KLISHA MITCHELL SCIENTIFIC SOCIETY. 35 



intensity of the thrust at the crown, it is evident that some 

 additional principle must bet introduced to enable us to 

 choose the true one. Mosely introduced for this purpose 

 the principle of the least resistance^ which at once fixed the 

 true curve as the one corresponding to the minimum hori- 

 zontal thrust. This caused the results to agree with those 

 of Coulomb, in most cases, though not in all, as the curve 

 so determined does not, for some arches, pass through either 

 edge of the crown joint, as Coulomb's theory requires. 



In this and previous theories the arch and load were 

 taken as symmetrical with respect to the vertical through 

 the crown which thus restricts the theory to structures 

 having fixed loads and rendering it of little service in the 

 investigation of the strength and stability of road or rail- 

 road arch bridges subjected to a moving load, which pro- 

 duces a maximum distortion when placed over one haunch 

 of the arch; further, the theories demanded incompressible 

 voussoirs of infinite strength, which do not exist. 



Scheffler developed very completely the theory of curves 

 of resistance for the least horizontal thrust, for both sym- 

 metrical and unsymmetrical arches and loading; but as his 

 theory requires the thrusts at the critical joints to pass 

 through the very edges, it cannot apply to ordinary stones, 

 where crushing would result, as a matter of course. Now, 

 as crushing does not occur at the joints in well-designed 

 arches, it follows (without other considerations) that 

 Schefiler's theory must, at least, be modified. The writer 

 did this in introducing the theory to American readers in 

 1874, by empirically limiting the curve of resistance to the 

 middle third of the arch ring. With such a restriction, for 

 a joint with mortar, there would be no. tension exerted 

 anywhere along the joint, and for a joint without mortar 

 there would be a compression throughout the whole length 

 of the joint, so that no joint would open. Such restrio 

 tions had alreadv been sucrorested bv Rankine, Woodburv 



