336 ANNUAL OF SCIENTIFIC DISCOVERY. 



" The points of equal attraction between the planets severally (when 

 in conjunction) are situated as follows: 



Miles from the former. Miles from the latter. 



Between Mercury and Venus, 8,029,600 23,943,400 



Venus and Earth, 12,716,600 13,599,400 



" Earth and Mars, 36,264,600 13,540,400 



" Jupiter and Saturn, 266,655,000 145,710,000 



" Saturn and Uranus, 678,590,000 238,538,000 



" It will be seen from the above, that the diameter of the earth's 

 sphere of attraction is 49,864,000 miles. Hence the diameters of the 

 respective spheres of attraction of the other planets, according to my 

 empirical law, will be found to be as follows : 



Diam. of Sph. of Attr. 



Mercury 19,238,000 



Venus 36,660,000 



Mars 74,560,000 



Jupiter 466,200,000 



Saturn 824,300,000 



"The volumes of the sphere of attraction of Venus, Mars, and 

 Saturn, in this table, correspond with those obtained from the preced- 

 ing one ; that of Mars extending sixty-one million miles beyond his 

 orbit, or to the distance of two hundred and six million miles from the 

 sun. This is about two or three million miles less than the mean dis- 

 tance of Flora, the nearest discovered asteroid. That of Mercury ex- 

 tends about eleven million miles within the orbit ; consequently, if 

 there be an undiscovered planet interior to Mercury, its distance from 

 the sun, according to my hypothesis, must be less than twenty-six mil- 

 lion miles. Jupiter's sphere of attraction extends only about two hun- 

 dred million miles within his orbit, leaving eighty-nine million miles 

 for the asteroids. It is only in the most distant portion of this space, 

 where small bodies would be less likely to be detected, that none have 

 yet been discovered." 



Mr. Kirkwood then modestly concludes : " The foregoing is sub- 

 mitted to your inspection with much diffidence. An author, you know, 

 can hardly be expected to form a proper estimate of his own perform- 

 ance. When it is considered, however, that amy formula involves the 

 distances, masses, annual revolutions, and axial rotations, of all the 

 primary planets in the system, I must confess I find it difficult to resist 

 the conclusion, that the law is founded in nature." 



After this letter had been read, Mr. Walker said, that, induced by 

 the importance of the subject, he had at once proceeded to verify the 

 data and conclusions of Mr. Kirkwood, and had found that there was 

 nothing in them requiring modification, except, perhaps, the substitu- 

 tion of some more recent values for the masses of Mercury and Ura- 

 nus. This theory, and that of Laplace with reference to nebulae, 

 mutually strengthen each other, although the latter has been a mere 

 supposition, while the former rests upon a mathematical basis. In a 

 later letter, which was also read, Mr. Kirkwood says that he has pur- 



