APPENDIX.
609
table, constructed by Prof. Peirce, exhibits an interesting view of theresidual errors in the longitude of Uranus , corresponding to four distincttheories of the planet. The numbers in the second column are theresults of Le Verrier ’s attempt to account for the irregularities of theplanet without supposing it to be influenced by any foreign cause of dis-turbance. The third and fourth columns contain the errors of the theoriesof Le Verrier and Adams, founded on the assumption of the existence ofa disturbing planet. The fifth column exhibits the residual errors of theplanet after taking into account the action of Neptune as calculated byProf. Peirce, from the elements of Walker. The mass of Neptune employed in these calculations was deduced by Prof. Peirce from Bond’sobservations of the satellite discovered by Lassell. The results due toLe Verrier inserted in the second and third columns, represent the excessof theory over observation. The same is true with respect to the numbersin the fourth column containing the results of Adams’s theory; but, inconsequence of this circumstance, their signs are contrary to those of thesame numbers in Peirce’s table. Prof. Peirce does not state whether thenumbers in the fifth column represent the excesses of theory above obser-vation, or those of observation above theory; but this point is immaterialin so far as our present purpose is concerned.
EESIDTJAL DIFFERENCES BETWEEN THE THEORETICAL AND OBSERVEDLONGITUDES OF URANUS .
Date.
Without any ex-ternal planet.
By Le Yerrier’stheory of a dis-turbing planetmass = 53 ^ 5 .
By Adams'stheory (Hyp. II.)mass of disturbingplanet =
By Peirce’stheory of theplanet Neptune mass = -rg 33 0 .
1846
+
6 ". 5
_
0".3
—
0"9
1840
H-
0.7
+
2.2
—
1.3
—
1.1
1836
—
4.5
—
0.8
+
1.2
+
2.0
1829
—
7.8
—
2.2
_
2.0
+
0.8
1824
—
7.6
—
5.4
—
1.7
_
2.0
1819
+
3.8
+
0.4
+
2.2
+
1.0
1813
+
4.5
—
0.9
+
1.0
—
0.3
1808
+
3.8
+
0.8
0.0
—
0.4
1803
—
3.4
+
0.8
—
1.6
+
0.8
1797
—
6.7
—
1.0
+
0.5
+
0.3
1792
—
7.8
+
0.3
+
1.1
+
0.3
1787
+
2.0
—
1.2
+
0.2
—
0.5
1782
+
20.5
+
2.3
0.0
—
3.0
1769
+
123.3
+
3.7
—
1.8
—
6.0
1766
+ 230.9
—
4.0
+
4.0
+
4.0
1715
+ 279.6
+
5.5
+
6.6
+
8.7
1690
+ 289.0
—
19.9
50.0
+
0.8
_ (82.) Le Verrier has attempted to defend the conclusions at which he ar-rived relative to the limits of the mean distance of the hypothetical planetupon the ground that he assigned too small a probable error to the obser-vations. “ When the calculation of the limits of the mean distance,” says he,“ is resumed with other probable errors of observation than 5", it willreadily be seen that the interval included between these limits by no
R R