282 



same notation as before, we get, in this case, for the value 

 of the over coining -force, 



why sin (2c' + /3 - ^) 



~2" "" sin (S - 2c' + (^) * 



Where y is equal the perpendicular from (F) on the face, or 

 face produced. 



If we put 



/3i=2c'+^, 

 and 



Si = S-2c'; 



the above equation, after a few reductions, becomes 



why cos j3i tanj3i-tan^ ,._> 



2 cos Si tan 8i + tan ' 



When this is a minimum, 



tan /3i \/(tan0 tan 8,) .^- 



*^"^~ v/(tan0tan8i)-v/{(tan0-tan|3i)x(tan^, + tanSi))' ^ '' 



„ wW tan sin /3i tan j3i 

 2 cos 8i 

 1 



V {tan0 (tan /3i + tan8i)}- yj (tanSi (tan0-tanj3 



0)) ' . 



(17) 



in which the usual changes of signs are to be made for the 

 negative values of Si, and for arcs greater than 90°. 



When the direction of the force makes an angle equal to c 

 with the face, then Si = 0, and, 



= 0, (18) 



R = ^%ini3,. (19) 



If the force exceed the value of R here found, it will slide along 

 the face, and when the face is vertical this value is equal to 

 the maximum maximorum value of the resistance, in the same 

 case, already found ; or, 



