APPENDIX. 



313 



itself corresponds to the limiting points of osculation denoted by Professor ENCKE S 

 m and m&quot;, and the points K and K correspond to the extreme points of oscula 

 tion of the second order, for which ENCKE has given the values q = =p 36 52 

 and m = 4.2976, and m&quot; 9.9999. 



On the delineations, 8 is the centre of the circle for our example of Ceres, 

 and 8 the same for Dr. GOULD S exceptional case. A careful examination of the 

 singular position of the point 8 will illustrate the peculiar difficulties attending 

 the solution of this rare example. 



159. 



&quot;We add another example, which was prepared with great care to illustrate the 

 Method of Computing an Orbit from three observations published in pamphlet 

 form for the use of the American Ephemeris and Nautical Almanac in 18-52. It 

 furnishes an illustration of the case of the determination of two orbits from the 

 same three geocentric places, referred to in article 142. 



We take the following observations, made at the Greenwich Observatory, 

 from the volume for the year 1845, p. 36. 



From the Nautical Almanac for the same year, we obtain 



The computation is arranged as if the orbit were wholly unknown, on which 

 account we are not at liberty to free the places of Ceres from parallax, but must 

 transfer it to the places of the earth. 



40 



