C. N. Littleh—Knots, with a Census for Order Ten. 29 
5. An inspection of form Aa of Plate I will make clear some jerms 
already introduced and others that we shall now require. Regarding 
the curve Aq as alone in a plane, it divides it into twelve parts, two 
9-gons, two 3-gons and eight 2-gons. The external 3-gon or am- 
plexum differs in no way from the other parts. Of these twelve 
parts, two 9-gons and one 2-gon form one group—the leading par- 
tition; the two 3-gons and seven 2-gons form the other group—the 
subordinate partition. The terms leading and subordinate are rela- 
tive merely, but that partition will be taken as leading which has 
1 19°2 
! {379"" 
6. The double points common to the perimeters of two parts of the 
same partition will be called bonds of those parts, and the parts are 
said to be bound by these bonds. It is well known that a type- 
symbol does not determine a form. For this, it is necessary to know 
the numbers of bonds between the several parts of either par- 
tition, together with the arrangement of these parts. 
In general the parts of a given partition may be bound in more 
than one way giving forms that may be projections of either links or 
knots. Each set of numbers of bonds of the several parts of the 
given partition is a clutch of that partition. 
The class p of a partition is the number of parts in it. The class 
of a form is the class of its leading partition. The order of any par- 
tition is equal to m and is the same as the order of all knot-forms 
derivable from it. The deficiency x of a partition is its order minus 
its greatest part. 
7. Let the parts of 2n be A, B,C, ... P arranged in order of 
magnitude, and the numbers of bonds of eack part be respectively 
a, B,y,... a. Let the number of bonds common to any two parts 
as A and B be (AB). Then 
the smaller number of parts. The type-symbol for Aa is 
GAS PA EAR) Aor cee. = Hae ): 
GAB) PEt O) oe ey aie (BP)=£ | 
(AG) BEBO wo ale oe ee y ne 
(AP) WEBEye ete ee OR ey) 
or m equations with $7(2—1) unknown quantities which can have only 
positive integral values. The possible solutions of (@) will evidently 
give all the clutches for this partition. 
