SQ^, .lOUKNAL. OF THE 



and others, as leading to safer results in proportioning an 

 arch. The writer, however, called attention to the fact 

 that, as in most well-bnilt arches, the joints did not open, 

 therefore, by experiment on a big scale, it was shown that 

 the trne curve of resistance in arches, as g-enerally built, 

 did not leave the middle third; hence, for usual depths of 

 key-stone and usual loads, the true curve of resistance was 

 found somewhere in the middle third. Its position in the 

 middle third of the arch ring could be provisionally found 

 by the principle of least resistance, though it was admitted 

 that its exact position was dependent on the deformation of 

 the arch ring under stress, due to its elasticity, the laws of 

 which were not known at the time. 



However, after mathematicians had developed a true 

 theory of the so/id elastic arch^ "fixed at the ends" in 

 position and direction, it seemed possible to apply it to the 

 voussoir arch, and thus locate accurately the true curve of 

 resistance, provided the following conditions were fulfilled: 



1. No mortar was to be allowed between the arch stones 

 or voussoirs; 



2. The arch stones must be cut so perfectly that they 

 will fit exactly, when not under stress, in place on the 

 "center" — supposed unyielding; 



3. Under these circumstances the curve of resistance, 

 determined after the theory of the solid arch for the full 

 sections of the arch ring, must lie in its middle third. If 

 this last condition does not obtain, the solution is still pos- 

 sible, though the full sections cannot be used at certain 

 joints, which involves a tentative method of finding the 

 parts of the joints under stress and the resulting resistance 

 curve, which makes a practical solution of the case much 

 more difficult. 



Under the conditions assumed above the deformation of 

 the voussoir arch is exactly that of the solid arch and 

 there can be no question as to the theory applying. 



