of Flow in a Strained Elastic Solid. 



50: 



less 

 J to 



greater again 

 is therefore 



from 

 con- 

 line is 

 since p 



-ed 



and 



m , k I m 

 cave upwards ; this 

 straight from m to n, 

 is constant and \—l 2 . 



The line o p q is curv 

 concave upwards throughout 

 the entire length, since p di- 

 minishes from o to p and in- 

 creases from p to q. 



The line rst will be concave 

 downwards, since p diminishes 

 from r to s and increases from 

 s to t. 



The line u v will remain 

 straight, since p is constant 

 and li = l 2 - 



To turn now to the curva- 

 ture of the vertical lines. If 

 consider one of these as 



we 



w xy z, from iv to d l\ = / 2 , at 

 xl 2 is <Z 1? while at a/ Zi = Z 2 

 again, so that from d to #' this 

 line will be curved in convex 

 towards o x. Again, at y l 2 is 

 < l 1} and at z l x = Z 2 , therefore 

 x f y z is also curved in convex 

 towards o #. 



It would appear then that 

 the horizontal lines will have 

 three distinct changes of cur- 

 vature, while the vertical lines 

 will be pinched in above and below the shoulder. 



To test the accuracy of these conclusions, I prepared a 

 copper bar as shown in the following way. The sides and 

 faces were very carefully planed and polished, and on one 

 face I inscribed a series of vertical and horizontal lines in a 

 lathe. I then strained the bar so as to produce a considerable 

 permanent set. An impression was then taken from the bar, 

 which is reproduced in Ag. 3*. 



By placing the eye very nearly in the plane of the paper 

 and looking along the lines, the curvatures can be seen to 

 follow very closely those sketched on fig. 2. I would specially 

 draw attention to the partial curvature of such lines as c d ef 

 and j kirn n. 



* The diagonal lines in fig. 3 were ruled on the impression to serve as 

 lines of reference. 



