XIV PREFACE TO 8ECOND EDITION. 



girder and the braced arch remaining, which he is not able to 

 solve. Should it be deemed undesirable to consider these, he 

 can at once pass to Chap. II. and then to the stone arch, Chap. 

 XV. If, however, a knowledge of the above is desired, he is 

 now ready to extend his principles and methods to them also. 

 Thus he has already recognized that provided only all the 

 outer forces are known, he can both diagram and calculate 

 any framed structure. In such structures as he has hitherto 

 had, these outer forces are either given or are easily found. In 

 the cases now considered they are not all given, and must, 

 therefore, first be found. Once known, however, his way is 

 clear. Recognizing clearly, then, what is aimed at, the supple- 

 ments to Chaps. VII. and XIII. are first taken, and he is now 

 able to find for the continuous girder the outer forces required. 

 Chap. XIII. will then give, exercises in finding these forces, 

 and handling the formula he has just deduced. Finally, Chap. 

 XII. resumes again in the light of his present knowledge the 

 same old two methods with which he is already so familiar, of 

 diagram and calculation, and a few examples actually worked 

 out by both methods complete his mastery of the continuous 

 girder and draw span. He can now pass on to the braced 

 arch, and in Chap. XIV. will find all that he needs. Here he 

 must take at first the formulae and constructions for finding the 

 outer forces on trust. Afterwards, if deemed desirable, he can 

 follow out the development of these formulae as given in Sup- 

 plement to Chap. XIV. 



In the case of the parabolic arch, at least, the constructions 

 are so simple that it is well adapted to class instruction. The 

 draw span is of such importance as to render some attention to 

 it, at any rate, desirable in any full course. Thus the student 

 is now able to solve any case whatever of framed structure in 

 two ways, by diagram and calculation. The same simple prin- 

 ciples have been applied throughout, and formula have been 

 called in only in a subsidiary way to determine certain forces 

 which are necessary to be first known before these principles 

 can be applied. 



Thus Chap. I., Appendix to Chap. I., Supplements to Chaps. 

 VII. and XIIL, then Chaps. XIII., XII., with Appendix, and 

 XIV. with Appendix, form by themselves and in this order a 

 complete and systematic course. 



If, however, it is deemed undesirable to consider the con tin- 



