﻿Wire or Tape including the Effect of Stiffness. Ill 



of which the particular integral only is required, as the 

 complementary function has already occurred in the ap- 

 proximate solution. The particular integral of the first 

 term is found to be 



ML\ (±aV + f<M) cosha*-(faV + f)sinh<M} *, 



of the second 



A 3 /sinh 3as 

 ~~96 



/' — -f- 3 sinh as — 6as cosh as ), 



and of the third 5/>*V 30b 5 s 



The full expression for ^ as far as terms in s 3 is thus 



Z> 3 s 3 . T . -, o 2 f / o - 3as\ . 



^ = &s-~- -+ ... +A sinh as + To— 2 ^ l«* + -yl cosh as 



/3aV 3\ . \ 



-(— 2~ + rjsinh as j> 



A3 



— ^ (£ sinh 3as 4- 3 sinh as - 6as cosh as) 

 % 



26 3 s 56 V 306°* 



+ -s-+—r*->.' ■ (21) 



a* 



It is remarkable that the coefficient of cosh as in the 



-, A . b 2 as z b 2 s 2 as . . -,. 



expression by A, viz., — — = is in ordinary cases 



greater than unity and so greater than the coefficient of 

 sinh as in the first term. For instance, in the example 

 already quoted the greatest value of the coefficient for 

 s = 5 chains = 3960 inches, 6s=0'1596, a=3"ll is 



b 2 s 2 as __ -1596* x 3-11 x 3960 _ 

 12 ~ 12 " 



This will give a smaller value for A when the end con- 

 ditions are put in, but the value of the term by A is again 

 increased by this factor, so that the expression for the 

 alteration in the sag correction due to the stiffness is not 

 altered in the most important term. This has been tested bv 



,'*/.! , ab 2 s° cosh as\ 

 yjr — bs + A I smh as -\ I 



* This particular integral was also found by Mr. Sawkins, to whom 

 the device of dividing -^ into <p and 9 is due, by another method. 



