87 
The equations apply also to finding the value of R and 
position of CF for ‘ dwarf walls” CD, at the toes of cuttings 
or embank- 
ments ;__ but 
when the frac- 
ture CF lies 
inside the top 
of the slope 
DG, the value 
of R and po- 
sition of CF 
are found as follows: 
Produce EG to A, and draw CA so that ACOD= 
AGOA, and as, therefore, AFAC = FGDC, we have only 
to determine R, and draw CF as if the bank to be supported 
was CAE. 
In the Encyclopedia Britannica, seventh edition, article 
‘*Masonry,” by Tredgold, there are given the following equa- 
tions: 
—1-+ (tane tan*z + tan*7 4+ tance tani +)!» 
tanz 
" (25)R Ea ee [ tani+tanc + —— 2(tanctani e+ + ryt 
“(23) tana= 
tani 
where a= < ECa, which the 
plane of fracture CE makes 
with the vertical line Ca; 
e = Z ACa; i = the com- 
plement of the angle of repose; 
h= AC the vertical height, 
and S = the weight of a cubi- 
eal foot of the material in 
ACE, AE being horizontal: and the following table of calcu- 
lated values of R from equations (26) and (25) : 
