34 M. G. Kirckhoff on the Relation of the Lateral Contraction 



strain, 6 



~T+26 

 For shortness' sake, I further make 



The alterations of form of the bar are to be considered as infi- 

 nitely small ; we have then always 



a o = l> P\ — ^-> 2 = 1; 



& + 7i = 0, y + « 2 =0, ai + /2 =o. 

 For the case in which the weights P do not act, we have* 



2N' 



,r —nO 



n _ o Gs * 

 a 2 — '* 2 ~~* 2N' 



/3" 2 =/3% 



(1) 



p/ = JO- a o^ + 



from which there follows, 



Gs 3 

 3N ; 



.« — 



Gs 2 



/3' 2 -/3" 2 =0. 

 For the case in which the weights P are placed at B' and B", 

 we have 



(G + P> 2 



.' — ~o 



«^+ 



2N 



P/s 



?=s°+«v+ 



(G-fP)s 3 , 



." _ ~o 



/3" 2 = 



3N 

 (G + P)s 2 

 2N ' 



m 



L' 



(2) 



5"=gO-.aV + 



(G + P> 3 

 3N 



* Compare my paper " On the Equilibrium and Motion of an infinitely 

 thin Elastic Rod," Journal for Pure and Applied Mathematics, vol. lvi. 



