If weights be suspended from various points of a hang ing chain, the intervening por tions will form arcs of equal ~ catenaries, since the horizontal tension (wa) is the same for all.
Again, if a chain pass over a perfectly smooth peg, the catenaries in which it hangs on the two sides, though usually of different parameters, wifi have the same directrix, since by (10) y is the same for both at the peg.
Hence for every tension greater than the minimum tension there are two catenaries passing through A and B.
Since the tension is measured by the height above the directrix these two catenaries have the same directrix.
Now let us consider the surfaces of revolution formed by this system of catenaries revolving about the directrix of the two catenaries of equal tension.