701] 
441 
701. 
ALGORITHM FOR THE CHARACTERISTICS OF THE TRIPLE 
^-FUNCTIONS. 
[From the Journal fur die reine und angewandte Mathematik (Crelle), t. lxxxvii. (1878), 
pp. 165—169.] 
The characteristics of the triple ^--functions may be represented, the 28 odd 
characteristics by the binary symbols or duads, 12, 78, and the even ones 
pother than qqq , = 0^, sa y the ^5 even characteristics, by the ternary symbols or 
triads 123, ..., 567: which triads may be regarded as abbreviations for the double tetrads 
1238.4567, ..., 5678.1234, the 8 being always attached to the expressed triad. The 
correspondence of the symbols is given by the diagram: 
upper line of characteristic 
•c 
C. X. 
000 
100 
010 
110 
001 101 
Oil 
111 
000 
0 
236 
345 
137 
467 
156 
124 
257 
100 
237 
67 
136 
12 
157 
48 
256 
35 
010 
245 
127 
23 
68 
134 
357 
15 
47 
110 
126 
13 
78 
145 
356 
25 
46 
234 
001 
567 
146 
125 
247 
45 
17 
38 
26 
101 
147 
58 
246 
34 
i6 
123 
27 
367 
Oil 
135 
347 
14 
57 
28 
36 
167 
456 
111 
346 
24 
56 
235 
37 
267 
457 
18 
56