ELLSHA MITCHELL SCIENTIFIC SOCIETY. 41 



Stone arches of the dimensions given should be perfectly 

 safe against rotation or sliding anywhere for the very 

 heavy rolling load assumed; but the depth of key should 

 not be less than the values given, as the true line of 

 resistance, for certain positions of the moving load, will 

 then pass outside the middle third at certain joints, and 

 although the arch may be stable, the factor of safety is 

 reduced too much and the joints of rupture may open, thus 

 admitting the infiltration of water, w^hich is not desirable; 

 besides, for the larger arches, the maximum intensity of 

 stress at the edges of the joints of rupture may exceed safe 

 limits. In fact, this intensity for the 150-foot span for a 

 7-foot key is 36 tons per square foot — an admissible value 

 for good solid voussoirs, well laid, though not at all for 

 rubble construction or for brick, except, perhaps, the very 

 best pressed brick. From experience it would seem that 

 an outside limit for this intensity for good granite should 

 be about 46 tons per square foot. 



The arch can preferably be built by increasing the radial 

 length of joint as we go from the crown to the springing, 

 as is done in arches of large span, in which case the depth 

 of key-stone can be decreased somewhat below the tabular 

 values with the same security against overturning, sliding 

 or crushing. 



In case the abutments or piers yield somewhat at the top 

 from defective foundations the depth of key should be 

 greater than as given in the tables. 



The formulas that have been proposed for depth of key 

 by many authorities are not founded on theory, but on the 

 successful practice of the past, particularly for common 

 road bridges and railroad 'bridges subjected to the lighter 

 loads of several decades ago. 



The writer has been convinced for a number of years 

 that the dimensions given by many of these formulas (in 

 current use to-day) are very inadequate for stone arches sub- 

 jected to the very much heavier rolling loads of to-day, and 

 that arches so proportioned probably are saved from destruc- 

 tion only from the extra resistance afforded by the span- 



