ELISHA MITCHELL SCIENTIFIC SOCIETY. 39 



be contained within the middle third of the arch rinsr, and 

 for the joint where the departure was greatest this line 

 should just touch the middle third limit. A slight decrease 

 in the depth of key would thus cause the true resistance 

 curve to pass slightly outside the middle third at some joint 

 or joints. 



The proper depth of key to meet this last condition was 

 found tentatively by assuming successive depths of key for 

 the same span until one was found in which the true resist- 

 ance curve could just be inscribed in the middle third for 

 the most unfavorable position of the live load. Only two 

 trials were needed in any case. 



It was found for the arches so desio^ned that no slidinor 

 could occur along any joint. The maximum stress, in tons 

 per square foot, at the most compressed edge, varied from 

 nine for the twenty-five foot span to thirty-six for the 150 

 foot span. 



Thus the arch ring possessed the requisite stability for 

 anarch of sandstone or limestone and an excess of stability 

 for granite, whose weight per cubic foot is over the 140 

 assumed. For material weighing over 140 pounds per 

 cubic foot the depth of key given below can be slightly 

 diminished or a heavier load can be assumed. 



The live load assumed is known in Cooper's Specifica- 

 tions as "Class Extra Heavy A." 



We give below the distances in feet from the front pilot- 

 wheel to each pair of wheels in turn, and on the same line 

 the weight of the pair of wheels in tons of 2,000 pounds: 



Pair of Pilot- wheels o feet 8 tons. 



Driver-wheels 8.1 " 15 " 



13-83 " 15 " 



18-33 " 15 " 



22.83 " 15 " 



" Tender-wheels 29.92 " 9 " 



34-75 " 9 " 



40.42 " 9 " 



45-25 " 9 " 



Pilot-wheels 54.25 " 8 " 



