342 Remarks on the Coal Formation of Pennsylvania. 



dh.l.r 1 J 80° 



const, then A.?.(pr=/ii.A-f nA.Z.r .'. jTi — =- and t;° = — ;=, (see 

 ^ . ' ah.Lfr n v^ ^ 



A 



Prin. B. I, prop. 45, ex.2,) if w=l, ?;° = 180°, and F=— ; in 



this case m=\/ — ^^ = 1, and (19) beconfiesr=R'(l — ecos. 1^) = 



R' 



r— , (24), neglecting quantities of the order e^ ; it is evident 



by (11), given at p. 73, Vol. XVII, that (24) shows the curve de- 

 scribed, in this case, to be an ellipse, the centre of force being at 

 the focus, R' = the semi-axis == the semi-parameter, neglecting quan- 

 tities of the order e^ ; also in this case (20), (21) become v= 

 n?-|-2esin. nt, r=R'(l — ecos. wf) which agree with (s), given at p. 

 73, Vol. XX, and (1), given at p. 291 of the same Vol., by neglect- 

 ing quantities involving e-, e^, etc. in those formulae. 



Art. XV. — Remarks on the Coal Region between Cumberland and 

 Pittsburgh, and on the Topography, Scenery, &fc. of that portion 

 of the Alleghany Mountains ; in a letter, dated Pittsburgh, Nov. 

 30, 1831, from Samuel Wyllts Pomero'y, Esqr. ; written by re- 

 quest of the Editor. 



Dear Sir — The advanced stage of the season will deprive me of 

 the pleasure of furnishing so promptly as I could wish, in accordance 

 with your request, an account of the statistics, as well as facts relating 

 to the geology and mineralogy of the coal fields on the banks of the 

 Ohio. The detention here has exceeded our anticipations a fort- 

 night. I cannot, however, relinquish the hope that winter will per- 

 mit me to stop a few days on our way to Cincinnati, where we shall 

 remain while the navigation is obstructed by the ice, which seldom 

 continues more than six weeks, when from the knowledge obtained 

 by explorations, that occupied three or four months last year, I con- 

 fidently expect to be able to put you in possession of the desired in- 

 formation by the 1st of March, so far as I may be competent to the 

 pleasing task. 



I am gratified, however, that a fortuitous circumstance has enabled 

 me to present an imperfect sketch or outline of the coal formation of 



