540 PRIMITIVE NUMBERS [ETH. ANN. 19 
it is of no small interest as a source of those vestigial features of 
almacabala still persisting in Aryan culture, still cropping out in 
“lucky numbers” and in other fantastic forms. 
The augmentation of the widely dittused quaternary-quinary system 
is made clear by aid of its mechanical symbolism, which combined 
with the egoistic concept to shape the system. The commonest (and 
nearly world-wide) symbol is the cruciform figure +, or the quincunx, 
in Now, magnification of the peripheral powers or objects is 
readily and intuitively represented by adding a line or dot to each of 
the four extremities of the symbol, whereby it is converted into the 
simple swastika in its prevailing forms, @,or-+ Actually the figure 
is sometimes developed (as among some Pueblo peoples, according 
to Cushing) by laying down four billets or arrows radiating from a 
fetishistic Middle toward the east, north, west, and south, and then 
adding, as the ritual proceeds, shorter transverse sticks touching the 
extremities of the four cardinal billets, the whole being done in such 
a manner as to harmonize ritual and symbol, and impress the former 
by the objective representation in the latter. In any case, the symbol 
is raised from its original value of 44+1 to 8+1; and the graphic rep- 
resentation accords with the shadowy concept lying behind the number 
system in which the mystical Middle is persistent, and can be counted 
but once howsoever the value be augmented. Similarly the periph- 
eral potencies may be multiplied by the addition of dots, as in a common 
form of the swastika noted by Wilson, rH or che or by the deyelop- 
ment of the ‘‘meander,” ch. which thus represent, respectively, 12+-1, 
20-+-1, and 20-+-1; and the augmentation may proceed indefinitely, by 
either mechanical or mental addition, though always in accordance 
with the primary principle that the Middle is reckoned but once. 
The mechanical conditions accompanying the development of the 
figure tend to maintain its symmetry, i. e., the supplementary trans- 
verse billets, or sticks, are naturally so laid as to form counterparts in 
relation to the primary billets and to the center; but, as pointed out 
by Wilson (after Max Miiller and Burnouf), the additional billets com- 
pleting the swastika proper may be turned either to right or to left, i. e., 
the development of the figure may be either clockwise or counter- 
clockwise. The question has even been raised whether distinct names 
should be applied to the alternative forms; but in view of the fact that 
the habitual motions of primitive peoples are predominantly centrip- 
etal, or toward the body, while the predominant motions of advanced 
peoples are centrifugal, it seems safe to infer that the clockwise swas- 
tika represents the higher cultural plane (just as writing toward the 
right represents a higher plane than the archaic mode of writing 
! The Swastika; Report of the United States National Museum for 189, p. 767. 
