11 



It will be seen that a small change in the stray length makes 

 a gi-eat change in the tension. 



18. It is important to examine into the form and tension of 

 the curve in one case (of which the results are included, for con- 

 venience, in the last line of last Table), namely, the case when c, 

 the only constant, receives the special value 0. It will be 

 remembered that c is sensibly the tension of the cable at the 

 point where it touches the ground. This tension cannot, in the 

 nature of things, be negative; for every case where it is positive, 

 the formulre already detailed are sufficiently complete; but when 

 the tension at the bottom =0, these formulae are without mean- 

 ing, and a new investigation must be made. 



19. Taking up the investigation where c is first introduced in 



Article 9, and making c = 0, we have -j^= ; then, as in 



Article 10, f ,f^f''\__jtl ^-^^ 



Put v' for*'— ey, and proceed as in Article 10; we ultimately find 



f e^ + 1 e /x — ey\~ ^'"^i^^"^' 



J ~~r~' ^(2e + l)-AT^; 



e e /x — etj\ ^ e'' 



Let us examine into the value of the terms of this equation 

 when X and y are 0, on the supposition that D' and E' have 

 finite values. The index of the first exponential term is nega- 

 tive, and therefore, when x — cy = 0, if D' have a value, that 

 term will be infinitely great; which is inconsistent with the 



L- 



= ^(^*+y)+E'. 



