THE SMITHSONIAN INSTITUTION. 141 



and Jupiter is a cluster of bodies whose orbits are so interlaced as to 

 suggest the apprehension of firequent and inevitable collision. The 

 orbit of Fortuna approaches the orbit of Metis within less than the 

 moon's distance from the earth, while the orbit of Massilia approaches 

 almost equally near to the orbit of Astraea, and the orbit of Lutetia to 

 that of Juno. 



It is evident then that these thirt3"-three small planets sustain to each 

 other a relation different from that of the other members of the solar 

 system. We see a family likeness running through the entire group ; 

 and it naturall}' suggests the idea of a common origin. This idea, as 

 has been already stated, occurred to the mind of Olbers after the dis- 

 covery of the second asteroid, and led to his celebrated theory, that all 

 these bodies originall}^ constituted a single planet, which had been 

 broken into fragments by the operation of some internal force. Have 

 we any means of testing the soundness of this theory? 



If the earth should be broken into fragments by the operation of 

 some internal force, (such for example as that which causes the erup- 

 tion of a volcano,) the fi-agments might be projected in various direc- 

 tions, and with ver}' unequal velocities, but each would describe an 

 ellipse, of which the sun would occupy one of the foci ; if we except 

 the extreme but possible case of a fragment projected with such a ve- 

 locity as to carry it beyond the limit of the sun's attraction. If we 

 leave out of view the disturbance arising from the mutual attraction of 

 the planets, which produces only minute effects, each fragment would 

 continue to describe the same ellipse in its successive revolutions about 

 the sun; in other w^ords, these ellipses ivotild all have a. common iioiiit of 

 intersection. The same conclusion must h(»ld true for the asteroids, 

 according to the theory of Olbers. The question, of course, arises, have 

 the orbits of the asteroids a common point of intersection ? A single 

 glance at a diagi'am of these orbits will settle this question in the nega- 

 tive. But it is replied that the orbits of the planets are disturbed by 

 their mutual attraction : these orbits should originally have had a com- 

 mon point of intersection; but at each revolution they suffer a slight 

 displacement, until in the lapse of time the position of the orbits has 

 become so completely changed as to leave scarcely a trace of their 

 original intersection. Is such a result possible? A few simple consid- 

 erations will satisfy us that if the orbits of the asteroids ever had a 

 •common point of intersection, such a result must have belonged to a 

 period of time indefinitely remote. 



The line in which the plane of a planet's orbit intersects some 

 other plane, selected for common reference, is called technically the 

 line of the 7iodes. If the asteroid orbits ever had a common point of 

 intersection, all the nodal lines upon one of the orbits must have 

 coincided. Now, as two of the asteroid orbits are inclined less than 

 one degree to the earth's orbit, we will, for greater convenience, em- 

 ploy the latter as the plane of reference. On referring to a table of the 

 planetary elements, we see that the ascending nodes of the asteroids 

 are distributed, though unequally, through the four quadrants of the 

 circle. Ten of them lie in the first quadrant, twelve in the second 

 quadrant, seven in the third, and four in the fourth. The nodes of all 

 the planetary orbits are in constant motion ; but the motion for a single 



