ASTEEOID SUPPLEMENT 



The large, and still increasing, number of the Asteroids has served to augment 

 the labors of astronomers in a rapid ratio ; so much so, that nothing short of gen- 

 eral tables, by means of which their ephemerides can be rapidly computed, will ever 

 reduce this department of astronomical labor to anything like its just proportion. 

 The Asteroid problem must always remain one of a purely scientific character; 

 and such results, based upon a solid foundation, can hardly be expected, so long 

 as so much mechanical labor is required merely to prevent these bodies from 

 being lost. The great work of Gauss, Theoria Motus Corporum Coelestium, and 

 the subsequent labors of many other distinguished astronomers, leave little to be 

 desired so far as the determination of their orbits is concerned. Such, however, is 

 by no means the case with regard to their perturbations by the larger planets. 

 While the variations of the elements of those having small eccentricities and incli- 

 nations may be obtained through the development of the usual form of the pertur- 

 bative function, there are others for which this method is practically nearly impos- 

 sible for any close approximation. This fact has led to the suggestion of new 

 theories of their general perturbations ; and the study which is now bestowed 

 upon this problem, in this country as well as in Europe, warrants the confident 

 expectation that it will erelong be presented in its simplest and most practical 

 form. 



In order to facilitate as much as possible the computation of the perturbations 

 of those to which the usual theory of development is applicable, I have thought it 

 best to take from the Tables the necessary constants, b (i s ] and its derivatives, depend- 

 ing upon the ratio of the mean distances, giving at the same time a simple table 

 for computing the variation of these constants relatively to this ratio, in order that 

 they may readily be corrected for any change in the Asteroid's mean distance. This 

 correction will be necessary for those Asteroids more recently discovered, and whose 

 mean distances are not therefore very well known. 



If, then, n and m are the mean motion and mass of the Earth, and n is the mean 

 motion of the Asteroid in a Julian year, its mean distance a will be 



« = (;) 5 (l + ™o)- 



