on the Form of a Suspended Wire or Tape. 171 



c and are unaltered by the rigidity, so that (to our order of 

 approximation) the correction to be applied for stiffness is 



EI r , , . -, ^, sinh d 2 sinh 61 



~ — , tan-^ (snih U) + — r^^ tttt . 



4livc'^ ]_ ^ ' cosh^t^ cosh tr J 



Putting sinh ^=tan (^, the correction is 



EI r^ tan(^(2-sec2(f))-i 



4.T-4* ^^^ J- 



It should be noticed that ^ in this formula is not quite the 

 same as t/t in (9). 



We shall use this formula to find the correction for stiff- 

 ness when a ten-chain steel tape or circular wire is suspended 

 symmetrically with a tension of fourteen pounds at the ends. 



Steel Tape. — Width=| in. ; thickness=gi^ in.; E = 3 x 10''; 



1A-. • 1. • 1, ^ o -Qi 2-5«4x2-204(> 



lO'l inches weighed z*oo4 grammes .*. iy = — r-rr— ycxs — 



pounds. 10-1x10 



^. , ^ , ^ ;sz^ 3960 X 2-584 X 2-2016 

 Sm <^ = tanh ^= ^ = " lO-lxlO^xU 



Whence 



</, = 9°ir = 0-1603 radian; tan (/> = 0-1617 ; sec <^= 1*0130 



s 3960 



tan^ -1617 

 EI 3xl0^xl0-lx 10^ x (-1617)2 



4zt'c2 3 x 8 X 16 X (60)^^ x 2-584 x 2-204o x (3960)^ 

 = -00000107 



tan<^(2-sec2<^)_. ^,^. 0-1617(2 -I-OIBO^) 

 7 sec^ -^' '^^^ (1-0130)^ 



= 0-0107. 

 Hence the correction for stiffness in ten chains 

 = 2 X 0-00000107 X 0-0107 inch 

 =--0-000000023 in. 



This is only 0-184 inch in a million miles, so that the 

 neglect of the stiffness of the chain need cause little anxiety 

 to the surveyor. 



Circular Wire. — We shall consider next one of the steel 

 wires used in Jadern's experiments. 



Diameter 2*66 mm. ; iy = 0-04 kilogramme per metre. Take 

 E = 3x 10^ and T=14 pounds as before. . j 



. , sw 3960 X -04x2-2046 

 ^^"*=T=-Ux^37 • 



