Provisional Theory of Leda. 



5 



and undoubtedly it has its advantages, among which it is not a trifling- 

 one, that a calculator is freed from all anxiety as to whether he have or 

 have not picked up all terms of any serious consequence: but on the other 

 hand it is extremely tiresome and a great defect in the method, that, if 

 one wishes to know the amount of perturbation at any assigned moment, 

 it is necessary to divide the time between that moment and the epoch of 

 the elements into short intervals, (usually, for the Asteroids, of 20 days), 

 and calculate the perturbations for each interval from the epoch of oscula- 

 tion till the given date; and, as each separate result is employed in ob- 

 taining the two next succeding results, any little error that may creep into 

 the calculation is dragged into all the following results, and that as pro- 

 bably in an exaggerated as in an attenuated form. I therefore on the whole 

 much prefer to use a method, that gives the perturbations of the polar coor- 

 dinates directly in explicite functions of the time. 



The inclination of Leila's orbit is about equal to, and its excentri- 

 city less than those of Mercury's. This planet seems therefore to be one 

 to which the Laplacean formula is fully applicable, and I have accordingly 

 constructed the theory entirely in accordance with the scheme of the Meca- 

 nique Celeste. The symbols used have the same signification and are the 

 same as in the great work of Laplace, excepting that I have written the 

 indices under the letters to the right thus, A { , instead of in a parenthesis 

 above thus A {i \ as is done by Laplace, and I have introduced, as others 

 have done before me, the letter Hi with its usual signification, viz 



The calculation, being merely provisional and intended for use only 

 for a very few years, that is, untill the orbit's elements are known with 

 sufficient certainty to justify the undertaking of a more elaborate theory ac- 

 cording to Hansen's method, has been carried only to quantities of the first 

 order. This, it is hoped, will be sufficient for the purpose aimed at, espe- 

 cially as there is no apppoximatc commensurability between the mean-motion 

 of Leda and that of any of the disturbing planets, except Saturn, in which 

 case it is true that 13 times the mean-motion of the disturbing planet sur- 

 passes twice that of Leda by only 7'.48", thus producing a long inequality 

 with a period of about 27G9 years, but a term of the 11"' order produced 

 by a planet so far distant from the disturbed body as Saturn is from Leda 

 can surely never be sensible. 



i 2 .{n — n'Y — n 



1 



