40 



JOUKNAL OF THE 



The second locomotive can be located from the last pair 

 of pilot wheels. 



For spans of fifteen feet and under, a pair of wheels car- 

 rying forty tons was used as producing a more hurtful 

 effect. The above load was placed over one-half of the 

 arch, roughly speaking, the heaviest part being over the 

 center of the haunch. Its exact position, however, was 

 determined very carefully so as to produce the most hurtful 

 effect upon the arch ring. 



An approximation to this load was made by omitting the 

 pilot-wheels in some of the computations. Also by the 

 independent partly analytical treatment, used as a check, 

 the load on drivers was supposed uniformly distributed as 

 well as that on the tenders, and for convenience the lengths 

 of each portion were slightly changed to suit the divisions 

 of the arch required in the theory. The pairs of wheels 

 were supposed to bear on cross-ties eight feet in length, so 

 that only one-eighth of this load was supposed to bear on 

 a slice of the arch contained between vertical planes per- 

 pendicular to the axis of the arch and one foot apart. 



The depths of key so determined for arches of constant 

 section and rise = I span are given in the following table, 

 the determinations for the spans 12.5, 25, 50, 75, 100, 

 125 and 150 having been found directly, the others by 

 interpolation from these values. All dimensions are in feet. 



RISE EQUAL ONE-FIFTH THE SPAN. 



