196 OUTLINES OF NATURAL PHILOSOPHY. 



ma longe difficillimum, and it may, therefore, be- 

 readily believed, that the solution does not fall 

 within the limits of an elementary treatise. At 

 the same time, a very simple geometrical problem 

 is the foundation of it. Arith. Universalis. The 

 determination of the orbit implies that of the five 

 quantities, which are its elements : 



1* The inclination of the orbit. 2. The position of 

 the line of the nodes. 3. The longitude of the pe- 

 rihelion. 4. The perihelion distance from the 

 Sun. 5. The time when the Comet is in the pe- 

 rihelion. 



NEWTON'S solution being a laborious and indirect ap- 

 proximation, the problem has been attempted by 

 many others. -LA CAILLE, Astron. 775, &c. 

 BOSCOVICH, Opera, torn. in. p. 14. &c. The so- 

 > lutions of BOSCOVICH and LA PLACE are illustra- 

 ted by Sir H. ENGLEFIELD, in his Determination 

 of the Orbits of Comets, Lond. 1793. 



LA LANDE has given a mechanical construction, that 

 serves for finding the orbit nearly, 3127. ; it is 

 followed by VINCE, 653. LAMBERT has demon- 

 strated some remarkable properties of the orbits of 

 Comets, in a work entitled Insigniores Orbitte Co- 

 metarum proprietates, Aug. Vind. 1761, 8vo. See 

 also LA GRANGE, Mem. de Berlin, 1783. 



; 



The most perfect solution of all is supposed to be 

 that of LA PLACE, Mechanique Celeste, 



The 



