88 







Angle 



of 



Repose. 



Weight of S. 



Value of R. 

 when c= 0° 



Value of R 

 when cm 10" 



1 



2 

 3 

 4 



Water 



Fine dry sand, 

 Do. moist . 

 Quartz sand, drj'. 



0^ 

 33" 



35» 



62-5lbs. 



92 — 

 119 — 

 102 — 



R = 31iA^ 

 R = 13-8A2 

 R = 17-85A2 

 R = 13-77 A^ 



11 = 311 h^ 

 Rz= 4-8 A2 

 R= 6-2 h^ 

 R= 4-6 h^ 



Now, using the same data, and calculating from equations 

 (6) and (2) here given, the values will be as follow : 











Value of R. 



Value of R 







Angle 





when 6 =: 0, 



when b = 10" 







of 



Weight of W. 



and C D ver- 



and D E ho- 







Repose. 





tical : equa- 

 tion (6). 



rizontal : 

 equation (2). 



1 



Water, .... 



0° 



62 5ft)S. 



Rz=z3llhi 



R = 31|A2 



2 



Fine sand, dry, . 



33" 



92 — 



R=:13-5A2 



R= 9-7 A2 



3 



Do. moist, . 





119 — 



R = 17-3 h^ 



R=12-6A2 



4 



Quartz sand, dry, 



350 



102 — 



R=13-8A' 



R= 9-7 A2 



The values in the last column have been calculated from 

 equations (2) and (5) respectively, which gave the same 

 results when the latter is multiplied by sec^b, as fi^ x 

 sec^b = H^ : they are fully double those given by Tredgold, 

 and made use of by him in calculating the dimensions of re- 

 taining walls given in another Table. The differences in the 

 Tables, when b = 0, are immaterial. Equation (25) is, how- 

 ever, incorrect, as will be seen by squaring the second part of 

 equation (3) here given, actually, when we get 



A'w 

 2tanc 



Aanc-htanft-F-l- -2 A/t^nct^nb+l +'-^^^^^^+1) 

 \ ^ ^tanc y ^ ^ tan«c / 



Whence it appears that the term 



tan c -f- 1 

 tan ^ ' 



equation (25) under the square root, should be 



in Tredgold's 

 tan c tan i + I 



this being the case, his equation is then reducible to equation 

 (3). Equation (23) can also be reduced to the form of equation 

 (1), which is general, whether DE is horizontal or inclined. 



