230 D. P. Todd—Search for a Trans-neptunian Planet. 
Adams (first hypothesis) 0°0001656 09 
LeVerrier 00001075 ato0 
Adams (second hypothesis) 0°00015003 ee 
While the most reliable mass of Neptune from observation is: 
Newcomb (motion of the satellite) 0.00005160 totsy 
We have thus reduced the inverse problem of perturbation 
to a very simple, rational form. The residuals of longitude of 
- Uranus were next treated in accordance with this method. 
In his Investigation of the Orbit of Uranus, Newcomb presents 
three series of residuals: the mass of Neptune finally adopted 
in the tables, ;54,y, corresponds very nearly to the mean o 
the first and third series. But the mass of Neptune which 
was employed in this investigation is that given by Newcomb’s 
discussion of the motion of the satellite of Neptune, and is 
: first step; then, was to correct these mean 
residuals into accordance with this adopted mass. The follow- 
ing table presents the date, the mean residuals, the correction 
for mass, and the corrected mean residuals. 
Date. $(Ail+ Asi). Mass-correction. 2. 
1691.0 —11’" +3" —8" 
1715.2 — 8.5 +19 —6.6 
1751.1 + 2.8 —0.7 + 2.1 
1769.0 — 1.5 +1.5 0.0 
1783.3 — 0.17 + 2.58 +2.41 
1790.0 + 0.76 +2.27 + 3.03 
1795.0 — 0.36 +1.73 +1.37 
1802.0 — 1.06 +0°72 —0 
1806.5 — 0.86 +0.09 0.77 
1810.5 — 0.21 — 0.32 —0.53 
1814.5 — 0.32 64 --0.96 
1819.5 — 0.37 —0.79 —1.16 
1824.8 + 1.45 —0.79 + 0.66 
1829.7 + 0.86 —0.76 +0.10 
1835.2 — 0.37 —0.77 —1.1 
1839.8 — 0.33 — 0.82 —1.15 
1844. — 0.02 —0.93 0.95 
1849.9 — 0.37 —1.08 —1.45 
1854.9 — 0.25 —1.20 —1.45 
1860.0 — 0.14 1.2% 1.41 
1865.0 + 0.49 —1.24 —0.75 
1870.0 + 0.12 1.05 —0.93 
