rs 



Bowditch on the elements of the orhit of a comet 



of being wholly independent of each otli 



the great advantage 



F 



The remarks made on La Place's method may be applied to New- 



and to other similar 



d of iQ the preceding section, 



methods 



SECTION THIRD. 



f 



The heliocentric 



tudes C 



d the heliocentric lati- 



tudes w, «•', of a comet being given, the angular distance V is com- 

 puted by La Place by the following method in Pag. 2S7; Vol. 1, 

 of his Mecanique Celeste, The auxiliary angle A is found by 

 this formula, 



^ 1 



sin. A^ = cos. ^ [C — Cf. cos. «-. cos. ■»■'. 



and then V by the formula 



sin.i-T 



72 



COS. (4 



+ Z.^' + A). cos. (4^ + 4- =r' 



A). 



But this computation may be made more easily in the followin 



J 



w 



manner. Find the auxiliary angle li by the formula 



or 



cot. B = cot. 2x\ COS. (• 



f 



t 



taking B acute in the first or last quadrant of the yalue of 

 otherwise obtuse. Then find V by the formula 



cos. V 



sin jr'. C03. (B 



) 



Bin. B 



The sign + is used when the latitud 



«* 



of difiTerent names 



7 



otherwise the sign 



. This method is easily deduced from the 

 of spherical triangles applied to the triangle formed 



T 



the 



;h V and the two arcs of latitud 

 the pole of the ecliptic. Then a 



90 



-zr 



90 



ss- 



; 



let fall 



a- 



perpendicular being 



upon the side 90 

 n\\ meet this last side in a point which is distant from the eclip 

 by the arcli we have called B, as is ev 



as is evident from the formula 

 above given, and the expression of cos. V is easily deduced from 

 Napier's rules. 



As 



an example of these methods 



C 



324j° 43 58^ 



> 



tt 



44 



16 



// 



? 



zs 



suppose C 

 59° 0' 46". 



95" 21 



,r; 



; 



i 



