PREFACE TO FIRST EDITION. V 



seems so especially designed. A subject of such importance, 

 which has already endured successfully so severe a test, and 

 made headway against such obstacles, we cannot certainly af- 

 ford any longer to ignore, and it is hoped that the present 

 work may serve to excite a more general interest in the method. 



For the practical engineer, the importance of graphical 

 methods needs, indeed, to-day no demonstration. Such methods 

 are everywhere in use. But a simple and general system, 

 which shall include all special solutions the development of 

 the few principles upon which all such solutions are based, and 

 from which they all flow is at least in this country unknown. 

 Even in English literature there is to be found little more than 

 the very elementary deductions of our first chapter, so that it 

 may justly be said that the entire method owes its existence 

 and development to the labors of German scholars and the en- 

 lightened appreciation of German engineers. How thorough 

 have been these labors, how widespread this appreciation, and 

 how various are the applications of the method itself, the reader 

 may gather from the Introduction to this work, and from the 

 appended list of literature upon the subject. A glance at this 

 list will also show that the selection of what was of most value, 

 and the omission of those applications of minor importance, 

 necessary to bring the present work within reasonable limits, 

 and at the same time preserve the logical unity and complete- 

 ness of the whole, was not the least difficult portion of our 

 task. It would, indeed, have been easy to have given the work 

 twice its present dimensions, though without a corresponding 

 increase in value sufficient to justify the additional cost. As 

 it is, no application -of real and practical value to the engineer 

 strictly deducible from the graphical statics has been over- 

 looked, and discrimination has been chiefly exercised in those 

 departments where graphical and analytical processes are still 

 of necessity combined. Here we have selected only those cases 

 where such union shows itself most advantageous, and the 

 graphical constructions most simplify, illustrate, or interpret 

 the purely analytical process, and where such cases, moreover, 

 presented a useful, practical, and not merely theoretical value. 



As to the plan of the work, a word of explanation is neces- 

 sary. We have endeavored to keep always in view the re- 

 quirements of both students and practitioners, of technical 

 schools and practical engineers, and thus to combine a text- 



