12

18

exhauster. Every given mathmatical theory must,
in that sense, eventually become exhausted. Whether
or not new theories ^{of interest} will continue to offer new
problems or not, I am not prepared to say.

But to come back to the matter in hand, I
give you without further preface, the following
rule for positively, ascertaining whether or not
a given graph is beta possible.

In the first place find in the graph every
lexis, (regarding θ as a lexis), of which
one replica is oddly enclosed ^{that it is within an odd number of cuts)} and another
evenly enclosed ^{[???} within an even number of cuts} the latter not being enclosed
by every cut that encloses the former; and
call every such pair of spots an adaptible
pair. Having found such an adaptible pair An adaptible pair is said to be conjoined

18

exhauster. Every given mathmatical theory must,
in that sense, eventually become exhausted. Whether
or not new theories ^{of interest} will continue to offer new
problems or not, I am not prepared to say.

But to come back to the matter in hand, I
give you without further preface, the following
rule for positively, ascertaining whether or not
a given graph is beta possible.

In the first place find in the graph every
lexis, (regarding θ as a lexis), of which
one replica is oddly enclosed ^{that it is within an odd number of certs)} and another
evenly enclosed ^{[???} within an even number of cuts} the latter not being enclosed
by every cut that encloses the former; and
call every such pair of spots an adaptible
pair. Having found such an adaptible pair An adaptible pair is said to be conjoined