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PROCEEDINGS OF THE AMERICAN ACADEMY. 



usually so great that the curvature with decreasing stress is the re- 

 verse of that with increasing stress, so that the loop has the general 

 shape of a double convex lens. Furthermore the loop is usually very 

 nearly symmetrical with respect to the line joining the extremities. 

 This is the only example of a loop of the above shape known to the 



writer. This single example is 

 sufficient to show that there is 

 no necessary connection between 

 hysteresis and departure from the 

 linear relation between stress and 

 strain, as might be supposed if 

 all loops were of the ordinary 

 type. 



This h)\steresis, while compara- 

 tively small, was nevertheless suf- 

 ficient to reduce the accuracy 

 of measurements made with the 

 gauge far below that desired. A 

 method of avoiding hysteresis 

 was therefore adopted. It depends 

 on the fact, well known for mag- 

 netism, that if the stress is varied 

 cyclically by small amounts about 

 any fixed point, a small hysteresis 

 loop is described about this point. 

 The result is that if stress is 

 relieved from the point A (see 

 Figure 5) after increasing pressure, the path AB will be described.while 

 if it is increased from the point C after decreasing pressure, the path 

 CB is described. Suppose that during increasing pressure the point D 

 has been reached, or that during decreasing pressure the same stress, 

 shown at E, has been reached. The difference between the points E 

 and D represents the error due to hysteresis. To make the readings 

 at these two points the same, we may evidently apply a small extra 

 load at D, raising the stress to A, and then remove the extra load, or 

 at E we may remove a slight portion of the load to C and then reapply 

 it. The same point B is finally reached, and the pressure readings 

 have become single valued. The extra load necessary to apply or 

 remove must be determined by experiment, and would be expected to 

 vary at different parts of the hysteresis loop. 



This extra load was applied in practise by a very simple lever ar- 

 rangement, by which the springs could be deflected one way or the 



STRESS 



Figure 4. Shows the unusual na- 

 ture of the hysteresis cycles described 

 by the springs. 



