Method for delervuning the Orbifs of Comets. 85 



Coal soil. I cannot particularize, at present, the im- 

 mediate stratum, in which the specimens principally 

 occur, throuo-h ihe coal-nieasures ; hut I liave had spe- 

 cimens of it in argillaceous gritstone from Alireton ; 

 in ironstone from Wingerworih, and in the coal shale 

 and the coal itself, from near Bnxlon. I have not yet 

 ohserved it in that peculiar siliceous gritstone, found ui 

 the coal-measures, called by the miners crowstone, al- 

 though this stone abounds with other vcgeuvt reliquia. 

 Phytolilhus c.irticiradix & Phytol. compres&iradixT. [). Mill- 

 stone grit stratum? Chapel-eu-le- Friih. l^he speci- 

 mens were found in a wall abo'jt -i a mile from the 

 town, on the Manchester road. I have not ascertained 

 the quarrv, from which the stone was brought. Coal- 

 measures, in argillaceous grit ; in a small quarry about 

 1 : mile from Leek, a few yards left of the first Toll- 

 bar on the road to Buxton, in considerable quantity 

 (shale-grit?). 



XIII. General Method for determining the Orbits (f Comets. 

 By M. Laplace. 



[Concluded from p. 49.] 



XlAViNG thus the true perihelion distance, and the true in- 

 stant of the passage of the comet by this point, we shall 

 conclude from them the other elements in this way. 



Letj' be the position of the node which would be ascend- 

 ing if the motion of the comet were direct, and o the in- 

 clination of the oibit : we shall liave the six following 

 equations, 



tan? or sin C — tan^: nr' sin f 



tansr; = — ; — ; 



taug CT cos t — tang w cos t 



tantr cr sin C" — tancr sr'' sin S 



tano- 7 = — — ^ (c) 



^"^ tang ■a! cos ?"— tang-w" cos S *^ ' 



tantj ot' s!n t" — X?,v.^ sr'' s'n f' 



langf 7 — — ^ — ;• — ^-t; — -.,- 



" ti'.ng 537 cos t — tang ■uj cos C 



tang ■uj 



sill {t—j) 



tanrr ot' 



tang a t= 

 tang « — 



s.n [Z'—j) 



tang & =z ~ — ;- .... (/) . 



We may choose ad libitum among ll-.e^e formulge : but it 

 will be most correct to enijiloy those whose numerators 

 and denominators are createst. 



■I' 3 Suppose, 



