408 Perturbations of the Leonids. 



The following were the adopted masses of the disturbing planets : 



Mars 



3,093,500 



Jupiter 



1,047-879 



Saturn . . 



3,501-6 



Uranus 



22,756 



In consulting the table, it has to be borne in mind that e, which is 

 there designated, in compliance with the usual convention amongst 

 computers, the " mean longitude in the orbit," is in reality the sum of 

 two angles lying in different planes, viz., the longitude of the node + 

 the angle between the radii from the sun to the node and to an imagi- 

 nary body starting from perihelion at the same epoch as segment A of 

 the meteors, and thenceforward moving uniformly in a circular orbit 

 round the sun in the same plane and with the same periodic time as 

 the meteors. So again TT, the so-called " longitude of perihelion," is 

 the sum of two angles, viz., the longitude of the node measured along 

 the ecliptic + the angle from the node to the perihelion measured in 

 the plane of the orbit. The second angle in each case, that in the 

 plane of the orbit, is measured in the direction of positive motion. 



The perihelion distance in Adams's orbit, of which the elements are 

 in the first column of the table, and which was the osculating ellipse on 

 1866, November 13, is 0-9855 ; that of the osculating ellipse on 1900, 

 January 27, of which the elements are in the last column, is 0*97296. 

 There is a corresponding difference in the distances of the node from 

 the sun, a difference which would be enough to carry segment A of the 

 meteoric stream inside the earth's orbit without intersecting it when it 

 passes the earth's orbit on January 27, 1900, unless the depth of the 

 stream towards the sun is greater than its width at right angles to that 

 direction a width which from observation has been estimated to be 

 about 100,000 miles. We have, however, satisfied ourselves, from the 

 dynamical conditions which must have prevailed when the Leonids 

 joined the solar system, that the depth of the stream is much greater 

 than its width. 



The longitude of the node at the epoch 1900, January 27, would be 

 52 25', if computed in the way which has been hitherto usual, by apply- 

 ing to the longitude at the time of the shower of 1866 the average 

 apparent shift of the node as determined from observation by Professor 

 Newton, viz., 102"'6 annually; whereas in the orbit of our table it is 

 53 42'. It thus appears that the amount of this perturbation upon 

 segment A of the stream has been more than three and a half times its 

 average amount, and, doubtless, the perturbations in this revolution of 



