34 JOURNAL OF THE 



He assumed the horizontal thrust at the crown always to 

 pass through either the upper or the lower edge of the 

 joint and found its minimum value, so that uo rotation 

 ivould occur about the lower or upper edge of any joint 

 below the crown and such that no sliding^ could occur along- 

 any joint. 



It is not necessary to explain the ingenious method by 

 which the true thrust, after his theory, was ascertained. 

 The theory was a marked improvement over the wedge 

 theory, and it has been followed by a host of authors, with 

 various improvements, even up to the present day. 



As the thrust either at the crown joint or the lower joints 

 of rupture cannot act along an edge without crushing 

 ensuing, it is evident that the true positions of the thrusts 

 at these critical joints has not been correctly ascertained; 

 further, there is nothing in the theory to raise the inde- 

 termination. 



The next advance in the theory was made by certain 

 authors who used a funicular poIygo)i in studying the resist- 

 ance at the various points, a method which is still the 

 basis for the analytical treatment of the arch. 



It required but an additional step to see that tlie curve 

 connecting the centers of pressure on every joint of the arch 

 ring (to which the proper "funicular polygon" approxi- 

 mates for segmental arches) was a surer test of the stability 

 of an arch ring and that, in a stable arch^ it must always 

 be possible to draw some "curve of resistance" (as the 

 curve connecting the centers of pressure is called) within 

 the limits of the arch ring, or, for safety, within much nar- 

 rower limits. 



The exact location of this curve, for any arch, loaded in 

 any manner, will completely solve the problem for that 

 arch; but where an infinite number of possible curves of 

 resistance can be drawn within the arch ring (or narrower 

 limits), all varying in the point of application, direction or 



