PEEFACE TO FIKST EDITION. 



IT is now ten Years since the appearance of the Graphical 

 Statics of Culmann,* during which time the method lias beeL 

 greatly extended in its applications, and has met with such 

 acceptance that there is now scarcely a Polytechnikum in Ger- 

 many where it is not a prominent feature in the regular course 

 of instruction. 



This rapid spread of a new discipline is the more remarkable 

 when we consider the obstacles which it encountered. Cul- 

 mann, with a boldness which we might almost term rash, based 

 his development upon the modern geometry of von Staudt, and 

 assumed in his readers a familiarity with this very terse presen- 

 tation of a subject then, as indeed now, but little known, and 

 which, therefore, but few possessed. To practical engineers, 

 therefore, to whom his methods specially recommended them- 

 selves, his presentation of those methods was almost unintelli- 

 gible. 



At a time when the students of the Zurich Polytechnic were 

 already overburdened, the new discipline was introduced ; while, 

 owing to want of familiarity with the fundamental principles 

 premised, they were unable to understand his lectures or read 

 his work. Yet such was the intrinsic value of the new method 

 that, notwithstanding these obstacles, even in spite of them, it 

 made rapid headway ; found friends everywhere ; crept into 

 other departments of the Polytechnic ; and finally the aim of 

 Culmann was completely attained when the modern geometry 

 was itself introduced, and a special lecturer in that branch ap- 

 pointed. Thus, as a direct result of the Graphical Statics of 

 Culmann, appeared the first and, till now, only complete text- 

 book upon the modern geometry, viz., Reyds " Geometrie der 

 Lage" Hannover, 1868. Since then, hand in hand and with 

 remarkable rapidity, these two studies have made their way, 



* Die Graphisohe Statik. Culmann. Zurich, 1860. Second Edition, let 

 vol., 1875. 



