VI PREFACE TO FIRST EDITION'. 



book for sell". >1 instruction, and a book of reference and manual 

 for practice as well. The attempt is a difficult, if not a dan- 

 gerous om. Mini one which, in other departments, has met with 

 more failure than success. If we venture to indulge a hope that 

 in this case at least partial success has been attained, and that 

 the attempt to occupy the two stools at once has not been dis- 

 astrous, our belief is due to the nature of the subject itself, 

 and not to any overweening estimate of onr own abilities to 

 succeed where so many have failed. The subject seems, indeed, 

 especially suited to such a method of treatment. In fact, no 

 other would appear at this period to properly meet the necessi- 

 ties of the case. Its geometrical principles are simple, its ap- 

 plications eminently practical. To present the principles alone 

 would be to deprive the study of its chief interest and attrac- 

 tion. To rest content with a few practical applications would 

 be to sacrifice, in a great measure, system and clearness of pre- 

 sentation. In the accomplishment of onr double task we are 

 fortunate to have had at our disposal such works as those of 

 JSauscMnger in the one, and Culmann in the other direction. 

 Our obligations to both authors are great, and are fully indi- 

 cated in the text. The same acknowledgment is due, in greater 

 or less degree, to Mohr and Winkler, Bitter and Reuleaux. In 

 every case where such assistance has been received, due ac- 

 knowledgment has been made. 



For the historical and critical Introduction, we are indebted, 

 with few alterations, to the pen of Weyraueh* It will, we are 

 sure, prove of value to the student, and serve to awaken an in- 

 terest in those highly important developments which geometry 

 has within the last decade undergone. 



Thus collecting in a connected form the scattered results and 

 researches of various authors, it has been a pleasurable duty to 

 recognize the labors of those men who have chiefly contributed 

 to this new branch of geometrical statics, and to whom our own 

 obligations are so great. While thus crediting fully that which 

 others have done, we have felt the more justified in calling at- 

 tention to any deviations of our own. We have especially 

 sought to extend the application of the method by resolution of 

 forces (known best, perhaps, as MaxweWs Method ) a method 



* Ueber die graphwche Statik zur Orientirung. Von Dr. phil. Jacob J. 

 Weyrauoh, Privat docent an der polyteohnischen schule zu Stuttgart. Leipzig, 

 1874. 



