302 Mk MOSELEY, ON THE 



found by eliminating the values of a; and y between the equation to 

 the surface and the equation to the line of pressure, involve only 

 such possible values of z as correspond to the points P and i*, where 

 the intersecting plane touches the surface, or to points where the line 

 of pressure touches it. 



It is a further condition of the equilibrium that the line of pressure 

 should not cut any section of the mass, at an angle with the perpen- 

 dicular to that section greater than a certain given angle, dependant 

 upon the friction of the surfaces in contact, and having for its tangent 

 the coefficient of friction. 



The resistance of surfaces is not exerted exclusively in the direction 

 of the normal, according to an hypothesis, which was probably in- 

 troduced into the theory of Statics in order to simplify the investi- 

 gations of those who originated that science, but which there seems 

 no reason for retaining any longer. It is exerted in an infinity of 

 different directions included within a certain angle to the normal, or 

 rather within the surface of a certain right cone, having the normal 

 for its axis and the point of resistance for its vertex. Any force, 

 however great, applied within this conical surface will be sustained 

 by the resistance of the surface of the mass — and no force however 

 small, without it. 



Let R represent a single force on the resultant of any number of 

 forces applied to a fixed surface, and let R' and R" be the resolved 

 parts of R in the directions perpendicular and parallel to the surface. 

 Also let p be the inclination of R to the vertical, and f the coefficient 

 of friction. The friction of the surfaces in contact is therefore repre- 

 sented by fR, and motion will, or will not, ensue according as R" is 



K" 



greater or is not greater than /R'. Or, according as -p, is greater or 



is not greater than f. Or, if y = tan (p, according as tan p is, or is 

 not, greater than tan (p, or as p is greater or is not greater than (p. 



