88 HISTOEY OF ASTKONOMY. 



being about fifty seconds a year. If we suppose the 

 nodal lines of all these orbits to move steadily toward 

 each other, it would require in some of them a motion of 

 fifty seconds a year, continued for more than 6000 years, 

 to bring them to a coincidence. 



It should also be observed, that not only must the 

 nodes of all the asteroids coincide, but the distance of 

 the planets from the sun must be the same at that instant. 

 Now the distances of these planets from the sun, when at 

 their nodes, differ by more than a hundred millions of 

 miles ; so that to bring .them all together requires some- 

 thing more than a change in the position of the nodes. 

 "We may bring about a coincidence, in the case of some 

 of the asteroids, by supposing the longer diameter of the 

 elliptic orbit to change its position in the plane of the 

 orbit. Such a change does really take place in the case 

 of every planetary orbit, but with none of the larger 

 planets does it exceed twenty seconds a year. This mo- 

 tion for the asteroids, so far as it has been computed, is 

 somewhat more rapid, amounting, in one instance, to 

 seventy seconds a year ; but even with this motion, it 

 would require the lapse of five thousand years to bring 

 about an intersection in the case of many of the asteroid 

 orbits. "When now it is, remembered, that in order to 

 give a common point of intersection to these forty orbits, 

 all the nodal lines upon one of the orbits must coincide, 

 and at the same instant all the distances from the sun 

 must be equal to each other, we must be prepared to 



