XIII. On the Equilibrium of the Arch. By the Rev. Henry Moseley, 

 B.A. of St John's College; Professor of Natural Philosophy and 

 Astronomy in King's College, London. 



[Read Dec. 9, 1833.] 



1. Let a mass acted upon by forces applied to any number of 

 points in it be imagined to be intersected by an infinite number of planes, 

 dividing it into exceedingly small laminse. Suppose the direction of the 

 resultant of the forces acting upon one of these, having for its ex- 

 ternal face a portion of the surface of the body, to be determined. 

 Combining this force with those acting upon the different points of 

 the next, contiguous lamina; let their common resultant be ascertained. 

 Proceed similarly with the next, and with each succeeding lamina. 



These lines will then be the tangents to a curved line, called in 

 the following paper the line of pressure, whose intersection with each 

 lamina, marks the point where a single force might be applied so as 

 to produce the same effect with all those impressed upon that lamina, 

 this single force being impressed in the direction of a tangent to the 

 curve. 



If any of these imaginary intersecting planes be supposed to become 

 real sections of the mass, so as to separate it into distinct parts, the 

 conditions necessary that no one of these parts may slip or turn over 

 on those contiguous to it, will manifestly be determined by the direc- 

 tion of the line of pressure in reference to the plane of the section. 



In general it will be observed that forces applied to a system of 

 variable form are, when in equilibrium, subject to the same conditions 

 as though its form were invariable, together with certain other conditions, 

 dependant upon the nature of the variation to which the form of the 

 system is liable. In other words the conditions of the equilibrium of 

 a system of invariable form are necessary to the equilibrium of a system 

 of variable form ; but they are not sufficient. We shall first determine 



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