CHAP. XV.] THE STONE AKCH. 317 



parallel forces whose intensities are directly as their distances 

 from a certain axis, 



Now, neglecting the influence of the mortar, the wall can 

 resist compression only. No tension can exist at any point of 

 the joint surface. 



Clearly, then, the neutral axis should lie wholly without the 

 cross-section, or at most only touch it. It should never be 

 found within the cross-section, as in that case all the material 

 on the other side is useless, and might be removed entirely 

 without affecting the pressure upon the actual bearing surface. 



The neutral axis, then^ should always lie witho ut the cross- 

 section of the joint. 



171. System of Parallel Forces whose Intenitie are 

 proportional to their Distances from a certain Axis The 

 Kernel of a Cross-section. If in a system of equal and paral- 

 lel forces we find the moment of each of these forces with 

 reference to a certain axis, and then consider these moments as 

 themselves forces, we shall have a system of the kind referred 

 to, since each moment force will be directly proportional to its 

 distance from a given axis. 



Now, as we have seen in Art. 60, Chapter VI., the centre of 

 action of such a system of moment forces does not coincide 

 with the centre of gravity of the- original simple forces, but for 

 any given axis is found from the central curve of the cross-sec- 

 tion. Li PL 11, Fig. 35, we have already given the construc- 

 tion for finding this centre of action, the semi-diameter of the 

 central curve being known, for any given axis. 



Suppose now this axis to envelop in all its different posi- 

 tions the outline of the given cross-section, and find the corre- 

 sponding positions of the centre of action of the moment forces. 

 These different points lie in a closed figure which we may call 

 the kernel of the cross-section. Then, in order that we may 

 always have compression in every part of the joint surface of 

 our wall, the resultant of the forces acting upon it should 

 always act within the kernel. 



In Plates 11 and 12, Figs. 36, 37, 38 and 40, we have con- 

 structed the kernels of the various cross-sections represented. 



Thus in Fig. 36, according to the construction of Art. 62, for 

 an axis at A ? we describe upon O C a semi-circle. Then with 

 as a centre and radius equal to semi-diameter of the central 

 ellipse on A C, describe an arc intersecting the semi-circle in a, 



