116

1 3. Theorem. All catenary curves makingequal angles with their ordinates at thepoints of suspension are similar.

Let ACB, acb, be any two catenarycurves having DB and D h for their ordi-nates at the points of suspension B and b ,and having the angles DBC, T)bc equal,then will ACB and acb be similar.

For let the angle DBC = D be = thetension at C = c, that at B=£, CB = z , CD= x and DB = y , and the correspondingquantities in the catenary D be, — c 1 , t', z,x', and y.

Then by Case I. article 9.z = c tang. <p, z = c' tang.p .*. -^-=-4-each = tang.<p

,, , t f

t =. c sec. <p, t —c sec. .*. —■=—

each = sec. <p