﻿Wire or Tape including the Ejject of Stiffness, 101 



with the second, since the latter is at least I times (in inches) 

 larger, and the fourth term is quite inappreciable. The 

 correction for stiffness is in this case, therefore, given by 



wH wnm. 



( 6 ) 



a 2 T 2_ T 3 ' • • • • 



which is to be subtracted from the catenary sag correction. 

 Professor Maclaurin' s expression for the correction is 



icEIlV tan 6(2 — sec 2 6)1 , , . \ wl 

 2TVL^- sec^ J where *= Sln 2T - 



Expanding this expression in terms of (£, which we may put 



, ;"■ , wl , , _ ,. wH^EI . . . 



equal to ^v , we get tor the correction - ^ rp 5 , which is 



equal to the writer's expression multiplied by ^(ttt-) . In 



the example taken by Professor Maclaurin, I = 10 chains = 

 7920 inches, width=] in., thickness = g X in., w = 0'000564 lb. 

 per inch, E = 3xl0 7 lb. per square inch, T = 14 lb. From 

 which, since l—^bt 1 we deduce 



a =\/m 



-3-110, a 2 =9-67, ^=0'3192, 



so that 



which though quite inappreciable is about 60 times as great 

 as Professor Maclaurin' s value. In working this example 

 T has been taken =T= 14 lb., though, strictly speaking, 



T< 2 __ T2 W \ _ 



or 



T =T(l-|(^) 2 ) nearly = 13-84 lb. 



The effect of the stiffness on the form of the tape is best 

 seen perhaps from the expression for the tangent of the 

 slope, 



<L'~T Q (' V To!)' 



u V a cosh -^ / 



The first part shows that the curve is a parabola with vertex 

 downwards, the second is the alteration to this caused by 

 the stiffness which tends to make the slope less, the effect 



