282 



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

 of the overcoming-force, 



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



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



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

 face produced. 



If we put 



/3i = 2c'+/3, 

 and 



gi = 8-2e'; 



the above equation, after a few reductions, becomes 



T, _ why cos j3i tan /3i - tan 

 2 cos §1 tan Si + tan ^ ' 



When this is a minimum. 



(15) 



tanrf,= tan/3i V(tan0tan8i) 



^ ^(tan0tangi)--v/{(tan0-tanj3i)x(tan/3i + tangi)}' ^ '' 



„ _ wh^ tan sin /3i tan j3i 

 2 cos Si 



(17) 



f_ ^ _v. 



\V{tan0(tan/3i + tangi)}- V{tangi(tan0-tanj3i)); ' 



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

 negative values of 8i, 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) 



„ wh^ . ^ 



R = -2-sm/3,. (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, 



