90 Proceedings of the Royal Society 
This result was confirmed in a second research communicated to 
the Society, 1880. 
Here I treated of the disturbances produced by the new planet 
on the longitude of Uranus, as shown by its residual tabular errors, 
favouring the hypothesis of the new planet moving nearly on the 
ecliptic. This research leaves not the slightest doubt about the 
longitude of the new planet, agreeing precisely with my previous 
work on comets. 
I was able further, by a comparison of the periodic fluctuations 
in these residual errors with the periodic fluctuations in the 
longitude of Uranus, produced by the action of Neptune (for 
which I am indebted to Professor Newcombs “ Theory of Uranus,” 
p. 100, &c.), to compare directly the map of Neptune with that of 
the new planet. By an easy harmonic analysis, the effect of 
Neptune is found to be about ten times that of the new 
planet. But the new planet is three times farther from the 
sun than Neptune, and the action is proportional inversely to the 
cube of the distance in equal times. Moreover, in the case of 
Neptune, the period during which this action lasts is 75 years, 
while in the case of the new planet it is only 45 years ; and the 
effects are proportional to the squares of the times. Hence the 
mass of the new planet is to that of Neptune in the ratio of 
i x 3 3 x : 1 = 10:1 nearly. 
1U 
The mass of Neptune adopted by Newcomb was HfcJS. This 
makes the mass of the new planet = T¥ ~, the mass of the sun 
being unity. This is the newest result at which I have arrived 
after a most careful examination. The new planet is then the 
largest but one in the solar system. 
It occurred to me lately that, with these well-defined perturba- 
tions, it will be easy to decide between the two hypotheses 
discussed in my first memoir. Por if the new planet be at present 
m a position so very far from the ecliptic as is indicated by the 
first hypothesis, then we should expect to find periodical fluctuations 
in the residual tabular errors of the latitude of Uranus. In fact, 
we might even hope by this means to determine its latitude approxi- 
mately. [As a first approximation the latitude of the new planet 
may without serious error be considered constant during a period of 
