fa rlleht att Mh 
85 
with CA, = @; then when the horizontal resistance R, neces- 
sary to support the wedge FCD, is a maximum,* 
sec.c V tanb tan c+l1 oe) 
tan¢@ = 
? tane (1) 
and cs 3 
W (seec —Y tanb tane + 1) 
R=-- est poh aad 
2 tane : (2) 
where W = the weight of a cubical unit of the stuff in FDC. 
Equation (2) may be changed into the following, 
pees e/a + cote — Ytanb+cotc)? (3) 
a simple form to calculate the values of R from. 
Also if CO is drawn parallel to DE, and we put 
6@= Z2GDE=2ZDCO; §=2Z OCE=80-—(c—B), 
and H= CD the slant height of the face: then 
tan (e—) = tan Z FCE = Y'tan?§+tandtand—tand (4) 
and 
H? Ww tan@ 
ar Nigel tang * am" (c— 9), (5) 
where d=c—b=2ZECD. 
When =0, CD coincides with CA, and we get from 
equation (1) 
secc — 1 
tang = —=— tanic 
? tane bs 
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 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. 
