Prof. J. Perry on Twisted Strips. 245 



obvious that the part of the untwisting moment due to one 

 filament is tpx 2 (f> . hx : so that 



^bfd = t(f>{* b px 2 .dx; . . . . (1) 



also 



Clb 



w~t\ p.dx (2) 



J— i* 

 I explained on the former occasion that, for a working theory, 

 it ought to be sufficient to take p constant over the section. 

 Hence, from (2), 



*-»» < 3) 



and inserting this value in (1), we have 



or 



V 4* 3 N w 



If 6 is small in comparison with <j>, it is allowable to take <p> 

 as the twist of the strip when no axial load is acting — that is, 

 its permanent twist. 



Now I announced on the former occasion that careful expe- 

 riments made upon large twisted steel strips of various dimen- 

 sions did not by any means agree with my result. It is true 

 that was proportional to w ; but it seemed rather indepen- 

 dent of </>, and instead of being proportional to b, 6 seemed to 

 get less as b was greater ; and, again, instead of f in the 

 denominator some power of t between 2 and 3 ought to be 

 taken. 



Under these circumstances I asked members of the Society 

 for assistance in obtaining a working theory, but hitherto 

 I have not obtained any. 



I wish now to announce that the experiments I referred to, 

 made very carefully by Mr. Still, of the Finsbnry College, 

 under my direction, were not sufficiently exhaustive. Mr. C. 

 E. Holland has lately been kind enough to make an experi- 

 ment for me on a very small strip of platinum silver. He finds 

 that when <£ is large his results agree very closely with the 

 former results ; but as c£ is made less and less, the law con- 

 necting 6 and cf> becomes more and more nearly what is given 

 by (4). The experiments were carried out upon double- 

 twisted si rips. That is, a straight strip was taken witli its 



