fo 



BowditcJi on th& elements of the orhit of a comet. 



the use of only Uyo elements D, P, even in the case where a feVv* 

 observations only are used. But when a very great number of ob- 

 servations are combined, and much accuracy is required, (as is the 

 case generally, when the elliptical orbit is investigated,) the com- 

 |)arative simplicity of the method in which each observation is sep- 

 •arately considered, and all the elements are varied, is very mucli 

 increased, and the labour of calculation is less than in the method 

 of La Place, To render this evident, we shall here give a brief 

 sketch of the method of computing each observation, as taught by 

 Euler, in his ^* Theoria Motuum Planetarum,'^ etc. and illustrated 

 by au example in the paper on the comet of 1807, in Vol. 3^ Part 

 1 of the Memoirs of the American Academy of Arts and Sciences : 

 also by Mr. Burkhardt in the " Memoires de VInstitiit &c." 1806, 

 Pag. la &c. where he has applied it to the orbit of the comet of 

 1770. This method of calculation was selected for the compari- 

 son on account of the simplicity of its pri7icq)les, though it might 



require a more laborious numerical calculation than some modern 

 • methods. 



Suppose the approximate values of fl]e elements of the orbit to 



symbols, namely t The perihelion 



he represented l)y the foil 



distance 



a* 



D 



Time of passing the perihel 



il^Q Perihelion counted upon the orbit of 

 the ascending node of the comet's orbit 



T. 

 P 



Place of 

 Place of 



N 



Inclination of the 



T 



With these ele 



we must 



o 



o 



itude and latitude 



comet's orbit to the ecliptic 

 Tor a first operation compul 



of the comet at the time of any observation. The same thing 

 must be done iu five successive operations, varying one of the cl. 

 ements iu each operation, the others remaining unaltered. Thus 

 in the calculation of the comet of 1807, the quantity D was chang- 

 ed into D 4- 0.004, in the second operatic 



T into T 



kd n% 



\ 



Jfh. 





