﻿120 Mr. A. E. Young on the Form of a Suspended 

 and since we have a T 2 P 



or 



(38) 



c=-(l_ __l nearly, 

 where T is the end tension, this reduces to 



Stretchy ^(1- 8T2 )(l + liT J = ^(l- jgp). (39) 



Now ^ is the amount by which the tape is stretched 



w 1 

 when it lies flat, so that ■ , ^ . m is the amount by which it 



12EAT J 



contracts in length i£ it has been standardized flat under an 



end tension T, and is then used in catenary under the same 



end tension, the contraction being due to a diminution in the 



mean tension owing to the curvature and having nothing to 



do with the sag correction. 



Professor Maclaurin in his paper compares the stretch 



correction with the stiffness correction, and finds the former 



= 1*757 inch ; but he assumes that the tape has been 



standardized under no tension, i. e. he uses the expression 



^rr« If ^ ne tape in question had been standardized flat 



under 14 lb. tension the shortening when used horizontally 

 in catenary owing to decrease of stretch would be 



—-^ — ^ — T7 . 7 — — : =0-01o0 inch; 



12x3xl0'xl4 



which we see is just about the same as the value found for 

 the stiffness correction with constrained ends, viz. 0*0123 inch: 

 and as these two corrections are of opposite sign they mutually 

 destroy one another in this case. 



Considering the stretch correction when the tape is on a 

 slope, we have 



f%7 T c/sinh2u s sinh 2mj , \ 



j Tds = -| (^ ^ - — j— + u 2 - tij J 



= ~-l cosh(it 2 +»i) sinh (u 2 — u^+^—u-^ ) 



^V' f o _V> ^ + U l) 9 :„l, ( W 2 r^) n^h ( M 2-Wl) 



cosh- — ^ — —2 sinh- — « — cosh 



= x{ 2 . 



— sinh [ii 2 —u 1 )-\-u 2 —u 1 > 

 = -|-^ - c °st ;i - cosh -^g — 2 cosh , smh - ., 



_(W 2 -Mi) 3 _ | 



3.2 ■■•/ 



