Chapter XV
On Inverted Transposition

The third method of changing the Power of Letters I have called Inverted Transposition.  This method differs from the preceding methods by reason of the object to be transposed.  For in Direct Transposition, there may be transposed one letter singly, or two or three letters taken together, while, in Oblique Transposition, one letter only is transposed at a time; but in this present Inverted Transposition, two letters must always be transposed at once.  However, this Transposition is called Inverted because it involves a different method of accomplishing the Transposition.  We make our starting point the two alphabets which half enclose the table, and we come to rest in the square or angle of union.  Such is not the case in Direct Transposition;  see c.8, the line: But should you prefer to use the square figure, &c.  Neither is it the case in Oblique Transposition; see c.14.  But this is not the only mark of distinction; the principle of Inversion is in the matter of detail far-reaching.  For there are times when not only is the aforementioned process followed, whereby we begin with the exterior alphabets and go to the angle of union, -- a process which in its own way may be looked upon as direct, -- but a further process is added thereto, by which we, as it were, retrace our steps and go from the angle of  union to the extreme alphabet and the letter corresponding to the square from which we start.  Sometimes, also, a single letter is used to transpose, by simple method, two letters, --in which case, however, signs are necessary.  From these facts it is surely easy to see that there result three Modes of the present Inversion.  The first of these is,. Rather, the Simple method; the second, which is more comprehensive, is the Artificial; while the third, which participates in the nature of the other two, is found to be Mixed.  I will now expound these Modes in order.