272 ON THE ORBIT OF THE NOVEMBER METEORS. [34 



Period 33'25 years (assumed) 



Mean distance 10'3402 



Eccentricity 0'9047 



Perihelion distance 0'9855 



Inclination 16 46' 



Longitude of Node 51 28 



Distance of Perihelion from Node 6 51 

 Motion Retrograde 



In order to determine the secular motion of the node in this orbit, I 

 employed the method given by Gauss in his beautiful investigation " Deter - 

 minatio attrctctionis, <&c." 



It may be proved that if two planets revolve about the Sun in periodic 

 times which are incommensurable with each other, the secular variations 

 which either of these bodies produces in the elements of the orbit of the 

 other would be the same as if the whole mass of the disturbing body had 

 been distributed over its orbit in such a manner that the portion of the 

 mass distributed over any given arc should be always proportional to the 

 time which the body takes to describe that arc. In the memoir just 

 referred to, Gauss shews how to determine the attraction of such an elliptic 

 ring on a point in any given position. When this attraction has been 

 calculated for any point in the orbit of the meteors, we can at once deduce 

 the changes which it would produce in the elements of the orbit, while 

 the meteors are describing any given small arc contiguous to the given 

 point. Hence, by dividing the orbit of the meteors into a number of small 

 portions, and summing up the changes corresponding to these portions, we 

 may find the total secular changes of the elements produced in a complete 

 period of the meteors. 



In this manner I have found that during a period of 3 3 '2 5 years, the 

 longitude of the node is increased 20' by the action of Jupiter, nearly 7' 

 by the action of Saturn, and about 1' by that of Uranus. The other 

 planets produce scarcely any sensible effects, so that the entire calculated 

 increase of the longitude of the node in the above-mentioned period is about 

 28'. 



As already stated, the observed increase of longitude in the same time 

 is 29'. This remarkable accordance between the results of theory and obser- 

 vation appears to me to leave no doubt as to the correctness of the period 

 of 33'25 years. 



