﻿Wire or Tape including the Effect of Stiffness. 121 

 Now 



T, + T, 



-0 



and 



. ^ 2 +«i T u 2 — it! , . Tg + T! 



1 cosh — 4> ~ cosh — g — = cosh ?i 2 + cosh « x = — m , 



o 1 Uz + Uj . . W 2 — I/] . . Z 



J cosh — : — smh — ~ — = sinh u 2 — sinn U\ = ; 

 2 2 ■ c 



.'. Stretch 



_ T c \l T 2 + T 1 _ (u 2 -ihf . x (ih-ihf 1 /jm 



= /. 



T 2 + T 1 _ wcEfe— u if. 



2EA 12EA 



mt t i' 2 — a'i _ I sin f 



Ml = — — = — , nearly, 



and I\ = To — wh = T 2 — wl cos f , nea rl y ; 



T 



ulso c =sin t— 2 , nearly; 



.-. Stretch 



To/ r 1 wl cos f wj2/ a sin 2 f - 

 = EA { 1- " 2TT " Tip?"" ' 1 nearly ' ' (41) 



This of coarse reduces to the expression (39) when f=90°; 

 and it will be seen that the second term rapidly becomes or 

 more importance than the third. In the example considered 

 these two terms are equal for £=$6° 50'. The correction 

 to be applied therefore to a measured distance when the 

 tape has been standardized on the flat under T 2 lb., and is 

 used on a slope inclined f to the vertical, is 



_ /.wl 2 cos J iv 2 l s sin 2 f \ 

 V 2EA " 12EAT 9 J' 



The first term is simply the stretch caused by the com- 

 ponent of the tape's own weight, and if the tension at the 

 lower end is used its sign must be changed. When the tape 

 hangs in several bays the above expression must be multiplied 

 by the number of bays to obtain the full correction. 



If the mean tension were kept constant as indicated in 

 the paper by Professor and Captain Henrici, the first term 

 of the correction would vanish. This would mean, however, 

 adjusting the tensions for every change of slope, which in 



