CATEXA I!!':; 



the constant added being such that y when * - ; there* 

 fore 



'-y' + av ..... (2). 



c 



- 



a 



the conn tan t being chosen so that x and y vanish tog- 

 The laat equation given 



Transpose and square ; thus 



therefore y + c- Jc( ; + ~' ...(4). 



Abo -V|(y + c)'-c f J by (a) 



-i (*-") ..... 



- may bo taken as the equation 



tuition (4) we wri , liicli 



nts to moving the origin to a point vertically below the 

 lowest point of the curve at a distance c from it, we have 



i the string v and thickness, as in 



the present instaix irve is called the common catenary. 



185. Tojindtfottntionoffattrtiy at any point. 



tension at P be e<jual to the weight of a length t of 

 string ; then, as shewn in the last article, 



' PT t dt 



therefore - -r-. 



weight ui CP~ TM' dy 



