246 



Prof. J. Perry on Twisted Strips. 



ends fastened in a frame ; it was caught in the middle and 

 there a twisting-couple was applied, so that one half of it took 

 a right-handed and the other a left-handed permanent twist. 

 Beginning from almost the condition 4> = 0, by giving more 

 and more permanent twist to the strip and applying loads in 

 each case, it was seen that, for a given axial load, 6 was nearly 

 proportional to (/> at first, but as <f> became greater and 

 greater the increase of 6 was less rapid, 6 eventually remain- 

 ing nearly constant, although (£ was increased. 



I now know that Mr. Still's experiments were carried out 

 upon strips in which there existed so much permanent twist 

 as to resemble the strips in the condition in which they were 

 towards the end of Mr. Holland's twisting operations, and 

 hence 6 seemed independent of <£. 



Now if, instead of taking p constant and using (3), we take 

 p as getting less for filaments at greater distances from the 

 axis, it is obvious that we shall arrive at a result which, 

 although more complicated than (4), will represent much 

 better the results of experiments. 



Thus, as is probable enough, if the tensile strain in every 

 filament is such as to keep a section at right angles to the 

 axis parallel to itself, it is easy to show that, instead of p 

 being constant, we must take 



k 



t(l+x 2 <P) 



(j)W 



p= 



Using this in (2), we find 



k= 2tan- J i^ 

 Substituting (5) in (1) we find, on simplifying, 



e= 3w r i 1 1 



N*'\2tan- 1 i^ <j>b J" ' ' ' 

 It is obvious that, except when b(j> is great, (6) becomes 



(5) 



e= 



4N* a 



fo- 



ld 



(6) 



(7) 



which agrees with (4) for small values of cj)b. 



And evidently from (6), as b(j> gets greater and greater, 

 6 reaches more and more nearly the limiting value, 



Sw 



Xt 3 <7T 



Making p any other likely function of x<f> than that given in 

 (5) will merely modify the constants in (7). 



