46 Saliferous Rock Formation in the J^alley of the Ohio. 



, A ,A 



that COS. /= y . .- , COS. w= . . : , cos. 



v/A=^+,A'+//A' a/A2+,A2+^,A2 



A 

 n==—r=====^=====~, (16) J then by substituting these values in 



V A^-f/A^+z/A^ 



the first of (14) it gives V K^ -\-,K^ -{-/A^ =B, (17) ; also the sec- 

 ond and third of (14) by substituting the values of A, /A, ,/A from (16) 

 give B (cos. I COS. /' + cos. m cos. m' -\- cos. n cos. n')=-^ =0, B 

 (cos. I cos. I" + cos. m cos. m" + cos. n cos. n") =,,B=0, since 

 cos. I COS. /'-{-COS. TO cos. m'-fcos. n cos. n'=-Q, cos. Zcos. Z''+cos. m 

 cos. m'^+cos. ncos. »''=0. The plane ,x, ,y, determined by (16) 

 is the invariable plane ; on which the sum of the products of each 

 body by the area which its radius vector describes in a unit of time 

 (or in any given time,) is the greatest possible ; and it is evident by 

 what has been proved that the sum of the products of each body 

 by the area which its radius vector descVibes on any plane which is 

 perpendicular to ^x, ^y, in any given time is always =0. See Mec. 

 Cel. Vol. I. p. 60, also Mec. Anal. Vol. I. p. 269. 



JVote. — By unit of masses, as used in this paper, is to be understood a portion of 

 matter, so small that it may be considered as a particle. 



Art. V. — Observations on the Saliferous Rock Formation, in the 

 Valley of^ the Ohio ; hy Dr. S. P. Hildreth, of Marietta. 



For many years after settlements had been commenced west of 

 the Alleghany Mountains, the inhabitants were entirely dependent on 

 their brethren, east of the Appalachian ridge, for salt ; an article so 

 necessary to the existence and the comfort of civilized man. It was 

 transported, with immense labor, through narrow defiles, and almost 

 impassable roads across the mountain ranges, on the backs of horses. 

 Long trains of these useful animals, might be seen toiling up the steep 

 sides of the mountains, their uncouth pack-saddles laden with kegs 

 of salt, iron ware, and other merchandise, destined for the use of the 

 early setders. This, for a long time, was the only mode of transpor- 

 tation. At length rude roads were constructed which could be trav- 

 ersed with wagons, and they caused some reduction in the cost of 

 transportation, but it was not until the completion of the " National, or 

 Cumberland road," that travelling in carriages could be efi'ected with 

 either ease or safety. From the year 17S8 to the year 1800, the 



