[satterly] 



STUDY OF A CATENARY 



39 



dy dY . ,,x 



also s = c^^ = c — =c Sinn - 



dx dx c 



also from (1) and (2) 

 Ti= VTvTw^T' 



(5) 



(6) 



tan^ 



w vc^ + s- = w (y + c) = wY 



i.e. the tension at P is equal to the weight of chain which would reach 

 from P down to the new axis of x. 

 Also from (1) and (2) 

 ws 

 T 



whence s = c tan 6 (7) 



which is the intrinsic equation. 



The Radius of Curvature at P may be shewn to be equal to 



Y* 



— and is therefore equal to the normal PG (Fig. 3). 

 c 



If a perpendicular is dropped from M, the foot of the ordinate of 



P upon the tangent PN intersecting it at N, then MN = c and PN=s. 



