91 
of Edinburgh, Session 1880-81. 
half a century.] The period of revolution of Uranus is 84 years, 
whilst its period synodical with the new planet is 92 years. It is 
unfortunate that these periods are so nearly alike, because it makes 
it difficult for harmonic analysis to discriminate between those 
errors of latitude due to errors in the assumed inclination and 
longitude of ascending node, and those which are due to the action 
of the new planet. Nevertheless, any large effect as we should 
expect upon the first hypothesis ought clearly to he distinguished. 
The errors of latitude are taken from Newcomb, p. 176. They are 
very small in the last 50 years, hut show a marked periodic 
fluctuation of about 92 years. There are two dates, however — 1861 
and 1864 — when the errors are completely discordant. I think we 
may with reason reject these two on the ground that up to 1861 
the observations used were almost entirely those of Greenwich and 
Paris. Those after 1868 are almost entirely Greenwich and 
Washington; while between these dates those of Greenwich, 
Paris, Washington, and Leyden are used. We have then residual 
periodic fluctuation, due to the action of the new planet from 
which we are able to determine its latitude. In this way I find its 
probable latitude to be about 2° south. 
This may not, perhaps, be extremely accurate, but it completely 
establishes the truth of the second hypothesis. 
Although from my study of Uranus I had no doubt about the 
accuracy of the conclusions in my first memoir, still it was with 
some gratification that I received the following letter from Mr D. 
P. Todd, of the Nautical Almanac Office in Washington : — 
“ Nautical Almanac Office, 
“Navy Department, Washington, 15 th June 1880. 
“ Dear Sir, — About a month ago I read with intense interest a 
copy of your memoirs “ On Comets and Ultra-Neptune Planets,’ 
which came to this office. You cannot fail of understanding my 
enthusiasm about the matter, in so far at least as it relates to the 
prediction of position, when I tell you that some three years ago I 
was engaged on a provisional treatment of residuals of longitude of 
Uranus and Neptune, having in view the detection of possible 
exterior perturbations. On my first reading of your paper I took 
the notion in some way that your assigned longitude was a long 
