4

ask, Why not simply apply these rules and
see whether they lend to that result or not? The
answer is, that such operations performed upon a graph
may lead to a result which can obviously never lead to
the cancelling of the sheet when the original graph otherwise
treated might have done so. But this would not be so,
if you only made such transformations as could be reversed;
for in that case any result could be reconverted into the
original graph. Let us see then what are the unreversible
transformations. They are none other than the operations
of erasure within even numbers of cut [??? enclosures] and of insertion in even within odd
numbers of cuts. Now, as to the erasure that may without [??] be limited
be restricted to unenclosed partial graphs, and instead of erasing elim
them entirely, they may be simply moved away into
another region. This you will observe is just what our

ask, Why not simply apply these rules and
see whether they lend to that result or not? The
answer is, that such operations performed upon a graph
may lead to a result which can obviously never lead to
the cancelling of the sheet when the original graph otherwise
treated might have done so. But this would not be so,
if you only made such transformations as could be reversed;
for tin that case any result could be reconverted into the
original graph. Let us see then what are the unseverable
transformations. They are none other than the operations
of erasure within even numbers of cut [??? enclosures] and of insertion within odd in even
numbers of cuts. Now, as to the erasure that may without [??] be limited
be restricted to unenclosed partial graphs, and instead of erasing elim
them entirely, they may be simply moved away into
another region. This you will observe is just what our