Turn the chair over. Look carefully around the chair's joints and seat for small nails and screws. Remove any nails and screws your come across.
Strike the underside of the chair's seat with the dead blow hammer as close to the back leg of the chair as possible to separate the chair leg from the seat. Continue striking the chair with the dead blow hammer until both back legs come free.
Strike the chair legs with the dead blow hammer to free the dowel rods.
Soak the tips of the dowel rods and chair legs in acetone for five minutes to dissolve the old adhesive. Scrape away remaining old glue with a putty knife.
Clean out old glue from the chair legs' dowel holes with a cotton swab dipped in acetone and a pipe-cleaning brush.
Place a generous amount of elephant glue into the dowel holes one at a time. Push the dowel rods back into place and hold them there for 30 seconds -- giving the adhesive time to work.
Glue the chair legs to the seat of the chair. You must glue both back chair legs at the same time. Apply downward pressure to the chair legs for 30 seconds to one minute to let the glue set.
Sit the chair in an out of the way area. Do not sit in the chair or let anyone else sit in the chair for 24 hours. This gives the elephant glue time to completely cure.