404 Drs. G. J. Stoney and A. M. W. Downing. 



were the average perturbations ; and he accordingly employed Gauss's 

 method, in which the mass of the disturbing planet is supposed to be 

 distributed round its orbit in quantities proportional to the time that 

 the planet occupies in travelling over each portion of its course. This 

 elegant method furnishes the average amount of each perturbation on 

 the supposition tha the periodic times of the disturbed body and of 

 the disturbing planet are incommensurable, so that in the course of 

 time the two bodies present themselves in every possible position to 

 one another. 



This condition, however, has been but imperfectly fulfilled within 

 the limited period of 1000 years over which the recorded observations 

 extend, especially in the case of the three planets which influence the 

 Leonids most, and indeed are almost the only planets whose attraction 

 needs to be taken into account. These are Jupiter, Saturn, and Uranus. 

 A comparison of the periodic times shows that fourteen revolutions of 

 Jupiter approximate in duration within about one-fifth of a year, to five 

 revolutions of the meteors ; two revolutions of Uranus occupy about 

 one and three-quarters of a year more than this same time, and nine 

 revolutions of Saturn correspond within a fraction of a year to eight 

 revolutions of the meteors. 



These cycles have been several times repeated within the period 

 over which the observations extend; and one consequence of these 

 cycles is that there have been oscillations in the rate of the advance of 

 the node about its mean value, so that the times for the showers 

 -assigned by applying to the orbit the average shift of its node, have 

 usually differed by several hours from the actual times. On one occa- 

 sion in A.D. 1533 the shower anticipated the computed time by 

 about twenty-six hours, and, as the present investigation shows, a 

 deviation of comparable amount and in the opposite direction is to be 

 expected this year. Accordingly, even if our sole object were to enable 

 astronomers in future to predict more satisfactorily the times of the 

 greater Leonid showers, it would be necessary to prepare for the task 

 by first studying the actual amount of the perturbations in each revolu- 

 tion, and moreover, for meteors occupying various stations along the 

 stream. 



For, in fact, the perturbations have not only differed in different 

 revolutions, but even within a single revolution, the meteors which 

 occupy successive positions in the procession are differently affected by 

 the surrounding planets, as is confirmed by the definite results which 

 Herr Berberich has obtained by assuming successively two epochs for 

 the perihelion passage.* The dense part of the stream, with which we are 

 chiefly concerned, and which we may call the ortho-stream,! is now so 



* See bis paper on the perturbations since 1890 of tbe orbit of the comet 

 which is associated with the Leonids, ' Astr. JSTach.,' No. 3526. 



f In order to facilitate the study of the Leonids it is convenient to distinguish 



