xl BIOGRAPHICAL NOTICE. 



periodic time of this group must be either 18OO days, 185 '4 days, 354'6 days, 376-6 days, 

 or 33-25 years, and that the node of the orbit must have a mean motion of 52"'4 with 

 respect to the fixed stars. Soon after the remarkable display of the November meteors 

 in 1866 Adams undertook the examination of this question. From the position of the 

 radiant-point observed by himself he calculated the elements of the orbit of the meteors, 

 starting with the supposition that the periodic time was 354'6 days, the value which 

 Professor Newton considered to be the most probable one. The orbit which corresponds 

 to this period is very nearly circular, and he found that the action of Venus would produce 

 an annual increase of about 5" in the longitude of the node, that of Jupiter about 6", 

 and that of the Earth about 10". Thus the three planets, which alone could sensibly 

 affect the motion of the node, would produce an increase of about 12' in 33'25 years. The 

 observed motion of the node is about 29' in 33'25 years, which is therefore inconsistent 

 with a periodic time of the meteors about, the Sun of 354'G days. If the periodic time 

 were supposed to be about 377 days, the calculated motion of the node would differ very 

 little from that in the case already considered, while if the periodic time were a little 

 greater or a little less than half a year, the calculated motion of the node would be still 

 smaller. Hence, of the five possible periods indicated by Professor Newton, four were 

 incompatible with the observed motion of the node, and it only remained to examine 

 whether the fifth period of 33-25 years would give a motion in accordance with obser- 

 vation. In order to determine the secular motion of the node in this orbit the method 

 given by Gauss in his memoir Determinatio Attractionis &c. was employed. By dividing 

 the orbit of the meteors into a number of small portions, and summing up the changes 

 corresponding to these portions, the total secular changes of the elements produced in a 

 complete period of the meteors was determined, the result being that during a period of 

 33-25 years, the longitude of the node is increased by 20' by the action of Jupiter, nearly 

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

 found to produce scarcely any sensible effects, so that the entire calculated increase of 

 the longitude of the node is about 28', agreeing very closely with the observed amount 

 of 29', and leaving no doubt as to the correctness of the period of 33'25 years. In order 

 to obtain a sufficient degree of approximation it was requisite to break up the orbit of 

 the meteors into a considerable number of portions, for each of which the attractions of 

 the elliptic rings corresponding to the several disturbing planets had to be determined. 

 These calculations were therefore of necessity very long, although a modification of Gauss's 

 formula was devised which greatly facilitated its application to the actual problem. 

 Subsequently certain parts of the orbit of the meteors were subdivided into still 

 smaller portions, with the view of obtaining a closer approximation. Unfortunately the 

 mathematical investigations which Adams carried out on this subject have not been 

 published. They exist among his papers, together with a great amount of numerical work 

 connected with the calculations. 



In 1877 Mr G. W. Hill published a memoir on the motion of the Moon's perigee, 

 in which he calculated that part of c which depends only upon m to fifteen places 

 of decimals by a new method in which the expansion in powers of m was avoided, the 

 numerical value of c being obtained by means of an infinite determinant. The publication 

 of this memoir led Adams to communicate to the Royal Astronomical Society in 

 November 1877 a brief notice of his own work in the same field, in which, after con- 



