333 



Eccentricity, e = 0.005052917 



Mean distance, a = 30.145119 



Epact Jan. 1, 1847, 31 = 326° 2' 1".34 m. noon Greenwich 



M. daily siderial motion, At = 21.437,843 



Period in Trop. years, T = 105^.51330 



I do not hesitate to pronounce them the most probable elements of 

 the present disturbed orbit of Neptune, that can be deduced from a 

 discussion of all the observations of Neptune extant to this date. 

 These have already accumulated to 479: viz. 113 American and 

 366 European. All have been compared with an ephemeris which I 

 computed from my IV. Elements of Neptune. Thirteen normal 

 places have been thus obtained, and the corrections of Elements IV. 

 computed from these normal places by the method of least squares. 

 In forming the equations of condition, I carried into effect the plan 

 sketched out in my former letter. The variations of the radius vec- 

 tor were made a function of the ascending powers of the intervals 

 from a date assumed for the origin of time. 



The variations of the true anomaly were derived from those of 

 the radius vector, by means of Laplace's formulae for mechanical 

 quadrations, on the condition that equal areas should be described in 

 equal times. This mode of forming the equations of condition, for 

 the purpose of deducing an orbit from direct observation, is new, as 

 far as I am informed. I send you the comparison of the Ephemeris 

 from Elements V. with the thirteen normal places in geocentric lon- 

 gitude and latitude : 



DATE. 



Observation less theorj'. 









Act 



A (f 



1846, Aug. 9, 



— 0".22 



— 0".72 



Sept. 28, 



+ .08 



+ .37 



Oct. 8, 



+ .17 



+ .28 



18, 



— .06 



+ .09 



28, 



— .20 



— .71 



Nov. 7, 



— .13 



— .42 



17, 



+ .25 



— .27 



27, 



— .25 



— .05 



Dec. 7, 



— .49 



— .08 



17, 



+ .29 



+ .25 



27, 



+ .14 



+ .33 



1847, Jan. 16, 



+ .35 



— .93 



April 6, 



— .10 



+ .65 



