36 ON THE PERTURBATIONS OF URANUS. [2 



It will be seen that the corrections of the eccentricity and longitude 

 of perihelion vary very rapidly with a change in the assumed mean distance. 



51. If these quantities be substituted in the expressions before given, 

 we obtain the following theoretical corrections of the mean longitude, each 

 of these corrections being divided into two parts, of which the first is due 

 to the changes in the elements of the orbit of Uranus, and the second to 

 the action of the disturbing planet. 



HYPOTHESIS I. 



Ancient Observations. 



Year. 



1712 -288-0 + 365-8= +77-8 



1715 -283-1+357-1 = +74-0 



1750 +210-5-2607= -50-2 



1753 +218-1-267-0= -48'9 



1756 +214-0-260-0= -46-0 



1764 +154-0-186-7= -32-7 



1769 + 79-6-100-7= -21-1 



1771 + 27-6- 41-8= -14-2 



Modern Observations. 



Year. Year. 



1780 -126-12 + 129-27=+ 3'15 1813 - 125'59 + 147'72 = +22'13 



1783 -180-28 + 188'70=+ 8-42 1816 68'21 + 91'02=+22'81 



1786 -227-66 + 240-36= +1270 1819 10'40+ 33'18=+2278 



1789 -26570 + 281-63= +15-93 1822 + 44'84- 23*64 =+21'20 



1792 -292-25 + 310-38= +18-13 1825 + 94'69- 77'64=+17'05 



1795 -305-84 + 325-27= +19-43 1828 + 13673 - 127'48 =+ 9'25 



1798 -305-67 + 325-72= +20-05 1831 + 168'94- 172'17 = - 3'23 



1801 -29177 + 312-05= +20-28 1834 + 189'85 -21T04= -2T19 



1804 -264-95 + 285-38= +20-43 1837 + 198'51 -243'59= -45'08 



1807 -22678 + 247-51= +2073 1840 + 194'54-269'36= -74'82 



1810 -179-43 + 20076= +21-33 



