CHAP. XYI.] THE INVERTED AECH. 341 



both by resolution of forces and by moments (Arts. 9 and 16 

 of Appendix). The latter being so general and simple in its 

 application, we have not felt justified in leaving it entirely out 

 of sight, and in those cases where it seemed of especial service, 

 or assisted the graphical solution, we have illustrated it more or 

 less fully (Chap. XII.). In this latter chap, we have also given 

 constructions as well as formulae, and developed principles 

 which, it is believed, render possible, for the first time, the com- 

 plete and accurate solution of the important case of the " draw 

 span" (Arts. 118-121.) 



The formulae of Chap. XIII. in connection with the method 

 of calculation by moments, render the calculation of the con- 

 tinuous girder generally as simple, and but little more tedious 

 than for the simple girder itself. Whatever may be thought 

 of the advantages or disadvantages of this class of structures 

 by engineers generally, it is at least time that such structures 

 as draws or pivot spans should be calculated under suppositions 

 which approach somewhat more nearly the actual case than is 

 at present the practice. As to the relative economy of con- 

 tinuous girders, we have endeavored to enforce the fact that 

 the saving over the simple girder is from 15 to 20 and even 50 

 per cent. We give in the Appendix a tabular comparison of a 

 few cases sufficient to show the point beyond dispute, and any 

 one may easily add to the list, or verify the calculations. 



The " graphical arithmetic," as it might be called, such as 

 graphical addition, subtraction, multiplication, division, extrac- 

 tion of roots, determination and transformation of areas, etc., 

 we have entirely omitted in the present work, judging it of but 

 little practical value, except in rare cases, when we have ex- 

 plained the necessary constructions as they occur, and unneces- 

 sary for the development of the graphical method proper. [See 

 Chap. IV. of Introduction.] 



