S45 PRIMITIVE NUMBERS [ETH. ANN, 19 
the families and most of the child-groups even of this country and of 
today. The concept survives, also, in all manner of trigrams— 
triangles, triskelions, hearts, ete.—of mystic or symbolic character. 
The quaternary-quinary system survives conspicuously in the form 
of graphic devices, especially the world-wide cruciform symbol, which 
has taken on meanings of constantly increasing nobility and refine- 
ment with the growth of intelligence. Hardly less conspicuous are 
the classic and later literary survivals in the Four Elements—air, earth, 
fire. water—of alchemistic philosophy, the Four Winds of astrology 
and medieval cartography, the Four Iddhis of Buddha, and the Four 
Beasts of Revelation, with their reflections in the ecclesiastic writing of 
two millenniums; while the survivals in lighter lore are innumerable. 
The system persists significantly also in its augmentals, especially 9, 
13, 25, 49,and 61. The numerical vestiges are naturally for the most 
part quaternary, since the quinary aspect is merged and largely lost 
in algorithm. 
The senary-septenary system survives as the bridge connecting 
almacabala and mathematics. In the graphic form it became Pythag- 
oras’s hexagram of two superposed triangles, the equally mystical 
hexagram of Brianchon, with which Paracelsus wrought his marvels, 
and the subrational hexagram of Pascal, while the current hexagram 
of the Chinese is apparently a composite of this and the binary as 
well as algorithmic systems. In the numerical form, 6 and more 
especially 7 play large rdles in lore and in the classic and sacred 
literature revived during the Elizabethan period; even so recently as 
the middle of the century the hold of the astrologie 7 was so 
strong as to retard general acceptance of the double discovery of the 
eighth planet, Neptune; and equally strong is the hold on the average 
mind of certain senary-septenary augmentals, particularly those coin- 
ciding with the augmentals of the lower systems. In idealized (or 
reified) form, the number 7 has exerted marvellous influence on thought 
and conduct, especially in the medial stages of human development; 
according to Addis, ‘*The common Hebrew word for *swear’ meant 
originally ‘to come under the influence of the number 7°”'; and this 
is but a typical example of reverence for the magical number among 
various peoples. 
In tracing vestiges in the form of augmentals, it is clearly to be 
borne in mind that their significance, like that of the primary num- 
bers, is mystical rather than quantitative, so that certain augmental 
numbers possess greater vitality than others of corresponding arith- 
metic grade. This is especially true of the almacabalic doubles, nota- 
bly 9 as the first augmental of 5, and 13 as that of 7; for in these and 
other cases the first augmental is commonly of opposite sign, in alma- 
cabalic sense, from its basis—thus, 5 and 7 are beneficent or ** lucky,” 
1The Documents of the Hexateuch, part 1, 1893, p. 35. 
