4

4

fundamental alpha permissible operations. Namely
of these six, there are three that complicate the
graph and three that simplify it. The three that
complicate is are insertion, iteration and the making
of a double cut. The three that simplify it are erasure,
deiteration, and the cancelling of a double cut. Furthermore
these are of the six operations, two only that are not re-
versable, that is which may not be undone as well
as done. These are erasure and insertion. Now my
idea in drawing up the rule was in the first place, to
to define to myself precisely on what occasions the complicating ope-
rations might be indispensable in ascertaining
whether a graph was possible or not, and to restrict
their virtual employment to these cases, and in the
second place, so to modify the non-reversible operations