694 Proceedings of the Royal Society 
In the circle of an unifilar every crossing is twice read, once in 
an odd and once in an even place, the thread passing alternately 
over and under itself at successive crossings. The only duads that 
occur twice are edges of 2-gons. The first knot has six 2-gons, 
bd , BD, cA, Ca, eG, E g. At the 2-gon bd the thread Fbdc passes 
over and under ebdA ; and . . Ybdc . . and . . ebdA . . are meshes 
collateral with the 2-gon bd. We take . . ebdA . . . for a base on which 
to project the first knot, observing that as Ee and E6 are edges, Ybe is 
a triangle collateral with our base . . ebdA ... At the 2-gon eG, 
beGf passes over and under FeGC, and . . beGf . . is a mesh collateral 
with eG. As be cannot be in three meshes, our base is . . AdbeGf . . , 
and since /A is an edge, this base is the 6-gon AdbeGf. The first 
circle is unaltered by exchanging throughout capital and small 
letters. There is then another 6-gon aDBEyF in the knot. Draw 
this within the base, a remote from A, D from d , &c., so that the 
meshes AdbeGf and ADBEGF are read in the same direction round ; 
and make the 2-gons db, DB, Ey, eG. There are two other 2-gons 
to construct. From c near A and C near a, between the 6-gons, 
draw 2-gons Ac and aC. Our fourteen summits are properly pro- 
jected, and we complete the projection by drawing the edges F&, 
/B, Fe, /E, CG, eg, CD, cd. 
It is evident that on this first knot in space every feature, edge, 
crossing or mesh, is diametrically opposite to a similar feature. 
There is no zonal trace, at every point of which the configurations 
on the right and left reflect each other ; nor is there a diameter 
about which in revolution a configuration is repeated; that is, two 
opposite eyes in every diameter read round exactly the same asym- 
metric sequence ; but this only when one reads with, and the other 
against, his watch. The opposite configurations are in every diameter 
asymmetric and contrajanal, and the knot is a contrajanal anaxine 
knot, on which a zonal trace is impossible. About a janal axis 
proper, zoned or zoneless, opposite observers read round like con- 
figurations when each reads with his watch. This first knot is a 
contrajanal anaxine subsolid , i.e ., one admitting section through no 
two points only, but through the crossings of a 2-gon. There are 
contrajanal anaxine unsolids , i.e., admitting linear section not 
through the two crossings of a 2-gon, which have 12 or 10 crossings 
only. 
