10. 



PERTURBATION OF THE ORBIT OF THE NOVEMBER METEORS. 



[!N a paper "On the Orbit of the November Meteors" (Mon. Not. 1867 

 April) Adams considers the problem of discriminating between a number of 

 possible periods deduced by Professor H. A. Newton as consistent with 

 the observed recurrences of the display of meteors, by computing the 

 perturbation of the node of the orbit corresponding to each period, and 

 comparing it with the observed perturbation. After excluding a number of 

 orbits by this test, the only remaining and, as it appears, the true orbit 

 is highly elliptical, with eccentricity 0'9047. It remains to compute the 

 perturbation of the node of this orbit, and the method and result of his 

 investigation Adams states as follows : ' ' In order to determine the secular 

 " motion of the node in this orbit, I employed the method given by Gauss 

 " in his beautiful investigation ' Determinatio attractionis &c.' 



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

 "periodic times that 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 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 



