THE ORBIT OF URANUS. I73 



It will be seen that the effect of these changes of weights is, tliat tlie older 

 observations are a little better, and the later a little worse represented. I conceive 

 that our choice must lie between the first and third solutions, the first being the 

 more probable if we conceive the outstanding residuals to be due to errors of 

 observation only, and the third if we suppose them equally due to errors of com- 

 putation. On the whole, I consider the mean of the two to be about the most 

 probable, and this will give the mass of Neptune very near the round number 



1 

 19700 



which will be adopted as the definitive value. The definitive corrections to 

 Elements III (p. 99) will then be 



(V (1830) — 3".56 



^f (1850) —12.45 



•* lO^y* — 4 .44 



he — 4.1-2 



ehn — 0.25 



V — 0.137 



Corrections to the LicUinitioa and Node. 



These corrections have been derived entirely from the modern observations, the 

 ancient ones being too uncertain to add anything to the weiglit of tlie result. The 

 mode in which the correction to the latitude of the provisional cphemeris has been 

 concluded from the observations has been sufficiently explained : it is only necessary 

 to add that the immediate results from the data of the preceding chapter require 

 two corrections, namely: 



(1) A correction to the theoretical latitude for the change in the adopted mass 

 of Neptune. The value of this correction, as derived from the data of Chapter V, 

 is with sufficient approximation 



h[3 = 0".2DTcosff. 



(2) A correction to tlie observed latitude on account of the difference between 

 the obliquity of the ecliptic adopted in the various cphemerides compared, and that 

 of Hansen's Tables du Sole'd, which having been adopted in the theory should be 

 used throughout. 



Applying the correction (3) — (1) to all the observed latitudes, we have the 

 following corrections to the latitude of the provisional ephemeris derived from all 

 the observations of each opposition since 1781. The third column gives the 

 number of observations in declination. These numbers may, however, in some 

 cases be inaccurate. The fourth and fifth columns give the sine and cosine of the 

 argument of latitude, to be used in forming the equations of condition. 



