JOURNAL 



OF THE 



Elisha Mitchell Scientific Society 



DEMONSTRATION OF THE METHOD OF LEAST 



WORK. 



BY \VM. CAIN, C. E. ; M. AM. SOC. C. E. 



I. A new method of ascertainino^ the stresses in elastic 

 structures by means of the principle of "Least Work" 

 has been elaborated by Castigliano, in his "Theorie de 

 I'Equilibre des Systemes Elastiques " (Turin, 1879), who 

 claims to have given the first complete demonstration of 

 the theorem of least work, though several authors have 

 touched upon it from 181 8 to the present time. 



In the ''Transactions of the American Society of Civil 

 Engineers" for April, 1891, the writer published an article 

 entitled "Determination of the Stresses in Elastic Systems 

 by the ]\Iethod of Least Work," in which two new and 

 complete demonstrations of the principle of least work are 

 given, both being founded on the w^ell-known principle of 

 "virtual velocities" of mechanics "applied to framed 

 structures." 



The following article is an abstract of the briefer demon- 

 stration, given in the article by the writer before men- 

 tioned, and is based on "the theory of deflections," which 

 will first be given. A few preliminary articles on " elastic 

 work" of a bar in tension or compression, "superfluous" 



