296 Mr MOSELEY, ON THE 



3. By the elimination of A,y B and C between the equations (2), (3) 

 and (5), a relation is obtained between the co-ordinates of a point in 

 the direction of the resultant force, applicable to every position of the 

 intersecting plane. Being in fact, the equation to that developable 

 surface which is the locus of the resultants, and, which has for its 

 edge of regression, the line of pressure. This surface will be properly 

 called the surface of pressure. 



It is evident that at that point where the line of pressure even- 

 tually cuts the surface of the mass, there must be applied a force equal 

 to the resultant of all the other forces impressed upon the system 

 and in the direction of a tangent to the line of pressure at that point, 

 or there must be applied to the surface of the last lamina cut off 

 by the intersecting plane, forces whose resultant is of that magnitude 

 and in that direction. 



4. These conditions may be expressed as follows. 



Let P' be the force — or the resultant of the forces — applied to the 

 last lamina, x^, y,, ss, the co-ordinates of the intersection of the line of 

 pressure with it, a, fi, y the inclinations of P' to the axps of x, y, %. 

 ^ Also let 



be the equations to the line of pressure. 



Since the point Xx, y^, %i is a point in the surface of the mass, 



.-. ^Xiy.z, = 0. 



Also, since it is a point in the line of pressure, 



.-. Xi = Fi%i 

 y, = F^%x 



Since the direction of P' is that of a tangent to the line of 

 pressure, 





tan a = 



tan /3 = 



d%, ' 

 d%i 



