294 Mr MOSELEY, ON THE 



the form and position of the line of pressure on the hypothesis, that 

 the form of the system is invariable, and then consider the modifica- 

 tion to which these are subjected by the opposite hypothesis. 



2. Let there be conceived a mass, the connexion between the parts 



of which may be any whatever, and the nature of whose surface is 



determined by the equation 



^ xy% = 0. 



Let it be intersected by an imaginary plane whose position in reference 

 to a given system of rectangular co-ordinates is determined by the arbi- 

 trary constants A, B, C, and whose equation is 



z = Ax + By + C (1). 



Let Ml, Mi, Ms represent the sums of the forces acting upon one 

 of the parts into which the mass is divided by the intersecting plane, 

 resolved in directions parallel to the axes of x, y, z, respectively. Also 

 let JVx, N'z, ^3 be the moments of these forces about the same axes. 

 Then Mi, Mi, Ms; Ni, N^, iVs are given in terms of the arbitrary 

 constants A, B, C — of the given forces — and of the constants involved 

 in the given equation to the surface of the mass. 



Let the position of the intersecting plane be supposed to be such, 

 that the forces acting upon the above mentioned portion of the mass 

 may have a single resultant, an hypothesis which involves the known 

 condition 



MiN, + M,N, + M,N, = (2). 



The equations to the resultant in any given position of the inter- 

 secting plane, are 



Ml ^Ni 



^'=M^-'Ms 



Let the arbitrary constant C be eliminated from this equation, and 

 from the equation to the intersecting plane by means of equation (2) ; 

 and let the plane be then supposed to take up a series of positions, 

 the law of which is fixed by its equation, and of which, each is im- 

 mediately adjacent to the former. 



