




176. | PROFESSOR TAIT ON KNOTS. 
§ 34. Examples. 7 
LAB BF CGDA ER leGp HB Kk Ci Hi 
—++et-+-4+-4¢+-4+-—-4+--- +--+ 
This is, of course, rendered irreducible.-by changing the sign of B. It is 
figured Plate XVI. fig. 1. 
[If we were to change the signs of F, L, H, the knot would acquire a great 
increase of beknottedness, and would consist, in its simplest form, of a pentacle 
and a trefoil knot linked together, as in Plate XVI. fig. 25. | 
(2) Now 
~~ Bok EK BK 
+++ —+— —— 
become 
am K 2K. B 
+ + —- 
(>) Two intersections being thus lost, the knot has now the form, Plate XVI. 
‘fig. 2, with the scheme 
ASOCowAk tL Gpik beat)” 
—-+—-4+-4+4+4+-4+--—>-4+-+4) 
Now in ; 
with G before or D after, we can at once get rid of K, L, if A be put close 
to G. 
(c) Hence the scheme becomes 
BC 2G) AG Denes. © as 
+--+ —-+—-4+-—+4++4 
and the knot is as in the figure 3, Plate XVI. 
Now | 
HB... B... sores 29): 
—- + + 
(d) The scheme is now 
CAl@ Dean Gmc vc 
—-—+—+4+-—-++4 
so that C goes out by § 28, and we have finally 
AG TAS Ge A: 
; ‘ : Ae SE ak ote 
the trefoil knot. f 
