v GRAPHICAL DYNAMICS. 



Winkler, B. " Neue Theorie des Erddrucks." Wicn, 1872. [Containing 

 graphical methods according to the old theory.] 



Hateler, C." Bcitrfige zur Theorie der Futter- und Stutz-Mauern." Zeit- 

 schr. d. hannov. Arch. u. Ing. Ver., 1873, p. 38. [Graphical deter- 

 mination of earth pressure according to Culuiann.] 



MISCELLANEOUS APPLICATIONS. 



Reuleaux " Die graphische Statik der Axen und Wellen." Published by 



polytech. Ver. in Zurich, 1863. [Autograph copy of lectures.] 

 Culmann, K. " Der Werth der Construct! onen." Seventh chap, of Graph. 



Statik, 1866. [Best and cheapest systems under given conditions, 



especially for bridges.] 

 Reuleauz " Graph ostatische Berechnung verschiedener Axen, Kranpfosten, 



Kurbeln," in the Constructeur, third ed., 1872. 



Scattering graphostatical constructions are to be met with in many text- 

 books upon construction, especially since the appearance of Culmann's 

 work, a second edition of which is in course of preparation, and expected 

 Boon to appear. 



XIL 

 GRAPHICAL DYNAMICS. 



The scientific or practical value of graphical solutions once recognized, 

 there remains no reason for limiting them to statical problems only, and 

 endeavors in the above direction are already forthcoming. We limit our- 

 selves to a passing notice. 



First, we have an attempt to employ graphical constructions in the 

 theory of the overshot and breast-wheel (Seeberger, " Arbeitung der Theo- 

 rie der oberschlachtigen Wasserrader auf graphischen Wege." Civil Ing. 

 1869, p. 398, and 1870, p. 339). We cannot here notice the value of the 

 solutions given, but the very sparing applications of geometry hardly jus- 

 tify the title of the work. 



A short article, which gives the graphical determination of the force at 

 every position of a moving point, may also be noticed. (Rapp, " Zur 

 graphischen Phoronomie," in Zeitsch. f. Math. n. Phys., 1872, p. 19.) 



The genuine foundation of a graphical dynamics has been first attempted 

 by Proll (" Begriinclung graphischer Methoden zur Losung dynamische 

 Probleme," in Civil Ingenieur, 1873). From the fact that the effects of 

 forces in dynamics are measured by the changes of velocity of any point or 

 points of a machine system, Proll concluded that it must be possible to 

 represent these force effects by geometrical relations, such as kinematic 

 geometry teaches. 



His investigations, since published in independent form (" Versuch 

 einer graphischen Dynamic," with 10 plates, 1874), fall into three parts. 

 The first part treats of the action of the " outer forces " in machines whost 



