40G NOTE TO CHAP. XIV. [APPENDIX. 



and from eq. (84) 



M- - 3 ,.* 

 * A 



Thus, instead of H = ^, as given in the paper, we have 



2 /i 



this into a certain coefficient which is less than unity. 



Taking pa = 936,000 Ibs., g = 6.025 ft., a = 257.88 ft, 

 and h = 46.65 ft. for centre line, we have H = 2,178,317 for 

 thrust at crown, instead of 2,586,184.9 Ibs. This thrust alone 

 would cause, then, 1,089,158 Ibs. compression in each flange. 

 Hut due to continuity of ends and crown, we have also a mo- 

 ment at crown M = 6,587,335, which being negative causes 

 tension in lower flange at crown. Dividing by 12.05, the depth 

 of arch, we have 546,666 Ibs. tension, and therefore only 

 1,089,158 546,666 or 542,492 Ibs. resulting compression. 

 Thia at 27,500 Ibs. per square inch, requires 19.72 square inches 

 area, while in the paper referred to we have 126.42 square 

 inches area. It is, however, but just to notice, that while this 

 loading (uniform) causes the maximum compression in lower 

 flange at crown for hinged arch, it does not for the arch fixed 

 at ends and continuous at crown. 



In this latter case, as we may see at once from the table for 

 M of Art. 18, Supplement to Chap. XIY., a load within the 

 centre half anywhere, causes tension in the lower flange, and 

 the maximum compression is when the flanks are loaded and 

 this portion is empty. It is with the maxima that the com- 

 parison must be made, and as Capt. Eads has, very properly, 

 taken the rolling load into account, it is with these maxima 

 that the comparison has been made. From such comparison 

 the paper finds that " every member of the two tubes is defi- 

 cient in area, many containing much less than half the material 

 that is necessary." As the results are correctly calculated for 

 a hinged arch, and Capt Eads' results are also correct for an 

 arch without hinges, we can only conclude not that "the 

 great importance of immediately strengthening the ribs of the 

 St. Louis bridge can no longer be ignored," but rather that, for 

 long spans of small .relative rise, the arch without hinges is 

 much preferable and more economical. The case is, indeed, 

 perfectly analogous to that of the continuous girder. Here 



