316 The Orbit and Motion of 



the effects of aberration and mutation, and reduced to the orbit, 

 and to the epoch of oppofition 1783, are as follow : 



M. T. Green. 



b. ' " s. ' " 



1781. Dec. 21. 17. 20. 17 3. oo. 53. 50 



1782. Dec. 26. 09. 09. 45 3. 05. 21. 16,5 



1783. Dec. 31. oo. 59. 13 3. 09. 50. 37,5 



1785. Jan. 3. 16.48.41 3.14.21.52 



1786. Jan. 8. 08. 38. 09 3. 18. 54. 58 



THESE give us the following intercepted arches, with their 

 firft and fecond differences : 



O ' " 



4. 27. 26,5 ' " 



4. 29. 21 I 



4. 31. i45 2 



4- 33- 6 



FROM thefe data, the elliptical orbit of the Planet is to be 

 conftrucled. Various methods prefent themfelves of doing 

 this, depending on the equations between the mean and true 

 anomaly. But I found that, unlefs the quantities involving the 

 fourth power of the excentricity were introduced into the equa- 

 tion, I could not determine the place of the aphelion with to- 

 lerable accuracy. The equation in this form would be alrnoft 

 intractable. I therefore fearched for a method which would be 

 more fimple, when applied to the prefent cafe, which has been 

 rendered b particular, by the determination already obtained of 

 the quarter of the orbit in which the Planet has been obferved. 

 The following method occurred to me, and is, indeed, as obvi- 

 ous as it is fimple, while it is alfo fufceptible of great accu- 

 racy. 



LET AGP (fig. i.) be the elliptical orbit of the Planet, P the 

 perihelion, S the focus in which the Sun is placed, and O the 



centre ; 



