342 Mr. G. Johnstone Stoney [Feb. 19, 



that time. A diagram illustrating these facts will be found in vol. ix. 

 of the Proceedings of the Royal Institution, opposite to page 43. 



It was by a study of this advance of the node, and by referring it 

 to its dynamical cause, that Professor Adams was able to discriminate 

 between five different orbits which had been found by Professor 

 Hubert Newton to be compatible with all other known facts. This 

 enabled hiin, in April 1867, to announce which was the real orbit. 



Professor Adams, in his computations, used a method of investi- 

 gation known as Gauss's method, in which what he really computed 

 was the perturbing effect on a meteor of two rings of attracting 

 matter with the form, size and position of Jupiter's and Saturn's orbits, 

 the masses of the rings being equal to the masses of the planets, and 

 being distributed round the ring not equally, but with a preponderance 

 where the planet, in travelling along its orbit, lingers longest. Now 

 the actual amount by which the node shifts between successive returns 

 of the meteors differs slightly from revolution to revolution ; because 

 the amount in any one revolution depends on what have been the 

 distances and directions of the planets from the meteors during that 

 particular revolution. But what Gauss's method does is to give the 

 average amount of this shift taking one revolution with another, and 

 this will in some revolutions be a little more, and in others a little 

 less, than the actual amount. The difference between the actual and 

 the average amount is well exemplified by the annexed diagram of 

 the times at which the great showers have been observed, and the 

 times at which they would have occurred if the advance of the node 

 had not deviated from its average amount. 



In the left-hand part of the diagram the longitudes of the node 

 along the earth's orbit corresponding to the observed dates of the 

 showers are plotted down. These show an irregular advance of the 

 node towards the right-hand side of the figure. The straight line 

 indicates where the node would have been if its advance had been 

 uniform ; and in the right-hand part of the figure are given the 

 number of hours by which the actual shower preceded or followed the 

 time when it would have occurred on the uniform hypothesis. 



Now there is nothing except the want of more accurate data than 

 we yet possess to prevent the calculation being carried farther than it 

 was by Professor Adams, and made to furnish the actual amount of the 

 Bhift in each individual revolution ; indicating not qnly that, but the 

 small difi'erence which must exist between the perturbations upon the 

 front, the middle and the back of the stream, so as to enable us 

 to determine the sinuosities which must have established themselves 

 in it. 



There is a circumstance to which it may be useful to invite 

 attention in connection with the calculation of the perturbations of 

 the Leonids. The planets that are massive enough and so situated 

 as to be able to atfect the meteoric orbit are Jupiter, Saturn and 

 Uranus, and in every one of these cases there is a remarkably simple 

 jiumerical relation between the periodic time of the Leonids and that 



