ZONE OF PLANETS BETWEEN MAES AND- JUPITER. 87 



have had a common 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 show scarcely a trace of their 

 original intersection. Is such a result possible ? A few 

 simple considerations 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 the planet's orbit in- 

 tersects some other plane selected for common reference 

 is called technically the line of the nodes. If the asteroid 

 orbits had ever 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 con- 

 venience, employ the latter as the plane of reference. 

 By referring to our table on page 83, it will be seen that 

 the ascending nodes of the asteroids are distributed, 

 though unequally, through the four quadrants of the 

 circle. Twelve of them lie in the first quadrant, thirteen 

 in the second, eight in the third, and seven in the 

 fourth. The nodes of all the planetary orbits are in 

 constant motion, but the motion for a single year is 

 extremely small. The animal motion of the node of 

 Mercury is ten seconds ; that of Yenus twenty seconds ; 

 Mars twenty -five seconds, etc. The nodes of the aster- 

 oids, as far as the computation has been made, move at 

 somewhat similar rates; the most rapid motion known 



