85 



with CA, — (jt; then when the horizontal resistance R, neces- 

 sary to support the wedge FCD, is a maximum,* 



♦or, jL _ sec.c V tan6 tanc+ 1 — 1 , , 



tan^_ Z (1) 



tanc ^ ' 



and 



_ ^ ^ fsecc — l/tan 6 tan c + 1 

 tanc 



^ = -2- r" ' ;::7""" — j > (2) 



where W =: the weight of a cubical unit of the stuff in FDC. 

 Equation (2) may be changed into the following, 



h-w , 



^ — 2tanc ^'^*^"^ + ^"^^~ Vtan6 + cotc/ (3) 



a simple form to calculate the values of R from. 

 Also if CO is drawn parallel to DE, and we put 



0= Z GDE=: Z DCO; g= Z OCE = 0- (c-6), 



and H =: CD the slant height of the face : then 



tan(c-0) = tanZ FCE = /tan^g + tan rf tang- tang (4) 

 and 



H^ w tan o , V 



^ = -^^tHI^03T^,^x*^«'(^-^)' (5) 



where d—c — h — Z. ECD. 



When 6 = 0, CD coincides with CA, and we get from 

 equation (1) 



secc — 1 



which shews that the equation of Prony holds good, whatever 

 the inclinations of CD and DE to the horizon may be, if these 

 lines continue at right angles to each other. We also get 

 from equation (2) or (5) in this case, 



* Generally we have R = W X DCF X tan. FCE, for any fraction CF ; a 

 very simple expression for finding the value of the resistance when the posi- 

 tion of the fracture is given. 



