210 



Mr. S. Tebay on the Law of Bode ; 



These equations are satisfied by 



e=0, 



We therefore have this curious result. The mean motions in 

 the elhptic and disturbed orbits being equal, the mean distances 



>'=0. 



result. 



will be most nearly equal when — = •6213, and at the same time 



the elliptic orbits of the disturbed and disturbing planets have 

 no exeentricities independent of perturbation. 



If n, n' be the mean motions, we have, neglecting the masses. 



^ = {:6k}"=^-»*2; 



or the periodic time of the second planet is a little more than 

 double that of the first. 



Our attention is next directed to the satellite system of Jupiter; 

 for we know that the orbits of the first three satellites have no 

 exeentricities independent of perturbation, at least the exeentri- 

 cities are very small ; and the periodic time of the second satel- 

 lite is a little more than double that of the first, and the periodic 

 time of the third a little more than double that of the second. 

 The mean distances of the first three are 



and 



3-03, 4-81, 7-68, 



^3_.g i:81_.62 

 4-81 - ^'^' 7-68 ~ ^'^' 



A closer agreement could scarcely be expected. I do not wish 

 it to be understood that this has reference to any law of mecha- 

 nical cosmogony; if, however, the time be regarded as indefi- 

 nitely great, the disturbed planet will be out of its elliptic place 

 by the least possible amount when the above conditions are 

 satisfied. This is curious, and it is the only approach which I 

 have been able to make towards a verification of the law of Bode, 

 out of twelve years' application. Even in this case there is a 

 pretty tolerable agreement in some instances, as will be seen 

 from the following Table, where the number opposite each pair 

 of planets is the ratio of their mean distances. 



Mercury and Venus 

 Venus and Earth . 

 Earth and Mars . 

 Mars and Ceres 

 Cei'cs and Jupiter . 

 Jupiter and Saturn 

 Saturn and Uranus 

 Uranus and Neptune 



•534 

 •732 

 •656 

 •550 

 •531 

 •545 

 •500 

 •635 



