ELISHA MITCHELL SCIEXTIFIC SOCIETY. 33 



degree of hardness of the morter joints (if any), settlement 

 and time of striking of the centers, the manner in which 

 the loads are transmitted to the arch ring, the relative 

 density of the various stones, and finally the dynamic effect 

 of moving loads. The true conditions are thus seen to be 

 so complex as to make the true solution of the stone arch 

 one of the most difficult, if not the most difficult, in all the 

 range of the application of the laws of mechanics to 

 engineering structures. 



The latest theory, given further on, includes the most 

 essentia] of the conditions just outlined, but not all of 

 them; so that it is not proposed as a final and complete solu- 

 tion of the problem, but as one sufficiently near to make 

 the results of decided practical value, approximating to the 

 exact trutli, as the hypotheses are more nearly realized in 

 the construction of the arch ring. 



Recurring now to earlier theories of the arch, Lahire, at 

 the beginning of the last century, considered that the arch 

 would break along "joints of rupture," half way betw^een 

 the crown and the springing, and he assimilated the action 

 of the upper part to that of a solid wedge, tending to slide 

 downwards along the joints of rupture, which l^st were 

 considered perfectly smooth, so that the pressure there was 

 directed normally to the point. 



This very crude hypothesis was adopted by Eytelwein, 

 who, however, found that joint of rupture for which the 

 pressure exercised against an abutment was a maximum. 

 As a matter of fact, friction can be exercised at any plane 

 joint, which Eytelwein only imperfectly considers; but 

 admitting it, the direction of the thrust at any joint of 

 rupture becomes indeterminate, so that apart from other 

 defects, the theory gives no definite solution. 



Coulomb, in 1773, made a great advance by considering 

 that an arch could not only fail by sliding along some 

 joint, but also by rotation along the edges of certain joints. 



