212 REMARKS ON THE SMALL PLANETS. 



adds that it would probably be confirmed by the discovery of new 

 asteroids. The results obtained by us are not in accordance with 

 this supposition. In whatever manner we may group the orbits, it is 

 impossible to arrive at any law for inclinations below 12 or 13 degrees. 

 The sole remark which remains true is, that the orbits, much in- 

 clined to the solar equator, are also in general very eccentric; but' 

 as, on the other hand, these orbits are much inclined to the ecliptic 

 as well as to the solar equator, we see that there is nothing in the 

 preceding remark which can be specially relative to this last plane. 

 Still, exceptions to the rule ought to be pointed out; for instance, 

 the most eccentric of all the orbits, that of Polymnia, makes but an 

 angle of two degrees with the ecliptic, and of six with the solar 

 equator: while the orbit of Egeria possesses, with inclinations of 16 

 and 11 degrees to these same planes, an eccentricity of only 0.089. 



VIII. 



INTERLACEMENT OF THE ORBITS AND APPROXIMATIONS OF THE SMALL 



PLANETS. 



If we compare two by two the positions of the orbits of the 

 asteroids, we see that it is rarely that one of them is completely 

 enveloped by another; most frequently they are intertwined after the 

 manner of the rings of a chain. M. d' Arrest was the first to remark 

 that if we represented all the orbits under the form of material hoops, 

 these hoops would be so intervolved that we might by means of one 

 of them raise all the rest. When but thirteen of the small planets 

 were yet known, they seemed to form two separate groups, btitween 

 which the planet Iris served as a connecting link; but at present this 

 remark is no longer applicable. 



M. Littrow, the learned director of the Observatory of Vienna, 

 has particularly^ occupied himself with the research of the 2)hysical 

 conjunctions which, from this time till the end of the century, may. 

 lead to remarkable approximations among the asteroids. The problem 

 consists of two parts: 1st, to find the shortest line which can be drawn 

 between two orbits; 2dly, to calculate the epoch at which the planets 

 describing those orbits shall pass nearly simultaneously by the two 

 extremities of that line. The first part of the problem is the most 

 important and most difficult. M. Littrow has investigated it by a 

 graphic method, which consists in seeking the intersection and mutual 

 inclination of the two orbits under consideration, tracing out the twO( 

 curves, taking the plane of one of them for the plane of projection, 

 and describing the other by the processes of descriptive geometry. 

 The astronomer of Vienna has thus found for the 42 orbits submitted i 

 to discussion, 548 mutual distances less than the tenth part of the 

 radius of the terrestrial orbit — that is, than four millions of leagues.- 

 In more than eighty cases the elements of the orbits are so com-i 

 pletely different that it is impossible to foresee between these curves i 

 any remarkable approximation, and yet the graphic method spoken; 

 of brings them nearly to an intersection. The cases of double ap^| 



