

164 — © PROFESSOR TAIT ON KNOTS. 
§ 17. When we come to the deformations of the single 4-fold knot 
we obtain a very singular result. If we place O external to the figure, we 
simply reproduce it ; but if we put O inside the two-sided. companion in the 
middle we get the perversion of the same figure. | 
Again, if we place O in either of the bowndary three-sided compartments 
we get 
but if we place it in either of the znterior three-sided spaces we get the perver- 
sion of this last figure. 
Thus this 4-fold knot, in each of its forms, can be deformed into its own per- 
version. In what follows all knots possessing this property will be called 
A mphicheiral. 
§ 18. The first of the two 5-fold knots (§ 7) has the following forms :— 
RO 6 ® 
These I found were long ago given by ListinG as reduced forms of a reduci- 
ble 7-fold knot, and I have now substituted for my former drawing of the 
second form his more symmetrical one. 
The second of the 5-fold knots has only two forms, viz. :— 
: 
; 
§19. Plate XV, figs. 2, 3, 4, give various forms of the 6-fold knot distinguished 
as a in the. classification in§ 8. It will be seen that in the first of these the 
crossings are alternately over and under, but that it is not so in the others. 
And in fig. 8 we have a collection (not complete) of forms of various species 
of the 7th order, drawn so as to show their relation to a lower form—the 
