﻿Wire or Tape including the Effect of Stiffness. Ill 



applied to the upper or lower end of the tape. It must be 

 remembered that this gives the difference between the curve 

 and its chord, and if the chord is inclined we must multiply 

 by sin f again to reduce to the horizontal, but in practice it 

 will be better to do this after applying any further corrections 

 such as for temperature or stretch to k. 



We have assumed that the tension observed is the full end 

 tension applied to the tape; and if the tape is used in one bay 

 and the spring balance or weight is applied directly to the 

 end without resting it on any other support, this will be the 

 tension recorded by the balance which will set itself to the 

 angle assumed by the tangent to the tape at its end. When, 

 however, as is generally the case in traverse work, the 

 tape is used supported at several points, part of the full end 

 tension is made up by the reaction of the adjacent support, 

 and the tension recorded by the balance or represented by 

 the weight will in this case be the component of the full 

 tension which is parallel to the chord, and which is with 

 chord horizontal simply T . In this last case formula (25) 



T 



with c put = — gives the sag correction. When the chord 



is inclined, however, let P 2 be the reaction at the upper end 

 normal to the chord and T 2 the component of the tension 

 parallel to the chord, then taking moments about the lower 

 support we have P 2 & = \ wlk sin £, or P 2 = ^ wl sin f, and 

 resolving T 2 and P 2 horizontally we have 



T == wc = T 2 sin f— \ wl sin f cos f ; 

 so that 



2 _ I 2 ~ sm- L, ( ^ wl cos c; y 



m- f a wl con f Y 

 i 5 \ 2To / 



Substituting this value of c 2 in equation (21) we have 



+ 



/ id cos t\ 2 



u7 4 sin-f / 3 7 cos* £ 



ui cos £\ 4 \l 



_ / ui cos t\ 4 



10 1152 



33) 



and if we carry the term in- ' '^ in the denominator 



