of Edinburgh, Session 1879-80. 
427 
of planets into the solar system. In answer to a question he said 
that his theory explained why the aphelion distance of a comet is 
generally about the same as the distance of the planet which rendered 
its orbit elliptic. The author then publicly stated that there could be 
no longer a doubt that two planets exist beyond the orbit of Neptune, 
one about 100 times, the other about 300 times the distance of the 
earth from the sun, with periods of revolution of about 1000 and 
5000 years respectively. 
If this be the case, the aphelion positions of a majority of the 
comets in each group would probably lie in one plane, which would 
be the plane of the planet’s orbit. The analogy of the Jupiter group 
requires this ; for although the orbits of the comets connected with 
Jupiter have every degree of inclination to the ecliptic, the aphelia 
of most of them are not far distant from the plane of Jupiter’s orbit. 
Some, of course, might be expected to have been deflected from their 
original orbits slightly by planetary perturbations, especially those 
which had been a long time in the solar system. 
The author calculated out the seven aphelion positions of comets 
which are grouped at a distance = 100, determining their latitude 
and longitude. 
The author presented to himself the following problems : — 1. Are 
there a fair number of these aphelion positions lying in one plane 
passing through the sun ? 2. Determine the position of the nodes 
and inclination of this orbit. 3. Is it possible to imagine a planet, 
moving with tolerable uniformity, to occupy in the course of a few 
revolutions the aphelion positions exactly at the aphelion dates? 
4. Is the velocity which we must for this reason assume about the 
same as that of a planet whose distance = 100 ? What is the present 
position of the planet ? The seven comets of this group are : — 
Date. 
Aphelion 
Distance. 
Date of 
Aphelion. 
Calculated 
Period. 
L. 
I. 
1840, iv. 
967 
A.D. 
1668 
Years. 
350 
313° 
II. 
1843, i. 
100-0 
1655 
376 
225° 
III. 
1846 
108-2 
1 
IV. 
1861, i. 
110-3 
1654 
413 
139° 
V. 
1793, ii. 
111-0 
VI. 
1861, ii. 
111-2 
VII. 
1855, ii. 
124-2 
1608 
493 
192° 
3 F 
VOL X. 
