4 



A. D. Wackerbaeth, 



to A\ years, (i. e. from an arc of about 27°) should be so perfect as to 

 represent with strict accuracy the motion of the planet for any very long: 

 time. Since the publication of M:r Alle's work the planet has nearly com- 

 pleted two revolutions, and accordingly it will soon be time to ascertain, by 

 the comparison of calculation with observation, what corrections it is neces- 

 sary to apply to the received elements in order that theory may faithfully 

 represent this heavenly body's actual motion, and it is with the view of 

 facilitating this work that the following provisional theory has been cal- 

 culated. 



There is one circumstance however which must not here be passed 

 over in total silence, since it is possible that it may cause all theory re- 

 specting the motion of the Asteroids to be for some time defective, name- 

 ly, our inability to determine the action of these bodies in disturbing one 

 another. It is indeed certain that their masses are too small even for their 

 united attractive energy to have any sensible effect in disturbing the other 

 planetary bodies of the Solar System, all of which are situated at a consi- 

 derable distance from them. But with eachother it may be otherwise. The 

 mean-distances in many instances differ so little from eachother and the 

 orbits are so interlaced that some of them can at times come extremely 

 near one another, and the effect of a very small body at a very short dis- 

 tance may be equal to that of a large body in a more remote position, 

 and thus it seems possible, that these little bodies may at times sensibly 

 disturb eachother. On this subject however nothing can with certainty be 

 known or asserted untill some method be devised for ascertaining and taking 

 into account the masses of these little planets. 



The excentricities and inclinations of the minor planets are in general 

 so considerable that the ordinary method of Laplace for determining the 

 perturbations cannot often be applied. Indeed that method, in order that 

 the disturbing function may be developable in a convergent form, requires 

 the condition*, 



~ . 1 a' — a 



2 . sm J < = , 



2 Vaa' 



where J is the angle of inclination between the orbits of the disturbed and 

 disturbing planets. It therefore becomes necessary in most instances either 

 to employ the method of Hansen, which however no one would do till the 

 elements were well determined, or to have recourse to the Method of Me- 

 chanical Quadratures. This last has been the course universally adopted 7 



* Kowalski, Recherches de l'Observatoire de Kasan. N:o 1. p. 108. 



