154 PROFESSOR TAIT ON KNOTS. 
C.D, EAB 
iD; B AB. 
B vA se a: 
This gives the following thirteen arrangements :-— 
(1) CDEAB 
Q) CEABD 
(3) CEBAD 
(4) CAEBD 
(5) DEABC 
(6) DEBAC 
(7) DE ACE 
(8) DAEBC 
(9) DAECB 
(10) ED ABC 
(11) AADAC B 
(12) EDBAC 
(13) EABCD. 
Now of these (1), (5), and (13) are unique; (6), (7), (8), and (10) can be 
obtained from (2) by cyclical alteration of the letters and bringing the last to 
be the beginning, and by the same process (4), (9), (11), (12) may be deduced — 
from (3). 
Hence the only possible forms are included in the following arrangements 
for the letters in the even places :— 
CD EAB 
CE ABD 
CEBAD 
DEABC 
HA. B.C, D-. 
Of these the 1st, 3d, and 5th violate the conditions laid down in § 5 above. 
Hence there are but two schemes for five intersections, viz. :— ; 
ACBECADBED|A 
of which this is one of the four forms 

