It was very simple.  With the following diagram as a key and a single hint as to its management, you will at once comprehend its apparent intricacies: 

Ab | CD | EF            \st/
___|____|___           UV\/WX
GH | IJ | KL             /\
___|____|___            YZ\
MN | OP | QR

The dot designated that the letter used was the second in the indicated division.

The hint to which I allude is this.  With every other word the paper is turned in the hands toward the left.  This alters the shape and direction of the angle or part of square symbolizing the several letters, and creates the confusion which interfered with my solution of its mysteries the night I subjected it, with such unsatisfactory results, to the tests which had elucidated the cryptogram in The Gold Bug.

THE END