10 



Scientific Proceedings, Royal Dublin Society, 



prism whose mean section is CAZB, and whose height is one foot, 

 will contain the mass of earth which, loy tending to slide (along 

 CD), would produce the maxi- 

 mum pressure on the portion 

 of the wall measured by CA, 

 while the horizontal force ne- 

 cessary to prevent this ten- 

 dency taking effect is in lbs. 

 weight equal to 62*5 |0 DS^, 

 where p denotes the specific 

 gravity of earth. It is not pos- 

 sible, of course, to apply this 

 theorem until the form of the 

 line AZDB has been assigned. 



It must here be mentioned, 

 that one of the ablest mathe- 

 maticians of our time, himself an engineer, Professor Eankine, has 

 taken exception to the assumption that the pressure of earth is 

 perpendicular to the supporting wall, and maintains that it is 

 inclined to it at a constant acute angle. It may be remarked, how- 

 ever, that the force can be supposed to be inclined to the wall at 

 an acute angle, only on the supposition that the friction of the 

 earth against the wall is taken into account ; but, as the mathema- 

 tical solution only gives us the least horizontal force consistent 

 with equilibrium, and as, in the construction of the wall, it would 

 be unsafe to limit its power of resistence to this minimum value, it 

 would not, in practice, be safe to allow, in addition, a margin on 

 account of taking into consideration the friction between the earth 

 and the wall. 



If, however. Professor Eankine's hypothesis be assumed, the 

 consideration of the problem, when thus modified, leads, in accord- 

 ance with Coulomb's principle, to a theorem differing but little 

 from that given by Doctor Hart. 



Let (fig. 2) a vertical plane, perpendicular to the surface of the 

 wall — supposed, for greater generality, to be inclined to the ver- 

 tical at an angle a — cut the surface of the wall in the straight line 

 AGO, and the surface of the earth in the line AZDB ; through C, 

 any point on the line AGO, draw C-P horizontal, GB inclined to GF 

 at the angle 0, the angle of friction of earth on earth, and CD a 



