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- r 



ments ; but 

 when the frac- 

 ture CF lies 

 inside the top 

 of the slope 

 DGjthe 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 Encyclopaedia Britannica, seventh edition, article 

 ^'•Masonry " by Tredgold, there are given the following equa- 

 tions : 



(23) tan a 



_ — 1 -|- (tan c tan^^ -\- tan^e -f- tan c tan i -f-)J » 



tan I 



"(25)R = #^.rtani + tanc + -^.-2('tanctani + i^^£±i + iy> 

 ^ ' 2tani|_ tani \ tani / J 



where a— ^ ECa, which the 

 plane of fracture CE makes 

 ■with the vertical line Ca ; 

 c = Z AC«; i = the com- 

 plement of the angle of repose ; 

 ^ = AC the vertical height, 

 and S = the weight of a cubi- 

 cal foot of the material in 

 ACE, AE being horizontal : and the following table of calcu- 

 lated values of R from equations (26) and (25) : 



