152 



IDENTITY OF THE PLANET LEVERRIER 



for the eccentricity 0.009875, whereas that of February 2d was made with the radius 

 vector of September 28th, 1846, supposed unchanged. 



The preceding table of the locus of n for the various values of e presents a striking 

 confirmation of the other arguments in favour of the supposition of a small eccentricity. 

 For the limits of e the table gives, 



it now, we suppose, in the original creation of the system, all points of the orbit as 

 having equal probability of being perihelion points; and from the analogies of the system 

 that 0.06, is the probable limit of the value of e, and that each degree of the orbit has a 

 unit of probability (a priori) of being the perihelion point, we have for the number of such 

 degrees within the above limits, 



P = 37° .1 + 50° .1 + 50° .1 + 37° .1 = 174° .4 



Calling p e ,_ e = the probability that the eccentricity should fall within the limits of c' and 

 e we have from loci derived from my Elements II. 



01 — 0.006471 



100.2 

 174.4 

 74.2 

 174.4 



= 0.5745 

 = 0.4255 



From which it appears that there are 575 chances in 1000 for the eccentricity to fall 

 between 0.006471 and 0.01; and only 425 chances in 1000 for the eccentricity to be 

 greater than 0.01. If Leverrier was the missing star, the eccentricity by Elements III. 

 was 0.0088 107, which is near the middle point of the most probable limit. 



I beg leave, in conclusion, to remark, that after a careful examination of all the circum- 

 stances known to me at this time, I find none that militates against the hypothesis that 

 Leverrier was the missing star of Lalande. 



I subjoin a table of all the stars in the Histoire Celeste situated within 15' of the locus 

 of Leverrier, (in declination in the above table,) reduced to their mean places for 1800. 



No. 



Mag. 



