PEEFACE TO FIKST EDITION. XI 



treated of, he will, in common with the practical engineer, find 

 in the other portions of the work and in the Appendix just 

 such assistance as he needs. We would also call the attention 

 of the mathematician more especially to the investigation in 

 Chap. V., Arts. 47-51, of the effects of a given recurring system, 

 of moving loads, the analytical treatment of which would be 

 almost impracticable by reason of the complexity of thte for- 

 mulae obtained, and in this respect certainly worthless, even if 

 possible, but the geometrical treatment of which gives rise to 

 some of the most elegant constructions of the graphical statics; 

 also to the Supplements to Chaps. XIII. and XIY., in which 

 the analytical treatment of the continuous girder and braced 

 arch is given. 



Finally, if our purpose in writing these pages is accom- 

 plished, the principles and methods here set forth will be found 

 easily acquired, accurate in their results, and amply sufficient 

 for the ready determination of the strains in the various pieces 

 of any framed structure which the civil engineer can legiti- 

 mately be called upon to design. 



With this much of introduction and explanation, we present 

 our work to the engineering profession in America and to 

 American technical colleges, in the hope that the spirit which 

 has led to its production, if not the method of its execution, 

 may win for it a favorable reception. 



In this spirit and in this hope we may, we trust, be allowed 

 to appropriate the closing lines of Culmann's preface " Und 

 nunfahre hin gern hdtte ich dich sum Fundament einer auf 

 wissenscJiaftlicherer Basis gegrundeten Ingenieurkunde ge- 

 macht, allein kaum darfich die Hoffnung hegen, soviet Kraft 

 in mir zu finden, um das Game dieses umfangreichen Faches 

 umzuarbeiten : dast ist ein Werk, das mir vor Augen schwebt, 

 wie einer jener alien mittelalterlic/ien Dome sich vor dem 

 Kunstler erhob, der ihn entwarf und der der Hoffnung sich 

 nicht hingeben konnte, ihn je in seiner Vollendung zu schaucn- 



" Doch es mogen dich Andere benutzen und weiter bauen" 

 und was ich nicht kann, werden ineine Nachganger voll- 

 bringen. 



NEW HAVEN, April 17th, 1875. 



