LM12 EXAMPLES. 



Thus the did of the string descends to the d< be- 



low the axis of x, ai tore to the depth c f 1 -f 



below the vertex of the curve. 



EXAMPLES. 



1. Two equal heavy beams, .4.7?, CD, are connected dia- 

 gonally by similar and equal elastic strings AD, BC: sln-w 

 that it' the natural Imgth of each string equals AB, and the 

 elasticity be such that the weight of AB would stretch the 

 string to three times its natural length, then 



J_ 



AC* 



2. An elastic string will just reach round two 



a horizontal plane; a ring wnose weight would double the 

 length of the string hauling from a point is slim- <>n it: 

 shew that if 6 be the inclination of two portions of the string 

 to the horizon, 



sin 26 = 2 (V2-1). 



3. An elastic string has its ends attached to those of a 

 uniform beam of the same length as the unstretched string, 

 the weight of the beam being such as would stretch the 

 string to twice its natural length ; shew that when the system 

 is hung up by means of the string on a smooth peg, tin- 

 inclination 6 of the string to the vertical will be given l>y 



equation 



tan + 2 sin 0-2=0. 



4. Three equal circular discs are placed in contaet in 

 tical plane with their contivs in the same horizontal 



line, and an endless elastic cord wound alternately above and 

 below them, so as to touch every point of their circumfe* 

 without being stretched bevond its natural length. V 

 the support of the middle disc is removed, the centres of the 



