428 
Proceedings of the Royal Society 
On marking upon a celestial globe tbe aphelion positions, it was 
immediately seen that four of them lay exactly upon a great circle, 
cutting the ecliptic at an angle of 53° and at the longitude 250°. 
This is the plane of the orbit of the supposed planet. It is remark- 
able that none of the four aphelion distances of the comets marked 
above I., II. , IV., VII., diverge from this plane by more than 2 or 
3 degrees. 
The longitudes of these four aphelion distances measured on this 
plane of the hypothetical planet were then calculated ; their values 
measured from,ib) are given in column L above. It is evidently 
impossible to suppose that the hypothetical planet could in one 
revolution, either by direct or retrograde motion, have passed each 
of the aphelion positions at the aphelion times. It was a matter of 
some labour to determine whether this could happen even in 2 or 3 
revolutions, and a large number of hypotheses were tried. Eventually 
one was found agreeing well with facts, but involving suppositions 
as to previous apparitions of comets. According to this theory comet 
IV. was introduced into the system in 409 a.d., comet I. in 968, 
comet VII. in 1608, and comet II. in 1655. These are dates when 
the comets reached their aphelion. A planet moving at the rate of 
2 ‘788 years to 1°, or 997 years to a revolution, would, if it was 8° 
ahead of the comet IV. in 409 a.d., be 9° behind comet I. in 968, 6° 
behind comet VII. in 1608, and 8° ahead of comet VI. in 1651. 
These are all very close, provided we have evidence that comets IV. 
and I. have been seen so often before. Comet I. ought from the 
known period to have been visible in the years 1490 and 1140. The 
comet of the previous date has always been suspected to be the same 
as comet I. The comets which were seen about 1140 are so vaguely 
described that they cannot be identified. 
Comet IV. ought to have been seen in 1861, 1446, 1031, 616 a.d., 
comets were seen in 1861, 1444, 1032, 617 a.d. 
All apparitions previous to 1861 were seen about July, and in each 
case the star j3 Leonis is mentioned as being close to the comet. It 
remained only to see if the orbit of the comet IV. which appeared in 
1861 suits these conditions. The author converted the heliocentric 
elements of the comet’s position just before reaching the ecliptic into 
geocentric elements on the supposition of the earth being in its July 
position. The result is that the comet would be seen to pass within 
