466 PROFESSOR MOSELEY, ON THE THEORY OF 



1. Let a continuous mass to which are applied certain forces of 

 pressure, be supposed to be intersected by a pkme whose equation is 



z = Ax + By + C (I.) 



Let the sums of the forces impressed upon one of the parts and 

 resolved in directions parallel to three rectangular axes, be respectively 

 ilf,, M.>, 31,, and the sums of their moments iV„ N., N-^. 



Let, moreover, the position of the plane be such that these forces 

 are reducible to a single resultant, a condition determined by the equa- 

 tion 



M,N, + 3I,N, + 3I,y, = (IL) 



The equation to this single resultant will then be 



(HI.) 



31, N.- 



3f, ^ N, 



If between the four preceding equations in which Af,, M., M-^, 

 iV„ iVa, Ni are functions of A, B, C, these three quantities A, B, C 

 be eliminated, there will be obtained an equation in .x, y, s, which is 

 that to a stu-face of which this is the characteristic property ; that it 

 includes all the points of intersection of the resultant force with its 

 corresponding intersecting plane in every position, which, according to 

 the assumed conditions, this last may be made to take up. 



This surface is the Surface of Resistance. 



If to the preceding conditions there be added this, that in each 

 two copsecutive positions of the intersecting plane the corresponding 

 resultants shall intersect, the surface of resistance will resolve itself into 

 a line, which is the Line of Resistance. 



Differentiating on this hypothesis the equation III. in respect to 

 A, B, C, we have 



