. Curtis — Pressure of Earth against a Retaining Wall. 19 

 therefore, 



^1 = ^ " • 1 = ^' ^^ " ought. 

 osi sm ^ o 



I may remark that Moseley, in his Engineering, has inves- 

 tigated, hy a different method, the problem where the friction 

 between the wall and the earth is neglected, and has deduced, in 

 certain cases, analytical expressions for the pressure. These ex- 

 pressions may also be deduced from the geometrical solutions 

 given in this Paper, but, as they are not logarithmic, they are 

 practically, of little value, and, I think, in practice, are of little 

 importance compared with graphic methods and geometrical 

 constructions. 



It has been objected to such discussions as the above, that, 

 after the solution has been obtained on mathematical principles, 

 it is necessary to introduce a factor of safety, to ensure stability, 

 making the wall from eight to ten times as strong as is in accord- 

 ance with the theoretical result ; but this objection is equally valid 

 against the application of mathematics to all cases where the 

 strength of materials is concerned, in which, as stated by Eankine, 

 Twisden, and others, it is usual to take the working stress as one- 

 eighth, or one-tenth of the proof stress, which is itself considerably 

 short of the ultimate strength. If a wall could be made perfectly 

 rigid, and would not in time become weakened if taxed to its ulti- 

 mate strength, then the mathematical deductions would in practice 

 be exact. 



2 



