325 
of Edinburgh, Session 1876-77. 
two linked ovals, C and E having become nugatory ; or 
ECADCEDA | E 
2 r 3 + r 2 ) 
2Z 3 + Z 2 1 
an amphicheiral knot, the only knot with 4 intersections, 
c.) Dividing at E we find the same results as for B and C. 
From the rules just given for removing an intersection, it is of 
course easy to pass to those required for the introduction of a new 
intersection. 
In endeavouring to frame a general method of determining 
whether a particular type-symbol necessarily denotes one continuous 
curve, or a superposition of two or more curves, I was completely 
unsuccessful. But, as indicated in a note to my last paper, I found 
the reason to be that no such distinction necessarily exists. And by 
the application of the methods of adding or removing intersections 
given, I found a number of instances in which the same type-sym- 
bol may represent many entirely different kinds of figures. Thus 
the following 
are all represented alike by the symbol 
r 5 _j_ ^4 r 3 + r 2 | 
Z 4 + 2Z 3 + 2Z 2 j 
But I have since succeeded in obtaining cases in which the same 
type-symbol represents two perfectly distinct single closed curves. 
One instructive example is the following 
