366 Prof. NECKER on the Determination of the 



it follows, that in the cliff on the northern bank of the Rhone, 

 the seams present an inclination a little to the south of east, while 

 the seams on the cliff of the southern bank shew a dip a little to 

 the north of east. 



From such an appearance some observers have been led to 

 conclude, that this opening in the chain had been produced by a 

 depression of the strata. But the remarks before stated show 

 that such appearances are merely superficial and external, and 

 that a similar inclination in the lines of stratification does not in- 

 dicate a corresponding inclination of the strata, but is owing 

 simply to the mere accidental direction of the section through 

 the stratified mass. In fact, the strata on both sides of the 

 Rhone, at the Fort de 1'Ecluse, although they have been traver- 

 sed by a wide and deep fissure, entirely occupied by the waters 

 of the river, have not experienced any change in their original 

 direction and dip ; so that this narrow transversal valley cannot 

 by any means be called a valley of depression. I am convinced 

 that the same will be found to be the case with many much lar- 

 ger and much more important transversal valleys of the Alps, 

 which have been supposed to be formed by the sinking of the 

 strata on both sides. 



Now, it has occurred to me, that such external appearances as 

 are the position of the seams of strata on the surface of cliffs, could 

 enable us, when combined together, to determine the true posi- 

 tion of the planes to which they belong, inasmuch as the posi- 

 tion of a plane is determined by that of two lines in the same 

 place. 



I am indebted to my learned friend M. GAUTIER, Professor 

 of Astronomy in the Academy of Geneva, for the following exact 

 and complete solution of the given problem by means of alge- 

 braical formulae. 



The angles a and a', which two straight lines form with their 

 horizontal projection, being given, as well as the angles /3 and /3', 



