812 



Dr. C H. Lees on the Depression due to 



Hence if z/i is the ordinate of d and y\ + h that of B, we 

 have 



b = c I cosh cosh - J 



9 . , I . ,2^ + Z 

 = Jc smn ?r- sinn — =r— 



(i) 



If s is the length of the curve from d to B 



I • l ^ + / • \. e \ o • l / i 2 ^ + / /ON 



6- = ?( sinn sinn ) = Ac sinner cosh- . (J) 



v 6' c; 2c 2c 



If is the angle of inclination of the catenary at any point 

 to the x axis 



i n dy • i * + * 

 tan ft = -^ = sinn 



Also if T is the stretching force at any point 



T = <rgy = gijc cosh 



e -+- x 



(3) 



where o- is the mass of the chain per unit length. 



When the chain is unloaded the centre of the catenary is 



