nndRetfiirmg IFulls. 403 



j>imple case of partial scarp revetements presents itself, which it 

 v/ould be as well to consider. 



Suppose the revetemcnt (fig. 13) to have aberm AB equal to 

 the breadth of the top of the wall, and that the plane of fracture 

 produced would intersect the earthen scarp at G ; also let /t' be 

 the height of this point above the top of the wall = FB ; h being 

 the height of the wall as before. It is obvious that the equation 

 (D) still expresses the conditions of equilibrium j that is, 



p W.ftan a — f) 



1 + '27'tan.a— /-' 



But if I be the angle which the front of the scarp BG makes 

 with the horizon ; then by supposition — — = — — : therefore 



• ' ^ tan. a tan. b ' ' 



W= IAS -'^- — . And as this change in the value of W will not 



'■ tan. a ^ 



affect that of the angle of fracture in any considerable degree, it 

 may be neglected ; in which case 



R=/.si±A'. (I) 



Hence the leverage becomes Dp ;= li —- — '--. and the value 



* o^/i 4- he y 



- I . . h tan. h 

 OX ft IS = -. 



tan. a— tan. v 



But in the actual construction of revetements the angle I is 

 generally 45^, and in that case /t'= -— ; consequently 



R=h^S ./'"•" -^. (K) 



And, Dp = h 



2((tan. n— 1) 

 2 tan. a + 1 



C tan. a 



The equation (K) might be applied to demirevetements, and to 

 partial revetements in general, where it would be accurate enough 

 tor practical purposes : and it must be remembered that the old 

 methods fail completely when applied to these revetements. 



According to the principles I have endeavoured to point out, 

 it appears, that when the earthen scarp exceeds the height //, 

 it might be raised to any height without increasing the pressure 

 against the wall ; as is indicated by the experiments of Col. 

 Pasley*. But if we suppose (with Belidor, Rondelet, &c. &cc.) 

 that the angle of fracture coincides with the natural slope of the 

 earth ; and also that the inclination of the earthen scarp BG 

 (fig. 13) is the same as the natural slope (which is generally taken 

 at 45°) ; it is obvious that the pressure ought to increase with 

 the height of the earthen scarp, without limit. 



• "Course of Military Instruction," vol. iii. chap. xxv. 



C c 2 This, 



