REMARKS ON THE SMALL PLANETS 



SITUATED BETWEEN 



MARS AND JUPITER. 



By M. G. LESPIAULT, 

 professor of the faculty of sciences of bordeaux. 



TEAN8L.\TED FKOM THE " MEM0IRE3 DE LA SOCIETB DES SCIENCES PHYSIQUES ET NATUEELLES DT. 

 BORDEAUX," 1861. ETC. A. ALEX.\NDEH. 



I. 



In proportion as the discovery of small planets between Mars and Ju- 

 piter has been multiplied, those bodies have become, especially in Ger- 

 many, the objects of a great number of highly interesting researches. 

 The powerful magnifiers of the refractors of Dorpat and Munich have 

 been applied to the study of their ph3'sical constitution and to the 

 measurement of their diameters; their elliptical elements have been 

 determined and rectified; their ephemerides calculated and occasion- 

 ally even the principal perturbations of their movements. Attempts 

 have been made to ascertain the law of the distribution of their orbits 

 in space, from the position of the nodes and the inclination of those 

 orbits to the ecliptic and other fixed planes, as well as from the meas- 

 ure and direction of their greater axes. It has been asked whether 

 the course of these small bodies, describing curves so singularly inter- 

 laced, might not some day bring about a collision, or at any rate some 

 approximation so considerable as to give rise to problems altogether 

 new in celestial mechanics. The chief results of these various re- 

 searches are to be found scattered through the publications of MM. 

 Encke, d' Arrest, Littrow, Moedler, &c., in the Astronomische Nacli- 

 richten, and the treatise on astronomy of Sir J. Herschel; as yet they 

 have not been collected, and are, in general, but little known in 

 France.* This defect I have endeavored to supply in the present 

 notice, in which the actual state of our knowledge with regard to the 

 small planets will be set forth, though for this purpose it has been 

 found necessary to extend to seventy of these asteroids wdiich we now 

 know certain calculations wdiich had been made only with respect 

 to a part of them. This undertaking, in which I have been 

 joined by M. Burat, professor at the Lyceum of Bordeaux, has led us, 

 as will be afterwards seen, to modify or even to reject some of the 

 conclusions at which the German geometricians had arrived. 



"-" Professor Alexander, of Princeton, has long been occupied with the subject of the rela- 

 tions of the asteroids, and is now preparing an account of his results for publication in the 

 " Smithsonian Contributions.' 



