146 



IDENTITY OF THE PLANET LEVERRIER 



Outstanding Error. 



1 

 % 



3 



4 

 5 



6 



7 

 8 

 It 



= _ 0.303 

 = + 3.016 

 = + 3.363 

 = + 3.685 

 = -f 4.038 

 = + 4.268 

 = + 4.594 

 = + 4.248 

 = + 3.332 



X X 



+ 

 + 

 + 



2.700 x y 



3.000 



2.400 



1.800 



1.000 



0.200 



1.267 



3.950 



6.133 



+ 0.333 X 



+ 1. 



+ 1. 



+ 1. 



+ I. 



+ 1. 



+ 1- 



+ I. 



+ 1. 



+ 3".88 

 + 1 .00 



— .27 



— 1 .10 



— 3 .07 



— 4 .12 



— 2 .44 



— 1 .73 

 + 1 .81 



v 



— 0".08 



+ .49 

 + .19 

 + .22 



— 1 .03 



— 1 .31 

 + 1 .03 



— .13 



— .16 



Whence the three normal equations, 



o = 

 o = 

 o = 



118.879 X X 



7.477 

 30.443 



And 



+ 

 + 

 + 



7.477 X y 

 85.149 

 0.250 



+ 

 + 

 + 



30.443 X z 

 0.250 

 8.111 



— 45".629 

 + 1 .687 



— 8 .627 



, 



x= + 



y= — 



3 .255712 



r = 29.939950 + ~ = 

 50 



— 0".272963 



— 11 .1475 



t—t 

 v Sept. 28th, 1846 



30 .005064 



21".65789 

 326°59'34".74 



The values of n and v are the result of a new computation with the new radius vector 

 30.005064. The sum of the squares of the errors in heliocentric longitude of Elements 

 (I.) for the nine equations is 55".96. The sum of the similar quantities for Elements (II.) 

 is 4".21, which is the sum of squares of nine errors, each of which is composed of the 

 united errors of theory and observation. 



In my paper on meteors in the Memoirs of the American Philosophical Society, New 

 Series, Vol. VIII., I have given the well-known equations, 



a r ° r \ Gauss's x f 

 IV. er cos v = a cos 2 $ — r = a (1 — e 3 ) — r 



In which g is the true orbital velocity in units of the earth's mean orbital velocity. 

 Equation (III.) by means of r and n in Elements (II.) gives a ±= 30.200585. Equation 

 IV. gives the value of v for any assumed value of the eccentricity. It is of the second 

 degree and gives the value of either in the first or fourth quadrant. It is not possible 

 from the process above pursued, to decide between the two quadrants of v. By hypothe- 

 sis the daily variation of r was neglected. Hence it remains uncertain whether the r of 

 Elements (II.) belongs to the first or fourth quadrant. 



It is possible that the insertion in the conditional equations of two more terms for the 

 daily variations of r and n might decide this point. Before attempting this inquiry I 

 resolved to examine the ancient catalogues for the purpose of detecting Leverrier as a 

 missing star. 



Among the catalogues to be resorted to were Bradley's, Lacaille's, Mayer's, Lalande's, 

 Piazzi's, Bcsscl's, Brisbane's and Taylor's. The first three of these catalogues do not 

 usually include stars of the 7 . 8th magnitude. In the recent publication of Piazzi's 

 original observations by the Vienna Observatory, extending from 1792 to 1798, I do not 

 find among the stars observed by Piazzi and not afterwards identified, any which came 



