APPENDIX.] THE BRACED ARCH. 405 



tion is as much justified by the remarks of Capt. Eads, which 

 are quoted, as the other and neither are correct. Apart, how- 

 ever, from the merits of the controversy, with which we have 

 nothing to do, the results given are undoubtedly correct for an 

 arch of the same dimensions as the St. Louis uniformly loaded 

 and hinged at the ends in upper flange and at the crown in 

 lower. If, then, a comparison of these results with those given 

 by Capt. Eads shows them all too large, then, since Capt. Eads' 

 formulae are, as we have seen, undoubtedly correct, it clearly 

 shows the superiority of the arch without hinges. This is the 

 only legitimate deduction which can be made. 



The formulae of the paper to which we refer, are undoubtedly 

 as " true as the principles of the lever," and apply, beyond 

 question, to an arch hinged as he supposes. Our formulae in 

 Art. 27 of the Supplement to Chap. XIV. are also as true as 

 these principles ; but to apply correctly even so simple a prin- 

 ciple as that of the lever, demands a knowledge of all the forces 

 and their points of application. From our formulae, as we 

 have shown in Art. 34 of the above Supplement, we may easily 

 deduce Capt. Eads', thus proving the accuracy of both. Though 

 the ''calculus will not determine the strains affecting a truss, 

 whether arched or horizontal," it may nevertheless be exceed- 

 ingly serviceable in determining the forces which act upon the 

 truss without an accurate knowledge of which the " principle 

 of the lever" can only mislead. This principle, upon which 

 so much stress is laid, is precisely that which we have employed 

 so often in this work, and shown to be of universal application. 

 In Art. 36 of this Appendix we have made use of it, just as in 

 the paper referred to, in the calculation of an arch similar to 

 the St. Louis. Our results differ from those there obtained, 

 simply because we take into account a force and lever arm 

 whose existence is there ignored. The paper assumes that V 

 and H and the load are all the forces which act, and these are 

 all of which the formulae given take account. In common with 

 Capt. Eads, we take in addition a moment due to the continuity 

 of the ends, while V and H themselves, by reason of this con- 

 tinuity, have very different values. 



Thus, for full load, we have from eq. (81), Art. 34 of Sup- 

 plement to Chap. XIY., 



H _ P a " 4 A' 

 ~ 2T 45 * + 4A' 



