Position of Strata in Stratified Rocks. 367 



which these projections form with a fixed horizontal axis, there 

 will be determined, 1st, the angle 7 comprised between the plane 

 passing through the two straight lines and the horizontal plane 

 by the formula. 



sin (a' + a) cos (j> 

 i a' cos a sir 



</> being an auxiliary angle, such that 



cos i (/3' /3) V sin 2 a' sin 2 a 

 sin V z sin (a' + a) 



#d, the angle a comprised between the line of intersection of the 

 two planes and the fixed axis by the formula 



tang 7 



in which every thing is known except u, when y has already been 

 determined. 



. '\t ' -j* -*'.. i.j 



It will be readily perceived that this solution, however satis- 

 factory it may be in a theoretical point of view, will never be 

 advantageously employed in practice, on account of its presup- 

 posing that the data given by actual observation should be of the 

 nicest accuracy. The measurement of the angle of dip of the 

 lines of stratification, and of the angle which the horizontal pro- 

 jection of these lines make with the magnetic meridian, espe- 

 cially when taken at a distance, can never reach the degree of 

 accuracy required by the nature of the formulas employed. 



In such a case, practical geometry, or that system of combined 

 projections which is known in French under the name of Geome- 

 tric descriptive, requiring less perfect data, will be in general better 

 adapted to the imperfect means which the geologist possesses 

 for ascertaining the data required, and at the same time will 

 give results sufficiently accurate for the present purposes of the 

 science. 



