258 DEEP BOREHOLE SURVEYS AND PROBLEMS 



Ad = another perpendicular dropped from A on to the 

 horizontal plane which passes through the inter- 

 section of the drill hole with the plane of the 

 bedding. 



abc = the above bedding or seam plane having a right 

 angle at c. 



adc = the above horizontal plane through the inter- 

 section of the drill hole and bedding plane. 

 cAh and cAd represent vertical planes at right angles to 

 ac, the strike of the bedding, and drawn through 

 A. 



Aa = the length of the seam or bed pierced as given 

 by the core. It will be found convenient in all 

 cases to express this as unity. 



The line Ac makes an angle ^ with the horizontal plane, 

 and an angle a with the plane of the bedding. (The words 

 "bedding" and ''seam" have similar meanings in the 

 following discussion.) These angles are Acd and Acb, 

 respectively, and, as in Case 1, their sum is equal to the full 

 dip. Then 



cos i = ad 

 cos 5i = ab 



sin i = Ad 

 sin 8i = Ab 



ac ac 



cos d = — 5 = : 



ad cos I 



.'.ac = cos i cos 6 

 and 



be = V{ab)^ — {ac)'' = Vcos- 5i — cos^ i cos^ 



Ac = V{bc)' + {Ab)^ = Vcos- 5i — cos^ i cos^ d + sin^ 5i 



= VT — cos- i cos- 6 



. , . 1 Ab sin 5] 



Angle sm-^ -r— — 



Ac Vl — cos^ i cos^ 6 



