This section is from the book "Experimental Glass Blowing For Boys", by Carleton J. Lynde. Also available from Amazon: Experimental Glass Blowing for Boys.
Wind a strip of blotting paper or wrapping paper 2 inches wide around the bottle at one side of the line along which you wish to cut. Make three or more thicknesses and then tie the paper with cord within 1/2 inch of the edge to be cut. Wrap another similar piece on the opposite side of the place to be cut and 3/16 inch from the first piece (Fig. 88).
Now stand the bottle in a pail of water until the paper is thoroughly wet (about five minutes), take it out, rotate it in a horizontal position and direct the blowpipe flame against the glass between the papers (Fig. 89).
Continue this for four or five minutes, then if the bottle has not dropped apart, plunge it vertically into the pail of water.
The bottle will break into two parts along the line between the two papers (Fig. 90). If it does not do so, repeat the operation until it does. Smooth the rough edges outside and inside with the file. You cannot do this with the flame because the glass is too brittle.