc., of the planetary 

 system, whether purely speculative or otherwise. 



