WITH A CENSUS OF THE AMPHICHEIR ALS WITH TWELVE CROSSINGS. 243 
and all possible combinations of these. It is found that the above form possesses 
only the four variants — 
§ 3. Amphicheiralism. 
The perversion of a knot is the form obtained by replacing each crossing with 
one of the opposite character. The amphicheiral - knot was originally' defined by 
Tait as one which can be deformed into its own perversion. From this definition 
it is to be inferred that to every compartment ^ there corresponds a similar and 
similarly placed compartment \ ; that is to say, a necessary condition for an 
amphicheiral knot is the identity of the primary and secondary symbols. 
Since the primary and secondary symbols of the amphicheiral knot are the same, 
the plane is divided into an even number of compartments by the plane projection 
of the knot, and consequently an even number of crossings is involved. 
TRANS. ROY. 'sol EDIN., VOL. LII, PART I (NO. 11 ). 
39 
