270 



PRACTICAL MATHEMATICS 





4A/2 + 4A/3 4 + 4\/2 16A/6 16V21 

 loff 1 



log 



16 



V2+ 1 



= 2(0-2648+ 1-0353} 

 = 2-6002 



V6 - V2J 



143. The Sag in a Telegraph Wire. Let I be the half span, 

 d the sag, and s the whole length of the wire, and suppose that 

 the resulting curve is a parabola whose equation is x z = 4<ay. 



Now when x = Z, y = d. 



Hence 



= 4<ad 

 and a = -n 



Also 



4a 



dy _ x 

 dx 2a 



V 1 + hri = V 1 + T-S 

 \dx/ 4>a 



Then length of wire = *=2 A/ 1 +^-5 



J o ' 4or 



ifl 



aJo 



Put x 2 = 4a 2 sinh 2 



Then A/4a 2 + * 2 = 2a cosh 

 and dx = 2a cosh dQ 



X 



